Leon and Marisol biked the Brookside Trail to the end and back. Then they biked the Forest Glen Trail to the end and back before stopping to eat. How far did they bike before they stopped to eat?
Answers
The question is incomplete because you haven't attached the map with it. I am attaching the photo of the map here and answering according to it.
Answer:
Before stopping to eat, Leon and Marisol biked a total distance of 12 [tex]\frac{1}{3}[/tex] miles.
Step-by-step explanation:
Leon and Marisol first biked the Brookside Trail to the end an back. According to the map, this trail is 3 [tex]\frac{2}{3}[/tex] miles long and the distance from the trail to the end and back can be calculating by adding this distance twice. The distance is a mixed fraction and we need to convert it into a simple fraction to add it.
To convert the mixed fraction, we will first multiply the denominator with the whole number, i.e. 3x3 = 9 and then add the numerator to it i.e. 9 + 2 = 11. The new denominator will be the same as the previous denominator.
The fraction can now be written as [tex]\frac{11}{3}[/tex]. The distance of Brookside trail to the end and back is
[tex]\frac{11}{3}[/tex] +
Then, they biked the Forest Glen Trail to the end and back. The distance of this trail is 2 [tex]\frac{1}{2}[/tex] miles. We will add this distance twice as well to obtain the total distance traveled for this trail.
To convert the mixed fraction into a simple fraction, multiply the denominator with the whole number i.e. 2 x 2 = 4. Then add the numerator to this answer i.e. 4 + 1 = 5. This is the new numerator and the denominator stays the same. The fraction is [tex]\frac{5}{2}[/tex].
The distance of Forest Glen Trail to the end and back is:
[tex]\frac{5}{2}[/tex] +
The total distance traveled can be calculated by adding both the distances traveled in the individual trails. i.e.
[tex]\frac{22}{3}[/tex] + 5
This can be written as:
[tex]\frac{22}{3}[/tex] + [tex]\frac{5}{1}[/tex]
The denominators are different so we will find out the L.C.M (Lowest Common Multiple) of 3 and 1 which is 3.
We will multiply the numerator and denominator of second fraction with 3 to make the denominator equal to 3.
[tex]\frac{22}{3} + \frac{5 X 3}{1 X 3}[/tex]
= [tex]\frac{22}{3} + \frac{15}{3}[/tex]
= [tex]\frac{22+15}{3}[/tex]
= [tex]\frac{37}{3}[/tex]
To convert [tex]\frac{37}{3}[/tex] miles into a mixed fraction, divide 37 by 3 and write down the answer as a whole number, the remainder as the numerator and the previous denominator i.e. 3 as the new denominator.
3 x 12 = 36. So dividing 37 by 3 will yield 12 as the whole number. The remainder is 37-36 = 1. So, the mixed fraction will be 12 [tex]\frac{1}{3}[/tex]
Before stopping to eat, Leon and Marisol biked a total distance of 12 [tex]\frac{1}{3}[/tex] miles.
Answer:
Step-by-step explanation:
The question is incomplete because you haven't attached the map with it. I am attaching the photo of the map here and answering according to it.
Answer:
Before stopping to eat, Leon and Marisol biked a total distance of 12 miles.
Step-by-step explanation:
Leon and Marisol first biked the Brookside Trail to the end an back. According to the map, this trail is 3 miles long and the distance from the trail to the end and back can be calculating by adding this distance twice. The distance is a mixed fraction and we need to convert it into a simple fraction to add it.
To convert the mixed fraction, we will first multiply the denominator with the whole number, i.e. 3x3 = 9 and then add the numerator to it i.e. 9 + 2 = 11. The new denominator will be the same as the previous denominator.
The fraction can now be written as . The distance of Brookside trail to the end and back is
+
Then, they biked the Forest Glen Trail to the end and back. The distance of this trail is 2 miles. We will add this distance twice as well to obtain the total distance traveled for this trail.
To convert the mixed fraction into a simple fraction, multiply the denominator with the whole number i.e. 2 x 2 = 4. Then add the numerator to this answer i.e. 4 + 1 = 5. This is the new numerator and the denominator stays the same. The fraction is .
The distance of Forest Glen Trail to the end and back is:
+
The total distance traveled can be calculated by adding both the distances traveled in the individual trails. i.e.
+ 5
This can be written as:
+
The denominators are different so we will find out the L.C.M (Lowest Common Multiple) of 3 and 1 which is 3.
We will multiply the numerator and denominator of second fraction with 3 to make the denominator equal to 3.
=
=
=
To convert miles into a mixed fraction, divide 37 by 3 and write down the answer as a whole number, the remainder as the numerator and the previous denominator i.e. 3 as the new denominator.
3 x 12 = 36. So dividing 37 by 3 will yield 12 as the whole number. The remainder is 37-36 = 1. So, the mixed fraction will be 12
Before stopping to eat, Leon and Marisol biked a total distance of 12 miles.
Related Questions
given examples of relations that have the following properties 1) relexive in some set A and symmetric but not transitive 2) equivalence relation in some set A 3) serial in some set A but not transitive
Answers
Answer: 1) R = {(a, a), (а,b), (b, a), (b, b), (с, с), (b, с), (с, b)}.
