Answer:
[tex]A.\ 1\frac{17}{30}\ hours[/tex]
Step-by-step explanation:
[tex]Let\ second\ jet\ overtake\ first\ in\ x\ hours.\\\\[/tex]
Distance covered by first jet:
[tex]Speed\ of\ first\ jet=564\ km/h\\\\Time=x+\frac{1}{2}\\\\Distance\ covered=speed\times time\\\\Distance\ covered=564\times (x+\frac{1}{2})=564x+564\times \frac{1}{2}\\\\Distance\ covered=564x+282[/tex]
Distance covered by second jet:
[tex]Speed\ of\ second\ jet=744\ km/h\\\\Time=x\\\\Distance\ covered=speed\times time\\\\Distance\ covered=744\times x\\\\Distance\ covered=744x[/tex]
[tex]Distance\ covered\ by\ both\ the\ jet\ in\ x\ hours\ is\ equal.\\\\744x=564x+282\\\\744x-564x=282\\\\180x=282\\\\x=\frac{282}{180}=\frac{6\times 47}{6\times 30}\\\\x=\frac{47}{30}\ hours\\\\x=1\frac{17}{30}\ hours[/tex]
(SAT Prep) Find the value of x in each of the following exercises:
Answer:
The value of x is 120°
Step-by-step explanation:
To solve for x, you need to introduce a third line that is parallel to the two parallel lines.
This line should divide the angle at x into two as shown in the attachment.
By the alternate interior angle property, m=70°
and
n=50°
This implies that, x=50+70=120°
what is value of (4g+h)(8)? G(x)= x+7; h(x)= (x-3)^2
Answer:
85
Step-by-step explanation:
hello :
if : g(x)= x+7; h(x)= (x-3)² so : (4g+h)(x)=4g(x)+h(x) = 4(x+7)+(x-3)²
(4g+h)(8)= 4(8+7)+(8-3)² = 60+25=85
A certain radioactive isotope has a half life of 6 hours. The starting amount is 100 grams. Write an exponential function to model this scenario. How much of the isotope remains after 12 hours?
To model the scenario, we can use the exponential function A = A0 · (1/2)^(t/h), where A is the amount remaining, A0 is the initial amount, t is the time, and h is the half-life. In this case, the initial amount is 100 grams and the half-life is 6 hours. After substituting t = 12 into the function, we find that 25 grams of the isotope remain after 12 hours.
Explanation:To model the scenario, we can write an exponential function using the formula:
A = A0 · (1/2)t/h
Where:
A is the amount remaining after a certain timeA0 is the initial amountt is the time that has passedh is the half-lifeFor this scenario, the initial amount is 100 grams and the half-life is 6 hours. So, the exponential function would be:
A = 100 · (1/2)t/6
To find out how much of the isotope remains after 12 hours, we can substitute t = 12 into the function and solve for A:
A = 100 · (1/2)12/6 = 100 · (1/2)2 = 100 · (1/4) = 25
Therefore, after 12 hours, 25 grams of the isotope would remain.
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WILL MARK BRAINLEIST!!!!!!
Suppose that it takes Calvin 3 hours to wax a car if he works alone and it takes Alvin 5 hours to wax a car if he works alone. How long does it take them to wax a car if they work together? Write an equation and solve for the unknown. Show your work.
Answer:
4 hours
Step-by-step explanation:
I am not sure, what I did was, if Calvin and Alvin both waxed half the car, their original time would split in half, then I added those values together, which is also the average.
y=mx+b is a pretty safe form to follow
C=3
A=5
if you are doing variables
I tried my best.
2(4x-9)=14 simplify your answer as much as possible
If the 4th and 7th terms of a GP are 250 and 31250 respectively. Find the two possible values of a and r
Answer:
a = 2 , r = 5
Step-by-step explanation:
The n th term of a geometric progression is
[tex]a_{n}[/tex] = a[tex]r^{n-1}[/tex]
where a is the first term and r the common ratio
Given the 4 th term is 250, then
ar³ = 250 → (1)
Given the 7 th term is 31250, then
a[tex]r^{6}[/tex] = 31250 → (2)
Dividing the 2 equations gives
[tex]\frac{ar^6}{ar^3}[/tex] = [tex]\frac{31250}{250}[/tex], that is
r³ = 125 ← take the cube root of both sides
r = [tex]\sqrt[3]{125}[/tex] = 5
Substitute r = 5 into (1)
a × 5³ = 250, that is
125a = 250 ( divide both sides by 125 )
a = 2
Answer: a = 2, and r = 5
Step-by-step explanation: What we have been given here is a geometric progression. Every term in the sequence of numbers is derived by multiplying the previous term by a particular number called the common ratio, otherwise known as r. Hence if the first term is 1 for instance, the second term would be derived as 1 x r (which equals 1r), the third term would be derived as 1r x r (which equals 1r squared) and so on.
