Let [tex]v[/tex] be the usual speed, and [tex]t[/tex] be the usual time.
Following the equation [tex]s=vt[/tex], where s is the space, v is the velocity and t is time, we know that usually we have
[tex]200=vt[/tex]
But this time we were 10mph faster and it took one hour less, so we have
[tex]200=(v+10)(t-1)[/tex]
Since both right hand sides equal 200, they must equal each other:
[tex]vt=(v+10)(t-1)=vt+10t-v-10 \iff 10t-v-10=0 \iff v=10t-10[/tex]
Plug this value in the first equation and we have
[tex]200=vt=(10t-10)t \iff 10t^2-10t-200=0[/tex]
This equation has solutions [tex]t=-4,\quad t=5[/tex]. We can only accept positive solutions, so we have t=5. We finally deduce, again from the first equation,
[tex]200=5v \iff v=\dfrac{200}{5}=40[/tex]
Find the HCF of 27, 63, 54 using prime factorization method.
Answer:
27 = 3 , 3, 3
63= 3 , 3, 7
54= 3 , 3, 3, 2
HCF OF 27, 63 AND 54 = 3 X 3 = 9
HOPE THIS HELPS YOU MATE Plz mark it as brainliest answer
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How do you write -9 is -16 as an equation
Answer:
Replace "is" with an equal sign.
Step-by-step explanation:
It looks like you want the equation ...
-9 = -16
which makes no sense at all. Perhaps you intend ...
-g = -16
henry rolls 2 number cubes numbered 1 through 6 while playing his favorite board game. he will get a second turn if he rolls a sum that is an even number less than 10. what are henry’s chances of getting a second turn when he rolls the number cubes
Henry has 13 chances to get a second turn.
Step-by-step explanation:
When two number cubes numbered from 1 to 6 are rolled, the number of possible outcomes are 36.
The 36 possible outcomes are as follows :
(1,1), (1,2), (1,3), (1,4), (1,5), (1,6)
(2,1), (2,2), (2,3), (2,4), (2,5), (2,6)
(3,1), (3,2), (3,3), (3,4), (3,5), (3,6)
(4,1), (4,2), (4,3), (4,4), (4,5), (4,6)
(5,1), (5,2), (5,3), (5,4), (5,5), (5,6)
(6,1), (6,2), (6,3), (6,4), (6,5), (6,6).
It is given that, Henry gets the second turn if he rolls a sum that is an even number less than 10.
Therefore, the even numbers less than 10 are {2,4,6,8}.
Check for the sum of outcomes that gives the result of even number less than 10.
Sum of (1,1) (1,3) (1,5) gives 2,4,6 which are even numbers less than 10 ⇒ 3 chances.Sum of (2,2) (2,4) (2,6) gives 4,6,8 which are even numbers less than 10 ⇒ 3 chances.Sum of (3,3) (3,5) gives 6 and 8 which are even numbers less than 10 ⇒ 2 chances.Sum of (4,2) (4,4) gives 6 and 8 which are even numbers less than 10 ⇒ 2 chances.Sum of (5,1) (5,3) gives 6 and 8 which are even numbers less than 10 ⇒ 2 chances.Sum of (6,2) gives 8 which is a even number less than 10 ⇒ 1 chance.The total number of chances to get second turn = 3+3+2+2+2+1 = 13 chances.
Therefore, Henry has 13 chances to get a second turn.
Solve the following equation
sin¢=cos(¢+20°)
Step-by-step explanation:
[tex] \sin \: \phi = \cos( \phi + 20 \degree) \\ \\ \therefore \: \cos (90 \degree - \phi )= \cos( \phi + 20 \degree) \\ \\ \therefore \: 90 \degree - \phi = \phi + 20 \degree \\ \\ \therefore \: 90 \degree - 20 \degree = \phi +\phi \\ \\ \therefore \: 70 \degree = 2\phi \\ \\ \therefore \: \phi = \frac{70 \degree}{2} \\ \\ \huge \red { \boxed{ \therefore \: \phi = 35 \degree}}[/tex]
∠A and \angle B∠B are supplementary angles. If m\angle A=(3x+18)^{\circ}∠A=(3x+18)
∘
and m\angle B=(5x+2)^{\circ}∠B=(5x+2)
∘
, then find the measure of \angle A∠A.