It is clearly not transitive since (a, b) ∈ R and (b, c) ∈ R whilst (a, c) ¢ R. On the other hand, it is reflexive since (x, x) ∈ R for all cases of x: x = a, x = b, and x = c. Likewise, it is symmetric since (а, b) ∈ R and (b, а) ∈ R and (b, с) ∈ R and (c, b) ∈ R.
2) Let S=Z and define R = {(x,y) |x and y have the same parity}
i.e., x and y are either both even or both odd.
The parity relation is an equivalence relation.
a. For any x ∈ Z, x has the same parity as itself, so (x,x) ∈ R.
b. If (x,y) ∈ R, x and y have the same parity, so (y,x) ∈ R.
c. If (x.y) ∈ R, and (y,z) ∈ R, then x and z have the same parity as y, so they have the same parity as each other (if y is odd, both x and z are odd; if y is even, both x and z are even), thus (x,z)∈ R.
3) A reflexive relation is a serial relation but the converse is not true. So, for number 3, a relation that is reflexive but not transitive would also be serial but not transitive, so the relation provided in (1) satisfies this condition.
Step-by-step explanation:
1) By definition,
a) R, a relation in a set X, is reflexive if and only if ∀x∈X, xRx ---> xRx.
That is, x works at the same place of x.
b) R is symmetric if and only if ∀x,y ∈ X, xRy ---> yRx
That is if x works at the same place y, then y works at the same place for x.
c) R is transitive if and only if ∀x,y,z ∈ X, xRy∧yRz ---> xRz
That is, if x works at the same place for y and y works at the same place for z, then x works at the same place for z.
2) An equivalence relation on a set S, is a relation on S which is reflexive, symmetric and transitive.
3) A reflexive relation is a serial relation but the converse is not true. So, for number 3, a relation that is reflexive but not transitive would also be serial and not transitive.
QED!
f(x) = -16x2- 4x+ 382 find x
Answers
Answer:
calculator that what I got 56
Step-by-step explanation:
Hilton Hotels wishes to conduct a study on the determinants of brand loyalty among Hilton Hotel customers. The Hilton organization estimates that 10% of its 2,600,000 Hilton Honors club members are loyal to the Hilton brand wherever they travel. However, the remaining members may choose other hotel brands at times. The organization wants to understand how to increase loyalty among the other 90% of club members.
Answers
Answer:
Sampling Frame
Step-by-step explanation:
If you are finding the representation of this style than it isHilton Honors membership list represents the Sampling frame
Josh's death is 36 in tall,when he measured the desk using a yard stick, it was 1 yard tall. Why did the number decrease when he measured with the yard stick
Answers
Explanation:
A yard is a larger unit of measure than an inch, so it takes fewer yards to equal the distance of a larger number of inches.
__
As it happens, 1 yard is exactly the same as 36 inches (by definition). So the measurement that is 36 inches will be a measurement that is 1 yard.
Final answer:
Josh's desk appeared to have different measurements because of the change in units from inches to yards; 1 yard is equal to 36 inches, so the desk's height didn't actually decrease.
Explanation:
The question seems to contain a typo. Assuming the question should read as 'Josh's desk is 36 inches tall, when he measured the desk using a yard stick, it was 1 yard tall,' the discrepancy in numbers is because of the different units used to measure the desk. There was no actual decrease in size; it is merely a difference in the units of measurement. Inches and yards are both units used to measure length or height, with 1 yard being equivalent to 36 inches. When Josh used a yard stick, he measured the desk in yards, which is a larger unit compared to inches. This is why the number appears to be smaller (1 instead of 36), even though the height of the desk remained the same.
Cameron took a science test on Thursday that had thirty questions. He got all but six questions correct. What percent score did Cameron get on his science test?
Answers
Answer:
20 percent
Step-by-step explanation:
Percentage score = [tex]\frac{actual score}{total score}[/tex] × 100
= [tex]\frac{6}{30}[/tex] × 100
= 20 percent
A circle has a diameter with endpoints (-10, -6) and (-2, -4).
What is the equation of the circle?
r2 = (x + 4)2 + (y + 5)2
r2 = (x + 6)2 + (y + 5)2
r2 = (x + 4)2 + (y + 1)2
r2 = (x + 6)2 + (y - 1)2
Answers
Answer: [tex](x+6)^{2}+(y+5)^{2}=r^{2}[/tex]
Step-by-step explanation:
The formula for finding the equation of circle with center (a,b) is given as :
[tex](x-a)^{2}+(y-b)^{2}=r^{2}[/tex]
The end point of the diameter is given as :
(-10, -6) and (-2, -4) , this means that the coordinate of the center is the Mid -point of the end point .
The mid - point = ( -6 , - 5)
substituting into the formula , we have
[tex](x-(-6))^{2}+(y-(-5))^{2}[/tex][tex]= r^{2}[/tex]
[tex](x+6)^{2}+(y+5)^{2}=r^{2}[/tex]
This is the equation of the circle
A function f(x) = 3^x is transformed into the function g(x) = 1/2 • 2^x+3 -5
Choose the transformations that occurred. CHOOSE ALL THAT APPLY.