Having this in mind , we can calculate the Nth term of a geometric progression as
Nth term = a x r{to the power of n - 1}
So if we want to calculate the 4th term for instance, that would be
4th = a x r{to the power of 4 - 1} OR
4th = a x r{to the power of 3}
Similarly to calculate the 7th term would be
7th = a x r{to the power of 7 - 1}
7th = a x r{to the power of 6}
Now that we have been given the 4th (250) and 7th (31250) terms, what we now have is
a x r{to the power of 3} = 250 AND
a x r{to the power of 6} = 31250
a x r{to the power of 6}/a x r{to the power of 3} = 31250/250
After reducing both sides to their simplest form, what we now have is
r{to the power of 3} = 125
If we add the cube root sign to both sides of the equation we would have
r = 5
Having computed r as 5, we can now go back to calculate a as follows;
If a x r{to the power of 3} = 250, then
a x 125 = 250
Divide both sides of the equation by 125
a = 2
Therefore, a = 2 and r = 5
Find the area of a circle with a circumference of 81.68cm
Answer:
A= 20959.52 cm
Step-by-step explanation:
Formula: A= π x r^2
A= π x 81.68^2
A= 20959.52
Cube Root Function Question! 15 points!
The graph of h(x) is a translation of f (x) = Root Index 3
Which equation represents h(x)?
Answer: Second option.
Step-by-step explanation:
Below are some transformations for a function f(x) :
1. If [tex]f(x)+k[/tex], the function is shifted "k" units up.
2. If [tex]f(x)-k[/tex], the function is shifted "k" units down.
3. If [tex]f(x-k)[/tex], the function is shifted "k" units right.
4. If [tex]f(x+k)[/tex], the function is shifted "k" units left.
The Cube root parent function is:
[tex]f(x)=\sqrt[3]{x}[/tex]
By definition, the graph of this function passes through the origin, as you can observe in the picture attached.
In this case, you need to analize the graph given in the exercise. You can see that the the graph of the function h(x) is like the parent function f(x), but shifted 2 units left.
Therefore, based on the transformations explained above, you can determine that the equation of the function h(x) is the following:
[tex]h(x)=f(x+2)\\\\h(x)=\sqrt[3]{x+2}[/tex]
There are 28 boys in the band
The 28 boys are 7/10 and the girls are 3/10 of the students
What is the total number of students in the marching band
Answer:
t = 40
Step-by-step explanation:
Start by breaking the equation down to a simpler form. To do this you would need to divide 28 by 7.
28 / 7 = x
x = 4
Now we can create a new equation.
4x = t
T would represent the total number of students in the band. X would be the any number from 1 to 10. This is because 10 is the highest faction to make the fraction a whole. Since we a looking for the total we would put ten in place for x.
4 x 10 = t
t = 40
There you go.
Hope this helped.
What number can be written as 400,000 + 8,000 + 400 + 70 + 1?
180.417
480.417
057 8047208.17
408,471
480.471
408,417
Answer:
it's 408,471
Step-by-step explanation:
[tex]400000 \\ + 8000 \\ \: + 400 \\ \: \: + 70 \\ \: \: \: + 1 \\ = 408471[/tex]
HELP PLEASE, I REALLY DONT UNDERSTAND THIS!
Answer: Since 3−5+2=0, then 2
is the additive inverse of 3−5 is 2
Since 5−3−2=0, then −2is the additive inverse of 5−3. is -2
Step-by-step explanation: additive inverse
The additive inverse of any number
x
is the number that gives zero when added to
x
. Example: the additive inverse of
5 is −5.
when looking at an equation how do you know if it is a function?
Simplify:
2(d + 3) + 3(d – 3)
A. –5d – 1
B. 5d – 3
C. 5d + 15
D. 6d – 3
Answer:
I would say it is c but im not sure.
Step-by-step explanation:
Well you use distributive property to solve this to get a simplified answer.