Answer:
Angle A = 78
Step-by-step explanation:
Start with the equation 8x+20=180 and solve for x which equals x=20. You then substitute for x with the equation for angle A. A=3(20)+18 which makes angle A = 78
The measure of ∠A is 78 degrees.
What are supplementary angles?Two angels whose sum is 180° are called supplementary angles. If a straight line is intersected by a line, then there are two angles form on each of the sides of the considered straight line. Those two-two angles are two pairs of supplementary angles.
Which means, if supplementary angles are aligned adjacent to each other, their exterior sides will make a straight line.
∠A and ∠B are supplementary angles. If ∠A=(3x+18) and ∠B=(5x+2)
then find the measure of ∠A.
Now Start with the equation
8x+20 = 180
solve for x which equals x=20.
then substitute for x with the equation for angle A.
A=3(20)+18
angle A = 78
Hence, the measure of ∠A is 78 degrees.
Learn more about supplementary angles here:
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There are 10,000 people at a concert.
Of those people, 6,250 are adults.
What percent of the people at the
concert are adults?
Answer:
62.5%
Step-by-step explanation:
Total number of people at the concert = 10000
Number of adults = 6250
Percentage of adults = number of adults/ total number of people at the concert x 100%
That’s
6250/10000 x 100%
0.625 x 100%
62.5%
62.5% of the people at the concert are adults
in a right triangle, the 58cm hypotenuse makes a 51 angle with one of the legs. rounded to two decimals places, how long is that leg?
Answer:
36.50
To two decimal places
Step-by-step explanation:
The hypothenuse side in a right angle triangle has 58cm. While the angle touching one of its leg is 51°. How long is that leg.
From the right angled triangle, the size of the leg touching the hypothenuse is the adjacent side of the triangle, hence in trigonometry, the cosine rule is used, because it involves the adjacent and the hypotenuse.
Cos 51°=x/58
Let the size of the leg be x
Making x the subject
x=58(Cos51°)
x=36.500058
Correct to two decimal place
x=36.50
Triple the difference between 18 and four
Answer:
42
Step-by-step explanation:
3 * (18 - 4) = 3 * 14 = 42
Answer:
42
Step-by-step explanation:
18-4=14. 14*3=42
Please answer ASAP! Thank you in advance, and remember to wash your hands consistently for 1 minute.
Please help me let me know how you got the answer
Area of building is [tex]3,84,000m^3[/tex] .
Step-by-step explanation:
Here we have , a figure in given below picture where we have to find volume of this office building , Let's find out:
If we look closely we see that it's basically cuboid with dimensions 50 m by 110 m by 70 m . But there's one small cuboid sliced off from this cuboid with dimensions 50 m by 10 m by (110-90) m i.e. 50 m by 10 m by 20 m .
Area of building = Area of larger cuboid - Area of smaller cuboid
Area of cuboid = [tex]length(width)(breadth)[/tex]
⇒ Area of building = Area of larger cuboid - Area of smaller cuboid
⇒ [tex]Area = (50(110)(70))m^3 - (50(10)(20))m^3[/tex]
⇒ [tex]Area = 3,85,000m^3 - 10,000m^3[/tex]
⇒ [tex]Area = 3,84,000m^3[/tex]
Therefore, Area of building is [tex]3,84,000m^3[/tex] .
Part A: A graph passes through the points (0.2). (1.3), and (2, 4). Does this graph represent a linear function or a non-linear function? Explain your answer in
words
Part 3: Write one example of a linear function and one example of a non-linear function (Use x and y as the variables)
Answer
a) Linear because there is a constant slope
b) Linear: y=x
Non-linear: y=1/x
Step-by-step explanation:
First we find the slope using the formula:
[tex]m = \frac{y_2-y_1}{x_2-x_1} [/tex]
For the points (0,2) and (1,3), we have
[tex]m = \frac{4-3}{1-0} = \frac{1}{1} = 1[/tex]
For the points (0,2) and (2,4), we have
[tex]m = \frac{4 - 2}{2 - 0} = \frac{2}{2} = 1[/tex]
For (1,3) (2,4), we have;
[tex]m = \frac{4 - 3}{2 - 1} = 1[/tex]
Since there is a constant rate of change the graph represents a linear function.
b) For a linear function, the highest degree is 1.