-Vertical Shift Down
-Horizontal Shift Right
-X-axis Reflection
-Vertical Shift Up
-Vertical Compression
-Horizontal Shift Left
-Vertical Stretch
Answers
Answer:
Vertical compression, horizontal shift left, vertical shift down
Step-by-step explanation:
[tex]f(x) = 3^x => g(x) = \frac{1}{2} *2^{x+3} -5[/tex]
Let's break down what happened here:
[tex]\frac{1}{2}[/tex] - This indicates a vertical compression
[tex]2^{x+3}\\[/tex] - This indicates a horizontal shift left
-5 - This indicates a vertical shift down
Final answer:
Transforming f(x) to g(x) involves a vertical compression by ½, a horizontal shift left by 3 units, and a vertical shift down by 5 units. There is also an exponential base change, but it does not correspond directly to the given transformation options.
Explanation:
To transform the function f(x) = 3x into g(x) = ½ · 2x+3 - 5, let's analyze each part of the transformation. Break down g(x) into its components to determine the transformations:
The factor of ½ indicates a vertical compression by a factor of ½.The 2x+3 part involves an exponential base change and a horizontal shift. Since the function is initially 3x and we are transforming to 2x, there is a base change involved. To express 3 as a power of 2, we would get a vertical stretch (which is not the case here due to the mismatch in bases), so this part does not directly translate to one of the given transformations. Moreover, the addition of 3 inside the exponent of 2x+3 signifies a horizontal shift left by 3 units, not right as might be mistakenly assumed.The subtraction of 5 at the end of the function indicates a vertical shift downwards by 5 units.Based on this analysis, the correct transformations that occurred are a vertical compression, a horizontal shift left, and a vertical shift down.
While on vacation, Enzo sleeps 115\%115% as long as he does while school is in session. He sleeps an average of SS hours per day while he is on vacation
Answers
Answer: Let the Number of hours Enzo sleeps on average per day while School is in session be Y
Y = SS/115% = SS/1.15
Step-by-step explanation:
Given in the question:
- While on vacation, Enzo sleeps 115% as much as he sleeps when school is in session.
- Enzo sleeps SS hours per day during vacation
Mathematically, SS = 115% of Y
SS = 115% × Y
115% × Y = SS
Y = SS/115%
But 115% = 115/100 = 1.15
Therefore,
Y = SS/1.15
Solved!
Which is the equation of a parabola with a directrix at y = −3 and a focus at (5, 3)? y = one twelfth(x − 5)2 y = −one twelfth(x − 5)2 y = one twelfth(x + 5)2 y = −one twelfth(x + 5)2
Answers
Answer:
The answer to your question is y = 1/12 (x - 5)²
Step-by-step explanation:
Data
directrix y = -3
focus (5, 3)
Process
1.- Graph the directrix and focus to determine if the parabola is vertical or horizontal.
From the graph we know that it is a vertical parabola with equation
(x - h)² = 4p(y - k)
2.- From the graph we know that p = 3 because the distance from the focus to the directrix is 6 and p = 6/2.
3.- The vertex (5, 0)
4.- Substitution
(x - 5)² = 4(3)(y - 0)
5.- Simplification
(x - 5)² = 12y
6.- Result
y = 1/12 (x - 5)²
Answer:
y = 1/12 (x - 5)²
Step-by-step explanation:
On Monday Billy spent 4 1/4 hour study on Tuesday he spent another 3 5/9 hour study what is the combined time he spent studying answer as a mixed number
Answers
Answer: the combined time he spent studying is 281/36 hours
Step-by-step explanation:
The first step is to convert all mixed numbers to improper fraction.
On Monday Billy spent 4 1/4 hour study. Converting 4 1/4 hours to improper fraction, it becomes 17/4 hours.
On Tuesday he spent another 3 5/9 hour study. Converting 3 5/9 hours to improper fraction, it becomes 32/9 hours.
The combined time he spent studying answer as a mixed number would be
17/4 + 32/9 = (153 + 128)/36
= 281/36 hours
Zoey wants to use her iPad throughout a 6-hour flight. Upon takeoff, she uses the iPad for 2 hours and notices that the battery dropped by 25%, from 100% to 75%. How many total hours can Zoey expect from the iPad on a full battery charge?
a. 10 hours
b. 4 hours
c. 8 hours
d. 6 hours
Answers
Answer:
The answer is c. 8 hours
Step-by-step explanation:
Since her battery dropped 25% in 2 hours then for it to drop 100% would take 8 hours.
25%+25%+25%+25%= 100%
so with this logic
25%= 2 hours
2+2+2+2=8
Hoped this helped !
Cheers, Z
Zoey can expect 8 hours of use from her iPad on a full battery charge (c).
Explanation:To find the total hours Zoey can expect from her iPad on a full battery charge, we need to determine how many hours the battery percentage dropped for each hour of use.
If the battery dropped by 25% in 2 hours, that means it dropped by 12.5% (25% divided by 2) per hour.
To find the total hours, we divide 100% (full battery charge) by the percentage dropped per hour. In this case, 100% divided by 12.5% equals 8 hours.
Therefore, Zoey can expect 8 hours(c) of use from her iPad on a full battery charge.
Learn more about iPad battery life here:https://brainly.com/question/35390557
#SPJ3
When an object is droppednbsp on a certain earth dash like planet comma on a certain earth-like planet, the distance it falls in t seconds, assuming that air resistance is negligible, is given by s(t)equals=1818t2 where s(t) is in feet. Suppose that a medic's reflex hammer is dropped from a hovering helicopter. Find(a) how far the hammer falls in 44 sec, (b) how fast the hammer is traveling 44 sec after being dropped, and (c) the hammer's acceleration after it has been falling for 44 sec.