[tex]b. \: 5d - 3 \\ \\ 1. \: 2d + 6 + 3(d - 3) \\ 2. \: 2d + 6 + 3d - 9 \\ 3. \: (2d + 3d) + (6 - 9) \\ 4. \: 5d - 3[/tex]
If you do this you are officially skilled: (SAT Prep) In the figure, if PN = LN, NP Is parallel to MQ, and QL bisects ∠PQM, what is value of x?
Answer:
Try the suggested solution, shown on the picture attached
Step-by-step explanation:
Note, 'm(MNO)' means m(∠MNO), and for issues 2, 4 ,5 - the described angles are angles inside the declared triangle.
Answer:
67º
Step-by-step explanation:
8x+4(4x-3)=4(6x+4)-4
Answer:
x = 24
Step-by-step explanation:
8x + 4(4x - 3) = 4(6x + 4) - 4
8x + 16x - 12 = 24x + 16 - 4
24x - 12 = 24x + 12
24x = 24x + 12 + 12
24x = 24x + 24
24x/24x = 24
x = 24
Is it possible to show that G is congruent
The figure shows the 50 - foot side of a house and a proposed rectangular garden to be fences in on 3 sides.
The 3 sides, a,b, and x will be made of 40 feet of fencing.
Which of the following is an expression for a in terms of x?
A. 2x+40
B. 2x-40
C. 40-2x
D. 40-x+x
What is the area, in square feet, for the garden if 40 feet of fencing are used and x=15?
Option C 40-2 x
150 square feet
Step-by-step explanation:
Step 1 :
Given that the 3 sides, a,b, and x will be made of 40 feet of fencing,
we have a + b + x = 40
Since this is a rectangular garden , b= x
substituting b= x, we have a + x + x = 40
=> a+2 x = 40
=> a= 40-2 x
Step 2 :
To find the area in square feet,
when x = 15, a = 40 - 2 * 15 = 40-30 = 10 feet
The length and breadth of the rectangular garden are therefore 5 and 10 feet respectively
Hence, the area of the garden = length * breadth = 15 * 10 = 150 square feet
What is the slope between the points (0,-3) and
(-6, 7)?
Answer:
-5/3
Step-by-step explanation:
The box plots show the average wind speeds, in miles per hour, for various cities in two different countries. Average Wind Speeds of Cities in Country A 2 box plots. The number line goes from 1 to 11. For the average wind speeds of cities in country A, the whiskers range from 1 to 9.5, and the box ranges from 3 to 7. A line divides the box at 4. For the average wind speeds of cities in country B, the whiskers range from 1.2 to 11, and the box ranges from 4 to 9. A line divides the box at 6. Average Wind Speeds of Cities in Country B Which statement describes the symmetry of the data in the two box plots? The data in country A are more symmetric than the data in country B. The data in country B are more symmetric than the data in country A. The data in both countries have about the same symmetry. The symmetry of the data cannot be determined by looking at the box plots.
Answer:
"B"
Step-by-step explanation:
"the median wind speed for country B is greater than the median wind speed for county A"
got it right on the quiz, and good luck ;)
The median wind speed for country B is greater than the median wind speed for county A.
The answer is option B.
What is a median?A median is a number in the middle of a list of numbers that are sorted, ascended, or descended and can define a set of data. The median is sometimes used in contrast to the definition where there are outsiders in a sequence that may distort the value ratio.
Why is median important?The importance of median value is that it provides an idea about the distribution of data. If the definition and median of the data set are the same, then the data is evenly distributed from the smallest to the highest values.
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If 3 out of every 5 students in Mr.Pringles math class prefers pepperoni pizza topping how many of his 110 students would you expect to prefer pepperoni topping?
Answer:
Therefore out of Mr. Pringles 110 students we can expect the number that would prefer pepperoni pizza topping would be 66 students.
Step-by-step explanation:
If 3 out of every 5 students in Mr.Pringles math class prefers pepperoni pizza topping then the probability of a randomly selected student in Mr. Pringles prefers pepperoni pizza is [tex]\frac{3}{5} = 0.6[/tex].
Therefore out of Mr. Pringles 110 students we can expect the number that would prefer pepperoni pizza topping would be = 0.6 [tex]\times[/tex] 110 = 66 students.
HELP PLEASE
The area of a rectangle is 4w - 10 square units.
Factor this expression.
Given your answer in part A, describe what you can conclude about the dimensions of the rectangle in two or more complete sentences.