An example of a linear function is y=2x
For a non-linear function the degree of the variable is not equal to 1.
[tex]y = \frac{1}{x} [/tex]
What are the solutions? Check all of the boxes
that apply.
2x2 - 16x + 34 = x2 - 6x + 10
Answer:
4 and 6
:)
EDGE 2020
Answer:
B) 4
C) 6
Step-by-step explanation:
What is the value of x in this equation ? 5x -14 = 8x + 4
Twelve less than a product of a number and 6 is 60
Answer:
The number is 12
Step-by-step explanation:
Step 1: Convert words into an expression
Twelve less than a product of a number and 6 is 60
(n * 6) - 12 = 60
Step 2: Solve for n
(n * 6) - 12 + 12 = 60 + 12
n * 6 / 6 = 72 / 6
n = 12
Answer: The number is 12
Suppose a car burns 1 gallon of gas in 25 miles. How much gas will be burned on a trip of 400 miles.
16 gallons will be burned
Still not a clue what to do
The flag is 31.6 feet from the bottom of the sailboat.
Step-by-step explanation:
Step 1:
In the given triangle, the angle is 58°. Assume the opposite side has a length of x feet and the adjacent side has a length of 16 feet.
To determine the length of the opposite side of the triangle, we use the tan of the given angle.
[tex]tan \theta = \frac{oppositeside}{adjacent side} .[/tex]
Step 2:
In the given triangle,
The length of the opposite side = x feet,
The length of the adjacent side = 16 feet,
The angle of the triangle = 58°.
[tex]tan \theta = \frac{oppositeside}{adjacent side} , tan 58 = \frac{x}{16}, tan 58 = 1.6000.[/tex]
[tex]1.6 = \frac{x}{16} , x = (1.6)(16) = 25.6.[/tex]
Since Shianne's eyes are 6 feet from the bottom of the sailboat, the distance between the flag and the bottom of the sailboat [tex]= 25.6 + 6 = 31.6.[/tex]
So the flag is 31.6 feet from the bottom of the sailboat.
A psychology professor assigns letter grades on a test according to the following scheme.
A: Top 8% of scores
B: Scores below the top 8% and above the bottom 61%
C: Scores below the top 39% and above the bottom 16%
D: Scores below the top 84% and above the bottom 8%
F: Bottom 8% of scores
Scores on the test are normally distributed with a mean of 65.4 and a standard deviation of 9.7. Find the numerical limits for a D grade. Round your answers to the nearest whole number, if necessary.
The numerical limits for a D grade in psychology can be calculated using the Z-score formula. The cutoff scores are below the top 84% and above the bottom 8%. Using the mean of 65.4 and the standard deviation of 9.7, the numerical limits for a D grade are 52 to 79.
Explanation:To find the numerical limits for a D grade, we need to determine the cutoff scores. According to the given scheme, a D grade corresponds to scores below the top 84% and above the bottom 8%. To calculate these cutoff scores, we can use the Z-score formula. The Z-score is calculated as the difference between a score and the mean, divided by the standard deviation. Using the Z-score table, we can find the Z-scores corresponding to the top 8% and the bottom 8%. Finally, we can use the Z-score formula to find the corresponding scores for those Z-scores.
Given that the mean is 65.4 and the standard deviation is 9.7, we can calculate the Z-scores:
Z-score for the top 8% = 1.405
Z-score for the bottom 8% = -1.405
Using the Z-score formula, where X is the score, the mean is 65.4, and the standard deviation is 9.7:
X = Z * standard deviation + mean
For the top 8%:
X = 1.405 * 9.7 + 65.4 = 79
For the bottom 8%:
X = -1.405 * 9.7 + 65.4 = 52
Therefore, the numerical limits for a D grade are 52 to 79 (rounded to the nearest whole number).
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A circle passes through point (-2, -1) and its center is at (2, -1). Which equation represents the circle?