Answers
Final answer:
To solve for the distance, velocity, and acceleration of a hammer dropped from a hovering helicopter, calculations based on the given formula s(t) = 1818t^2 are used, yielding a fall of 29128 feet in 4 seconds, a velocity of 14512 feet/sec at 4 seconds, and a constant acceleration of 3636 feet/sec^2.
Explanation:
When an object is dropped on a certain earth-like planet, the distance it falls in t seconds, assuming that air resistance is negligible, is given by s(t) = 1818t2, where s(t) is in feet. To solve the problem involving a medic's reflex hammer dropped from a hovering helicopter:
(a) To find how far the hammer falls in 4 seconds, substitute t = 4 into the equation: s(4) = 1818(4)2 = 29128 feet.
(b) The velocity of the hammer after 4 seconds can be found using the derivative of s(t), v(t) = 2×1818×t. Substituting t = 4, v(4) = 2×1818×4 = 14512 feet/sec.
(c) The acceleration of the hammer is constant and equal to 2×1818 feet/sec2 = 3636 feet/sec2, which is twice the coefficient in the equation for s(t).
These calculations demonstrate the principles of kinematics, specifically how position, velocity, and acceleration relate to one another for an object in free fall on an earth-like planet with negligible air resistance.
HELP ONE MORE ANSWER PLEASEEEEE
Answers
Answer:
The length of the rope between the boat and the dock is of 30 feet.
Step-by-step explanation:
Given:
tan(40) ≈ 0.839
Angle of depression = 40 (deg)
Distance between boat and the floor of the ocean = 25.17 feet
If we look into the diagram we can see that,they form 2 right angled triangle.
Where we can say that :
Distance between boat and dock = Rope's distance = Base of the triangle.
Let the length of the rope be 'x' feet.
Considering the dotted triangle:
[tex]tan\ (40) =\frac{opposite}{adjacent}[/tex]
⇒ [tex]tan\ (40) =\frac{25.17}{x}[/tex]
⇒ [tex]tan\ (40)\times x =\frac{25.17}{x}\times x[/tex]
⇒ [tex]tan\ (40)\times x =25.17[/tex]
⇒ [tex]\frac{tan\ (40)\times x}{tan\ (40)} =\frac{25.17}{tan\ (40)}[/tex]
⇒ [tex]x =\frac{25.17}{0.839}[/tex]
⇒ [tex]x= 30[/tex]
Length of the rope between the boat and the dock is 'x' = 30 feet.
Energy drink consumption has continued to gain in popularity since the 1997 debut of Red Bull, the current leader in the energy drink market. Given below are the exam scores and the number of 12-ounce energy drinks consumed within a week prior to the exam of 10 college students.Exam Scores - 75 - 92 - 84 - 64 - 64 - 86 - 81 - 61 - 73 - 93Number of Drinks - 5 - 3 - 2 - 4 - 2 - 7 - 3 - 0 - 1 - 01. Referring to Problem Statement 7, what is the sample covariance between the exam scores and the number of energy drinks consumed?2. Referring to Problem Statement 7, what is the sample correlation coefficient between the exam scores and the number of energy drinks consumed?
Answers
Answer:
1. 3.767
2. 0.145
Step-by-step explanation:
Let X be the exam scores and Y be the number of drinks.
X Y X-Xbar Y-Ybar (X-Xbar)(Y-Ybar) (X-Xbar)² (Y-Ybar)²
75 5 -2.3 2.3 -5.29 5.29 5.29
92 3 14.7 0.3 4.41 216.09 0.09
84 2 6.7 -0.7 -4.69 44.89 0.49
64 4 -13.3 1.3 -17.29 176.89 1.69
64 2 -13.3 -0.7 9.31 176.89 0.49
86 7 8.7 4.3 37.41 75.69 18.49
81 3 3.7 0.3 1.11 13.69 0.09
61 0 -16.3 -2.7 44.01 265.69 7.29
73 1 -4.3 -1.7 7.31 18.49 2.89
93 0 15.7 -2.7 -42.39 246.49 7.29
sumx=773, sumy=27, sum(x-xbar)(y-ybar)= 33.9 , sum(X-Xbar)²= 1240.1 ,sum(Y-Ybar)²= 44.1
Xbar=sumx/n=773/10=77.3
Ybar=sumy/n=27/10=2.7
1.
[tex]Cov(x,y)=sxy=\frac{Sum(X-Xbar)(Y-Ybar)}{n-1}[/tex]
Cov(x,y)=33.9/9
Cov(x,y)=3.76667
The the sample co-variance between the exam scores and the number of energy drinks consumed is 3.767
2.
[tex]Cor(x,y)=r=\frac{Sum(X-Xbar)(Y-Ybar)}{\sqrt{Sum(X-Xbar)^2sum(Y-Ybar)^2} }[/tex]
[tex]Cor(x,y)=r=\frac{33.9}{\sqrt{(1240.1)(44.1)} }[/tex]
Cor(x,y)=r=33.9/233.85553
Cor(x,y)=r=0.14496
The sample correlation coefficient between the exam scores and the number of energy drinks consumed 0.145.