Answer:
Dimension is the square root of 4w-10
Step-by-step explanation:
The length=Breadth=√4w-10
Final answer:
The expression for the area of the rectangle, 4w - 10, can be factored as 2(2w - 5). This implies that one of the rectangle's dimensions could be 2 units and the other could be a linear expression of 2w - 5 units.
Explanation:
To factor the expression 4w - 10 square units, we can find the greatest common factor (GCF) of the two terms. The GCF of 4w and 10 is 2, so we can factor out 2 from the expression:
4w - 10 = 2(2w - 5)
Given the factored form, we can conclude something about the dimensions of the rectangle. The factored expression, 2(2w - 5), suggests that one dimension of the rectangle could be 2 units, and the other is a linear expression of width, specifically 2w - 5 units. This aligns with the area formula for rectangles, A = length × width, where one dimension is considered the length and the other the width for calculation purposes.
The focus of a parabola is (0, - 2) The directrix of the parabola is the line y = - 3 What is the equation of the parabola
Answer:
Option B: [tex]$ \textbf{y} \hspace{1mm} \textbf{=} \hspace{1mm} \frac{\textbf{-1}}{\textbf{2}} \textbf{x}^{\textbf{2}} \hspace{1mm} \textbf{-} \hspace{1mm} \frac{\textbf{5}}{\textbf{2}} $[/tex]
Step-by-step explanation:
When the focus (h, k) of a parabola and the equation of the directrix y = c are given, the equation of the parabola is given by:
[tex]$ \textbf{(x - h)}^{\textbf{2}} \hspace{1mm} \textbf{+} \hspace{1mm} \textbf{k}^{\textbf{2}} \hspace{1mm} \textbf{-} \hspace{1mm} \textbf{c}^{\textbf{2}} \hspace{1mm} \textbf{=} \hspace{1mm} \textbf{2(k - c)y}} $[/tex]
Here, we are given the focus: (h, k) = (0, -2)
Directrix: y = c = -3.
We substitute in the formula to get the equation of the parabola.
[tex]$ (x - 0)^2 + (-2)^2 - (-3)^2 = 2(-2 - (-3))y $[/tex]
[tex]$ \implies x^2 + 4 - 9 = 2(- 2 + 3)y $[/tex]
[tex]$ \implies x^2 - 5 = 2(1) y$[/tex]
[tex]$ \implies 2y = x^2 - 5 $[/tex]
Dividing by 2, throughout we get:
[tex]$ \textbf{y} \hspace{1mm} \textbf{=} \hspace{1mm} \frac{\textbf{-1}}{\textbf{2}} \textbf{x}^{\textbf{2}} \hspace{1mm} \textbf{-} \hspace{1mm} \frac{\textbf{5}}{\textbf{2}} $[/tex] which is the required answer.
Which number is irrational?
A. 3/17
B. Square root of 25
C. 0.666
D. Square root of 33
Answer:
B. Square root of 25
Step-by-step explanation:
It is a whole number.
Thus, it is not an irrational number.
The square root of 25 is equal to 5
Therefore
An irrational number is a number that cannot be written as a ratio of two integers. It is a non-terminating and non-repeating decimal.
A box of printer paper cost $25 each. Your school purchased 9 boxes of paper for $225. Which equation uses the distributive property to show that your school spent $225 on 9 boxes of paper? A) 9 x 25 = 225 B) 225 ÷ 25 = 9 C) 9 × (20 + 5) = 225 D) 25 + 25 + 25 + 25 + 25 + 25 + 25 + 25 + 25 = 225
Answer:
Step-by-step explanation:
Answer:
C) 9 × (20 + 5) = 225
Step-by-step explanation:
The answer is c
9 x (20 + 5 )
9x20 + 9x5
180 + 45 = 225
Every jump a game piece makes measures 8/9 . The piece starts at point A = 7 and jumps to the right. As soon as the piece jumps over B = 24, it switches direction and jumps to the left. The piece then stops at point A. How many jumps did the game piece take?
Answer:
There will be a total 40 jumps.
Step-by-step explanation:
Every jump a game piece makes measures [tex]\frac{8}{9} = 0.889[/tex].
Now, the piece starts at point A = 7 and jumps to the right.
So, the piece will jump over B = 24 after [tex]\frac{24 - 7}{0.889} = 19.122[/tex] ≈ 20 complete jumps.
Then it switches direction to the left and the piece then stops at point A.