The choices are missing, but we can solve the problem from the given information
Answer:
The equation which represents the circle is (x - 2)² + (y + 1)² = 16
Step-by-step explanation:
The form of the equation of a circle is (x - h)² + (y - k)² = r², where
(h , k) are the coordinates of its centerr is the radius of it∵ The coordinates of the center of the circle are (2 , -1)
∴ h = 2 and k = -1
The radius of the circle is the segment whose join the center of the circle and any point on the edge of the circle
∵ The circle passes through point (-2 , -1)
∴ The radius of the circle is the distance from the center (2 , -1)
and the point (-2 , -1)
The y-coordinates of the two points are equal that means the radius is a horizontal segment and its length is the difference between their x-coordinates
∵ r = 2 - (-2)
∴ r = 4
Now let us substitute h, k, and r in the form of the equation of the circle
∵ (x - 2)² + (y - -1)² = (4)²
∴ (x - 2)² + (y + 1)² = 16
The equation which represents the circle is (x - 2)² + (y + 1)² = 16
2z+5=5+2z is it commutative property or distributive ?!
Answer:
Commutative property: The formula for this property is a + b = b + a. For example, adding 1 + 2 or 2 + 1 will give us the same answer according to the commutative property of addition.
Point A is located at (3,6). The midpoint of line segment AB is point C(11,13). What are the coordinates of point B? Use the midpoint formula and show ALL work. DO NOT use Desmos.
Answer: The coordinates of point B are (19 , 20).
Step-by-step explanation:
The mid point (x,y) of line joining (a,b) and (c,d) is given by :-
[tex](x,y)=(\dfrac{a+c}{2},\dfrac{b+d}{2})[/tex] (1)
Given : Point A is located at (3,6). The midpoint of line segment AB is point C(11,13).
Let the coordinates of point B are (a,b) m, the according to (1) , we have
[tex](\dfrac{3+a}{2},\dfrac{6+b}{2})=(11,13)\\\\\Rightarrow\ \dfrac{3+a}{2}=11\ \ ,\ \ \dfrac{6+b}{2}=13\\\\\Rightarrow\ 3+a=22\ \ ,\ \ \ 6+b=26\\\\\Rightarrow\ a=19,\ \ b= 20[/tex]
Hence, the coordinates of point B are (19 , 20).
Can someone please help me and also explain it because I want to understand it.
Answer:
89.10
Step-by-step explanation:
To find the volume (how much soil can fit) you do Length x Width x Height in this case it is 4 x 9 x 3
4 x 9 x 3 = 108
Now you have to divide the volume by two because you only want to fill half the box.
108/2=54
Now you multiple the volume by the price to figure out how much soil will cost
54 x 1.65 = 89.1
It will cost $89.10
Heyo! I hope your day is going well! I hope I can help you understand this a bit better!
First things first we have to figure out the total volume of the flower box. To do this we do a simple multiplication problem, 3*4*9, or length*width*height. 3*4 is 12, and then 12*9 is 108. So our total volume for the flower box is 108 cubic feet.
Lucy only wants to fill half of her flower box, so we are going to go ahead and divide our total volume, 108 cubic feet, by 2. Our answer here is 54 cubic feet.
The soil Lucy wants to buy is 1.65 for each cubic foot, meaning we should multiply 1.65 and 54.Our final answer is 89.1!
Please help! A person standing 30 ft from a flagpole can see the top of the pole at a 35 degree angle of elevation. The person's eye level is 5 ft from the ground. Fond the height of the flagpole.
Answer: The height of the pole is 26 ft
Step-by-step explanation: Please refer to the attached diagram for details.
The diagram shows a right angled triangle labeled PEG. The point P is the top of the flagpole, the point E is the eye level of the observer, while point G is the point where the flagpole touches the ground. However, we must not forget that the observer’s eye is 5 ft from the ground. This means the height of the flagpole in the triangle has an extra 5 ft that would be added after our calculation. So, we have an opposite, which is the unknown and an adjacent, which is the side that lies between the reference angle and the right angle (that is, 30). Also we have the reference angle as 35.
Using the trigonometric ratios,
TanE = opposite/adjacent
Tan35 = PG/30
By cross multiplication we now have
Tan35 x 30 = PG
0.7002 x30 = PG
21.006 = PG
The height of the pole is approximately 21 ft.