Calculate sample covariance and correlation coefficient between exam scores and energy drinks consumed by students.
Explanation:Sample Covariance:
1. Calculate the mean of exam scores (77.3) and number of drinks (2.7).
2. Subtract the mean from each score and drink value to get the deviations.
3. Multiply the deviations of exam scores and drinks for each student, sum them up, and divide by 10 to get the sample covariance of approximately -22.6.
Sample Correlation Coefficient:
1. Calculate the standard deviations of exam scores (12.15) and number of drinks (2.51).
2. Divide the sample covariance by the product of the standard deviations to get the correlation coefficient of around -0.79.
A market analyst has projected that the cost of producing d dog leashes will be given by the polynomial 9000 + 3.2d. The revenue generated from the sale of d dog leashes will be given by the polynomial d(15 - 0.00005d). Which polynomial expression represents the profit earned from producing, and selling d dog leashes?
A. - 0.0016d³ + 47.55d² + 135,000d
B. 0.00005d² - 18.2d - 9000
C. - 0.00005d² + 11.8d - 9000
D. - 0.00005d² - 11.8d + 9000
Answers
Answer:
C. [tex]-0.00005d^2+11.8d-9000[/tex]
Step-by-step explanation:
Given:
Cost Price for producing 'd' dog lashes = [tex]9000+3.2d[/tex]
Revenue Generated from selling 'd' dog lashes = [tex]d(15-0.00005d)[/tex]
We need to find the profit earned from producing and selling 'd' dog lashes.
Solution:
Now we know that;
profit earned from producing and selling 'd' dog lashes can be calculated by Subtracting Cost Price for producing 'd' dog lashes from Revenue Generated from selling 'd' dog lashes.
framing in equation form we get;
Profit earned = [tex]d(15-0.00005d)-(9000+3.2d)[/tex]
Now Applying Distributive property we get;
Profit earned = [tex]15d-0.00005d^2-9000-3.2d[/tex]
Now Combining like terms we get;
Profit earned = [tex]-0.00005d^2+15d-3.2d-9000[/tex]
Profit earned = [tex]-0.00005d^2+11.8d-9000[/tex]
Hence Profit earned from producing and selling 'd' dog lashes is [tex]-0.00005d^2+11.8d-9000[/tex].
Final answer:
The polynomial representing the profit from producing and selling d dog leashes is -0.00005d² + 11.8d - 9000, calculated by subtracting the cost (9000 + 3.2d) from the revenue (d(15 - 0.00005d)).
Explanation:
The student's question relates to finding the polynomial expression that represents the profit earned from producing and selling d dog leashes. Profit is calculated by subtracting the cost from the revenue. The cost polynomial is given as 9000 + 3.2d, and the revenue polynomial is d(15 - 0.00005d).
To find the profit, we subtract the cost from the revenue:
Profit = Revenue - Cost
Profit = (d(15 - 0.00005d)) - (9000 + 3.2d)
Profit = 15d - 0.00005d² - 9000 - 3.2d
Profit = -0.00005d² + (15 - 3.2)d - 9000
Profit = -0.00005d² + 11.8d - 9000
Therefore, the correct polynomial that represents the profit is -0.00005d² + 11.8d - 9000.
Use the position function s(t) = –16t2 + 800, which gives the height (in feet) of an object that has fallen for t seconds from a height of 800 feet. The velocity at time t = a seconds is given by the following.If a construction worker drops a wrench from a height of 800 feet, how fast will the wrench be falling after 3 seconds?
Answers
Answer:
96 ft/s
Step-by-step explanation:
We can start by deriving the equation of the velocity, which is the derivative of the position equation:
[tex]v(t) = \frac{ds}{dt} = (-16t^2)' + 800' = -32t[/tex]
After 3 seconds, the wrench would achieve a speed of
v(3) = -32t = -32*3 = -96 ft/s
So it's falling at the rate of 96 ft per second after 3 s
Final answer:
To calculate the velocity of the falling wrench after 3 seconds, the first derivative of the position function s(t) is taken to get v(t) = -32t. By substituting t with 3, the velocity at three seconds is -96 feet per second.
Explanation:
To find how fast the wrench will be falling after 3 seconds, we need to calculate the first derivative of the position function s(t) to get the velocity function v(t). The position function given is s(t) = −16t² + 800. Differentiating this with respect to t gives v(t) = d/dt (-16t² + 800) = -32t.
To find the velocity after 3 seconds, we substitute t = 3 into the velocity equation, which gives v(3) = -32(3) = -96 feet per second.
Therefore, the wrench will be falling at a velocity of -96 feet per second after 3 seconds.
NB HG thje triangle proportionality theorem was used to create a proportion. what is the value of x?
Answers
Answer:
x=16
Step-by-step explanation:
Since triangle DGH is parallel to trianle DBN, the corresponding sides are also proportional.
We have [tex]\frac{DN}{DH}=\frac{DB}{DG}[/tex]
This implies that:
[tex]\frac{40}{40+x}=\frac{30}{42}[/tex]
We cross multiply to get;
[tex]30(40+x)=42*40[/tex]
This implies that:
[tex](x+40)=14*4[/tex]
[tex]x+40=56[/tex]
[tex]x=56-40[/tex]
[tex]x=16[/tex]
solve the question by completing the sqaure x² + 4x = 0?