So, there will be a total (20 + 20) = 40 jumps. (Answer)
The game piece took a total of 153/8 jumps.
Explanation:To determine how many jumps the game piece took, we need to find the total distance it traveled. The piece starts at point A = 7 and jumps to the right, so it covers a distance of 8/9. As soon as it jumps over B = 24, it switches direction and jumps to the left, covering a distance of -8/9. The piece continues this pattern until it reaches point A again.
To find the number of jumps, we can divide the total distance traveled by the distance covered in each jump. The total distance is 24 - 7 = 17. Dividing 17 by 8/9 gives us:
17 / (8/9) = 17 * (9/8) = 153/8
So, the game piece took a total of 153/8 jumps.
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What’s is 97 square root
The square root of 97 is 8.48857802, but you can round to 8.49 or 8.5 if you so desire.
Wendy has $60 to buy seed for her birdfeeders. Each bag of seed costs $8.
How many bags of seed can she buy?
Answer:7 bags
Step-by-step explanation:
Divide 60 by 8 because she has a total of $60 and each bag costs $8. The answer would actually be 7.5 bags but since you can’t buy half a bag your answer would be 7 bags.
PLEASE HELP... BRAINLIEST... PLEASE..
17. Determine the scale factor for each dilation. Determine whether the dilation is an enlargement, reduction or isometry dilation.
The given dilation is an isometry dilation.
Step-by-step explanation:
Step 1; First, we need to compare the dimensions of the two figures. We check to see if the side lengths are the same. If the parameters are the same, the dilation could be an enlargement or a reduction. Whereas if the parameters are the same, it could be an isometric dilation or just a reflection.
Step 2; The first shape has a side length of approximately 2.5 units. We compare this to the same side length as the second shape. The second shape has the same side length.
The first shapes side length of the / same side length of the second shape = 2.5 / 2.5 = 1,
So the scale factor is 1. As the parameters do not change, it could either be a reflection or an isometric dilation.
Step 3; The base side in shape 1 is BC whereas the same base side in shape 2 is [tex]A^{1}[/tex][tex]B^{1}[/tex]. So shape ABCDE has rotated to form the shape the dilation is isometric and not a reflection with a scale factor of 1.
Answer:
1: Isometry
Step-by-step explanation:
As both the shapes are having equal area hence the scale factor remains 1.
As scale factor remains 1this is neither enlargement or reduction.
It is the isometry that the distance between two pints remains the same.
In the skateboard design, VW bisects XY at point T , and XT =39.9 cm. Find XY
Answer:
The measure of XY is 79.8 cm.
Step-by-step explanation:
An image of the question is attached here.
Given:
Measure of XT = 39.9
VW is the bisector.
So T is the midpoint of XY .
Note: Bisector divides the line in two equal parts.
According to the question:
⇒ [tex]XT = TY[/tex] ...as T is the midpoint.
⇒ [tex]XY=XT +TY[/tex] ...Segment addition Postulate
⇒ [tex]XY=XT+XT[/tex]
⇒ [tex]XY=2(XT)[/tex]
⇒ [tex]XY=2(39.9)[/tex]
⇒ [tex]XY=79.8[/tex] cm
The measure of XY in the skateboard design is 79.8 centimeter.
End of day/Distance from home
1 /383
2 /682
3 /1132
4 /1503
5 /1906
6 /2196
- In the table, Adam recorded the miles he traveled each day while traveling from his home to California. Calculate the average rate
of change between day 1 and day 3.
A)283 miles per day
B)375 miles per day
C)450 miles per day
D)566 miles per day
Answer:
[tex]\large \boxed{\text{B) 374 mi/day}}[/tex]
Step-by-step explanation:
The average rate of change from one point to another is the slope of the straight line joining the two points.
[tex]\text{slope} = \dfrac{ y_{2} - y_{1}}{ x_{2} - x_{1}}[/tex]
From Day 1 to Day 3, your points are (1, 383) and (3, 1132).
[tex]\text{Slope} = \dfrac{1132 - 383 }{3 - 1} = \dfrac{749 }{2} = \textbf{374 mi/day}\\\\\text{The average rate of change from Day 1 to Day 3 was $\large \boxed{\textbf{374 mi/day}}$}[/tex]
The graph below shows the rate of change from Day 1 to Day 3 as a black line. It appears from the graph that Adam and his dad kept the same rate of change for the whole trip.