However, we remember that the eye of the observer is 5 ft away from the ground. That means the pole actually goes an additional 5ft when it touches the ground. Hence the actual length of the pole is 21 + 5 = 26
Height of pole = 26 ft
8.039 has _________ decimal places?
8.039 has three decimal places which are the tenths, hundreths, and the thousandths.
What’s is the answer for 50x50
Answer:
2500
Step-by-step explanation:
Answer: 50x50 is 2500
Step-by-step explanation:
5x5=25
you have two 0s you never used add them to the end of the answer giving you not 25 but 2500
NEED HELP URGENTLY ......................................................
I assumed that the unit of measure is ft.
Front+back:
S1=2×(4×3.5/2)=4×3.5=14ft²
2 sides+base:
S2=3×(9×4)=9×12=108ft²
Total area: 14+108=122ft²
Which statements are true about the expression 8 (a + 7)? Check all that apply.
1.To simplify, distribute a to 8 and to 7.
2.8(a) can be rewritten as 8a.
3.8 (a + 7) can be rewritten as 8 (a) + 8 (7).
4.8 (a + 7) can be rewritten as 8 (a) + (7).
5.An equivalent expression is 15a.
6.An equivalent expression is 8 a + 7
7.An equivalent expression is 8 a + 56
Answer:
Option 3)
8(a + 7) can be rewritten as 8(a) + 8(7).
Option 7)
An equivalent expression is 8a + 56
Step-by-step explanation:
We are given the following expression:
[tex]8 (a + 7)[/tex]
We can simplify the expression by distributing 8 over (a+7).
Distributive property:
[tex]a(b+c)\\=(a\times b) + (a\times c)\\=a(b) + a(c)\\=ab + ac[/tex]
Simplifying the expression, we get,
[tex]8(a+7)\\=(8\times a)+(8\times 7)\\=8a + 56[/tex]
Thus, the correct options are:
Option 3)
8(a + 7) can be rewritten as 8(a) + 8(7).
Option 7)
An equivalent expression is 8a + 56
The true statements about the expression 8(a+7) are 2, 3 and 7.
When evaluating the expression 8(a+7), several steps can be taken to rewrite or simplify it. Here's a closer look at the provided statements:
Statement 1 suggests to distribute 'a' to 8 and to 7, which is incorrect. The correct procedure is to distribute the 8 to both 'a' and the 7.
Statement 2 correctly suggests that 8(a) can be rewritten as 8a.
Statement 3 is true, as 8(a+7) can be rewritten following the distributive property as 8(a)+8(7), which simplifies to 8a+56.
Statement 4 is incorrect because it omits the distribution of 8 over both terms within the parentheses.
Statement 5 is incorrect as there is no reason to believe that 8(a+7) simplifies to 15a without any additional information.
Statement 6 is incorrect as it implies that the 8 is only multiplied by 'a' and not by the 7.
Statement 7 is correct because the expression 8(a+7) is correctly expanded to 8a+56.
(-3) + (-2) - (-4) please help please help please help
Answer:
-1
Step-by-step explanation:
Step 1: Combine
(-3) + (-2) - (-4)
Two negatives - (-4) makes a positive +4
-3 - 2 + 4
-1
Answer: -1
Answer:
-1
Step-by-step explanation:
It's quite simple! It is just like normal addition and subtraction but add the negative! Sorry it's a pretty bad response haha
-3-2+4
MAFS.912. G-C0.3.11
Which statement is true about every parallelogram?
A. All four sides are congruent.
B. The interior angles are all congruent.
C. Two pairs of opposite sides are congruent.
D. The diagonals are perpendicular to each other.
-2p-4=2
What does p equal to?
Answer:
Step-by-step explanation:
-2p-4=2
Collect like terms
-2p=2+4
-2p=6
p=6/-2=-3
Answer:
p=-3
Step-by-step explanation:
-2p-4=2
add 4 to both sides then get -2p =6
divide both sides by -2 and get p=-3
Hope this helped
Given the two points (3,6) and (-2,5), determine the slope of the line.
Answer:
1/5
Step-by-step explanation:
y2 -y1/x2 - x1
5 - 6/ -2 - 3
-1/-5
1/5