Answers
Answer:
x = 0 or -4
Step-by-step explanation:
x² + 4x = 0
To complete the square, take half of the middle coefficient, square it, then add to both sides.
(4/2)² = 2² = 4
x² + 4x + 4 = 4
(x + 2)² = 4
x + 2 = ±2
x = -2 ± 2
x = 0 or -4
Triangle DEF has sides with lengths of 6, 11, and 13 units. Determine whether this triangle is a right triangle. Show all work necessary to justify your answer. A right triangle has a hypotenuse with a length of 25. The lengths of the legs are whole numbers. What could be possible lengths of the legs?
Answers
Answer:
Triangle DEF is not a right triangle ; possible lengths are 20 & 15
Step-by-step explanation:
For right triangle;
the sum of the square of the two adjacent sides must equal the square of the hypotenus.
Therefore, (6^2)+(11^2)≠(13^2).
the possible length are 20 & 15 because
(20^2)+(15^2)=(25^2)
Triangle DEF with sides lengths of 6, 11, and 13 units is not a right triangle as the Pythagorean theorem is not satisfied. To find the lengths of the legs of a right triangle with a hypotenuse of 25, one can use the Pythagorean theorem to find whole number pairs that satisfy the equation.
To determine whether triangle DEF is a right triangle with sides of lengths 6, 11, and 13 units, we can use the Pythagorean theorem. This theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b): a² + b² = c².
Let's check if the sides of triangle DEF satisfy this condition:
a = 6, b = 11, and c = 13a² + b² = 6² + 11² = 36 + 121 = 157c² = 13² = 169Since 157 does not equal 169, triangle DEF is not a right triangle.
For the second part of the question, we are given that a right triangle has a hypotenuse with a length of 25 units and we need to find the lengths of the legs which are whole numbers. We can use the Pythagorean theorem to find pairs of integers (a and b) that satisfy the equation a² + b² = 25² = 625. Some possible pairs of legs that meet this criterion include (7, 24), (15, 20), and (9, 24). Note that there are multiple correct answers to this question.
Identify the equation of a line in slope- intercept form that is perpendicular to y = -1/3 x + 2 and passes through (2, 1) Show your work PLEASE!!
Answers
Answer: y = 3x - 5
Step-by-step explanation:
The equation of a straight line can be represented in the slope intercept form as
y = mx + c
Where
c = intercept
m = slope = (change in the value of y in the y axis) / (change in the value of x in the x axis)
The equation of the given line is
y = -1/3x + 2
Comparing with the slope intercept form, slope = - 1/3
If two lines are perpendicular, it means that the slope of one line is the negative reciprocal of the slope of the other line. Therefore, the slope of the line passing through
(2, 1) is 3/1 = 3
To determine the intercept, we would substitute m = 3, x = 2 and y = 1 into y = mx + c. It becomes
1 = 3 × 2 + c = 6 + c
c = 1 - 6 = - 5
The equation becomes
y = 3x - 5
Make a flowchart showing that the triangles below are congruent
Answers
Explanation:
It isn't clear what the elements of your flowchart are supposed to look like. In general, the proof would go like this:
1. List the "givens": PQ=6=TS; ∠P=120°=∠T; ∠PRQ and ∠TRS are vertical angles.
2. Note that the vertical angles are congruent
3. Claim ΔPRQ ≅ ΔTRS by the AAS congruence postulate since two corresponding adjacent angles and the corresponding sides not between them have been shown to be congruent.
HELP ASAP PLEASE!!!!!!!!!!!!
What is the measure of ∠CED and ∠ACD?
Answers
Answer:
[tex]\angle ACD=124\°\\\\\angle CED=64\°[/tex]
Step-by-step explanation:
To solve this exercise you need to remember:
1. The sum of the Interior angles of a triangle is 180 degrees.
2. Straight angles are those angles that measure 180 degrees.
3. Supplementary angles are those angles whose sum is 180 degrees.
4. Vertical angles are angles that share the same vertex and they are opposiste to each other. They are congruent.
Knowing the above, you can set up the following equation:
[tex]31\°+93\°+\angle ACB=180\°[/tex]
Solving the equation, you get:
[tex]\angle ACB=180\°-124\°=56\°[/tex]
Since [tex]\angle ACB[/tex] and [tex]\angle DCE[/tex] are Vertical angles:
[tex]\angle ACB=\angle DCE=56\°[/tex]
Knowing the measure of [tex]\angle DCE[/tex] , you can write the following equation to find [tex]\angle CED[/tex]:
[tex]56\°+60\°+\angle CED=180\°[/tex]
Solve the equation:
[tex]\angle CED=180\°-116\°=64\°[/tex]
As you can observe in the figure, the angles [tex]\angle DCE[/tex] and [tex]\angle ACD[/tex] are Supplementary. Then:
[tex]\angle ACD+\angle DCE=180\°\\\\\angle ACD+56\°=180\°[/tex]
Solving for [tex]\angle ACD[/tex], you get:
[tex]\angle ACD=180\°-56\°=124\°[/tex]
Combine the like terms to create an equivalent expression:
2s+(−4s)=?
Answers
Combining 2s and −4s gives an equivalent expression of −2s.
We need to combine the like terms. Like terms are terms that have the same variable raised to the same power. In this case, both terms involve the variable "s."
In the expression 2s + (−4s), both terms are like terms because they both contain the variable "s." The coefficients are 2 and −4.
To combine like terms, you simply add or subtract their coefficients while keeping the variable the same:
Coefficient of the first term: 2
Coefficient of the second term: −4
Now, perform the arithmetic operation:
2 + (−4) = −2
A supermarket is selling two types of candies, orange slices and strawberry leaves. The orange slices cost $ 1.29 per pound and the strawberry leaves cost $ 1.79 per pound. How many pounds of each should be mixed to get a 13-pound mixture that sells for $ 19.27?
Answers
Answer:
5 lb of strawberry leaves8 lb of orange slicesStep-by-step explanation:
Let "o" and "s" represent the number of pounds of orange slices and strawberry leaves in the mix, respectively. We want ...
o + s = 13 . . . . . . . . . . . . . . . total weight
1.29o +1.79s = 19.27 . . . . . .total cost
Solving the first equation for o, we can substitute that result into the second equation to get ...
o = 13 -s
1.29(13 -s) +1.79s = 19.27
0.50s +16.77 = 19.27 . . . . eliminate parentheses
0.50s = 2.50 . . . . . . . . . . . subtract 16.77
s = 5 . . . . . . . . . . . . . . . . . . multiply by 2
o = 13 -5 = 8
5 pounds of strawberry leaves should be mixed with 8 pounds of orange slices to get the desired mixture.
To find out how many pounds of both orange slices and strawberry leaves are needed for the mixture, we need to solve a system of equations involving weight and total cost.
The question involves solving a system of linear equations to determine how many pounds of orange slices and strawberry leaves should be mixed to achieve a 13-pound mixture that totals $19.27. Let's define two variables:
x for the number of pounds of orange slices at $1.29 per pound.y for the number of pounds of strawberry leaves at $1.79 per pound.We have two equations based on the weight and cost of the mixture:
x + y = 13 (Total weight of the mixture)1.29x + 1.79y = 19.27 (Total cost of the mixture)Solving this system will provide us with the values for x and y that satisfy both equations.
When 5655 is divided by a positive two digit intreger "N" the remainder is 11, when 5879 is divided by the same intreger N the remainder is 11.
What is the sum of the digits of N ?
Answers
Answer:
8
Step-by-step explanation:
Hi,
When we divide 5655 by N, we get remainder of 11, which means that 5655-11 is a multiple of N.
5655 - 11 = 5644 is a multiple of N.
Similarly, 5879-14 should be a multiple of N.
5879 - 14 = 5865 is a multiple of N.
Because 5644 and 5865 are both multiples of N, their difference must be a multiple of N.
5865 − 5644 = 221 then 221 is a multiple of N.
We have three number of which N can be a multiple of, however we choose to factorize the smallest possible number amongst these three, which is 221. (This is only for simplification of the solution, smaller the number, less the factors)
221 : 1, 13, 17, 221.
There are only two two - digit factors: 13 and 17.
We divide 5865 and 5644 by both numbers.
[tex]\frac{5865}{13} = 451.15 \\\frac{5865}{17} = 345 \\\frac{5644}{13} = 434.15 \\\frac{5644}{17} = 332\\[/tex]
Looking at these results, we know only 17 divides all three numbers.
Hence N=17.
The sum of both digits will be: 1 + 7 = 8
Subtract the two given numbers excluding their identical remainders to find a multiple of the divisor N. By then finding a two-digit factor of this multiple that can divide both numbers, we get N = 28. The sum of its digits is 10.
Explanation:When a number is divided by a divisor and leaves the same remainder, the difference between these numbers is a multiple of that divisor. Therefore, as given, when 5655 is divided by a positive two-digit integer N, the remainder is 11, and also when 5879 is divided by N, the remainder is 11. To find N, we subtract the two numbers before considering the remainder, which will give us a number that is a multiple of N: 5879 - 5655 = 224.
So, N divides 224 perfectly. The factors of 224 that are two-digit numbers are 14, 16, and 28. However, since the remainder when dividing both 5655 and 5879 by N is identical and equal to 11, we need to make sure that both 5655-11 and 5879-11 are divisible by N equally, thus 5644 and 5868 should be divisible by N. The correct N which fulfills this condition is 28.
The sum of the digits of N or 28 is: 2 + 8 = 10.
A tank contains 90 kg of salt and 1000 L of water. A solution of a concentration 0.045 kg of salt per liter enters a tank at the rate 8 L/min. The solution is mixed and drains from the tank at the same rate.a) What is the concentration of the solution in the tank initially?
b) Find the amount of salt in the tank after 4 hours.
c) Find the concentration of salt in the solution in the tank as time approaches infinity.
Answers
Answer:
Step-by-step explanation:
concentration = amount of salt/solution
A) Initial concentration= 90/1000 = 0.09
Q = quantity of salt
Q(0) = 90 kg
Inflow rate = 8 l/min
Outflow rate = 8 l/min
Solution = 1000 L at any time t.
Salt inflow = 0.045 * 8 per minute
= 0.36 kg per minute
This is mixed and drains from the tank.
Outflow = [tex]\frac{Q(t)}{1000}[/tex]
Thus rate of change of salt
Q'(t) = inflow - outflow = [tex]0.36-\frac{Q(t)}{1000} \\=\frac{360-Q(t)}{1000}[/tex]
Separate the variables and integrate
[tex]\frac{1000dQ}{360-q(t)} =dt\\-1000 ln |360-Q(t)| = t+C\\ln |360-Q(t)| = -0.001+C'\\360-Q(t) = Ae^{-0.001t} \\Q(t) = 360-Ae^{-0.001t}[/tex]
Use the fact that Q(0) = 90
90 = 360-A
A = 270
So
[tex]Q(t) = 360-270e^{-0.001t}[/tex]
B) Q(t) = 360-270e^-0.004 = 91.07784
C) When t approaches infinity, we get
Q(t) tends to 360
So concentration =360/1000 = 0.36
Final answer:
a) The initial concentration of the solution in the tank is 0.09 kg/L. b) The amount of salt in the tank after 4 hours is 3.6 kg. c) The concentration of salt in the solution in the tank approaches 0.045 kg/L as time approaches infinity.
Explanation:
a) To find the concentration of the solution in the tank initially, we need to calculate the total mass of salt and water in the tank. The concentration is the mass of salt divided by the volume of water. Since 1 liter of water weighs 1 kg, the initial concentration of the solution in the tank is 90 kg of salt divided by 1000 kg of water, which is 0.09 kg/L.
b) To find the amount of salt in the tank after 4 hours, we need to calculate the amount of salt entering the tank and the amount of salt leaving the tank in that time. The amount of salt entering the tank is the concentration of the incoming solution (0.045 kg/L) multiplied by the rate of flow (8 L/min) and the time (4 hours = 240 minutes). This gives us 0.045 kg/L × 8 L/min × 240 min = 86.4 kg. The amount of salt leaving the tank is the concentration of the solution in the tank (0.09 kg/L) multiplied by the rate of flow (8 L/min) and the time (4 hours = 240 minutes). This gives us 0.09 kg/L × 8 L/min × 240 min = 172.8 kg. Therefore, the amount of salt in the tank after 4 hours is the initial amount of salt (90 kg) plus the amount of salt entering the tank (86.4 kg) minus the amount of salt leaving the tank (172.8 kg), which is 3.6 kg.
c) As time approaches infinity, the concentration of salt in the solution in the tank will approach the concentration of the incoming solution, which is 0.045 kg/L.
Write the slope-intercept form (y=mx+b) of the equation of the line given the slope and y-intercept.
Answers
Answer:
A
Step-by-step explanation:
y = mx + c
y = -½x + 1
The formula to convert degrees Celsius to degrees Fahrenheit is 9/5 C + 32 equals F use this equation to find the Celsius equivalent of 86 degrees Fahrenheit
Answers
Answer:
86 °F = 30 °C
Step-by-step explanation:
Put the given number in the equation and solve for C.
86 = 9/5C +32
54 = 9/5C
(5/9)54 = C = 30
The equivalent is 30 degrees Celsius.
Final answer:
To convert 86 degrees Fahrenheit to Celsius, use the formula T°C = 5/9 (86 - 32). Subtracting 32 from 86 and then multiplying by 5/9 gives a result of 30 degrees Celsius.
Explanation:
The question asks how to find the Celsius equivalent of 86 degrees Fahrenheit using the formula to convert degrees Fahrenheit to degrees Celsius. The formula is T°C = 5/9 (T°F - 32), where T°C is the temperature in degrees Celsius and T°F is the temperature in degrees Fahrenheit.
To convert 86°F to Celsius, substitute 86 for T°F in the formula:
T°C = 5/9 (86 - 32)
First, subtract 32 from 86, which gives 54. Then, multiply 54 by 5/9 to get the final result:
T°C = 5/9 × 54
T°C = 30
Therefore, 86 degrees Fahrenheit is equivalent to 30 degrees Celsius.
A submarine was descending at a rate of 300 feet per minute. If 0 represents sea level and distances below sea level are negative, which expression represents the location of the submarine after 4.5 minutes?
25 points
Answers
Answer:
The submarine will be located 1350ft below sea level or (-1350ft)
Step-by-step explanation:
First we must find the distance traveled
[tex](\frac{300}{1} )(\frac{4.5}{1})[/tex]
From this, we are able to calculate that traveled distance of the submarine.
300 x 4.5 = 1350
1350 + 0 (sea level) = 1350
Therefore the distance traveled by the submarine is 1350ft
Answer:
-1350 ft
Step-by-step explanation:
Divide and Check...........
Answers
soo this may seem a little awkwark but it still should provide the same resault however its faster :)
so we have
(48x^5-16x^3+40x)/8x
What we are going to be doing is factoring out any and all possibilities for
(48x^5-16x^3+40x)
first factor
(8x(6x^4-2x^2+5))/8x
when we get to this step simplify 8x
we are left with 6x^4-2x^2+5
in order to get an answer that would often be used by long devision just get rid of the +5
This is just a remainder using long devision your instructer may ask for
6x^4-2x^2
Hope it helps
Answer:
6x⁴ - 2x² + 5
Step-by-step explanation:
[48x⁵ - 16x³ + 40x] ÷ 8x
[8x(6x⁴ - 2x² + 5)] ÷ 8x
6x⁴ - 2x² + 5
Check:
(6x⁴ - 2x² + 5)(8x)
= 48x⁵ - 16x³ + 40x (verified)