A dilation maps AB onto A'B'. If the coordinates of the
endpoints are
A(4,2),
A'(10,5),
B(10,6),
B'(25, 15), then
what is the scale factor?
Answers
Answer:
[tex]k = 2.5[/tex]
Step-by-step explanation:
Given
[tex]A = (4,2)[/tex]
[tex]A' = (10,5)[/tex]
[tex]B = (10,6)[/tex]
[tex]B' = (25,15)[/tex]
Required
Determine the scale factor (k)
Scale factor is calculated using:
[tex]Old * k = New[/tex]
In this case, we have:
[tex]AB* k = A'B'[/tex]
Make k the subject
[tex]k = \frac{A'B'}{AB}[/tex]
Using point A and A'
[tex]k = \frac{A'}{A}[/tex]
[tex]k = \frac{(10,5)}{(4,2)}[/tex]
Factorize the numerator
[tex]k = \frac{2.5(4,2)}{(4,2)}[/tex]
[tex]k = 2.5*\frac{(4,2)}{(4,2)}[/tex]
[tex]k = 2.5*1[/tex]
[tex]k = 2.5[/tex]
Related Questions
WILL MARK BRAINLIEST!!!
DUE SOON!!
Explain the need for businesses to use forecasting models and evaluate the use of Time Series Analysis as one of these models
Answers
Answer:
They can be used to develop alternate models with different factors.
Step-by-step explanation:
Jayden is driving 390 miles to visit the Gateway Arch in St. Louis. He drives at an average rate of 65 miles per hour. Explain how you can find the amount of time it will take her to get to the arch
Answers
Using the relation between velocity, distance and time, it is found that it will take her 6 hours to get to the arch.
What is the relation between velocity, distance and time?Velocity is distance divided by time, that is:
v = d/t.
For this problem, we have that:
She drives 390 miles, hence d = 390.Her velocity is of 65 miles per hour, hence v = 65.We can solve the equation for t to find the time, hence:
65 = 390/t
65t = 390
t = 390/65
t = 6.
It will take her 6 hours to get to the arch.
More can be learned about the relation between velocity, distance and time at https://brainly.com/question/24316569
#SPJ1
express using algebra A inscreased by 15%
Answers
Answer:
A(1.15)
Step-by-step explanation:
Use the shell method to write and evaluate the definite integral that represents the volume of the solid generated by revolving the plane region about the y-axis. y
Answers
Answer:
[tex]Volume = \frac{384}{7}\pi[/tex]
Step-by-step explanation:
Given (Missing Information):
[tex]y = x^\frac{3}{2}[/tex]; [tex]y = 8[/tex]; [tex]x=0[/tex]
Required
Determine the volume
Using Shell Method:
[tex]V = 2\pi \int\limits^a_b {p(y)h(y)} \, dy[/tex]
First solve for a and b.
[tex]y = x^\frac{3}{2}[/tex] and [tex]y = 8[/tex]
Substitute 8 for y
[tex]8 = x^\frac{3}{2}[/tex]
Take 2/3 root of both sides
[tex]8^\frac{2}{3} = x^{\frac{3}{2}*\frac{2}{3}}[/tex]
[tex]8^\frac{2}{3} = x[/tex]
[tex]2^{3*\frac{2}{3}} = x[/tex]
[tex]2^2 = x[/tex]
[tex]4 =x[/tex]
[tex]x = 4[/tex]
This implies that:
[tex]a = 4[/tex]
For [tex]x=0[/tex]
This implies that:
[tex]b=0[/tex]
So, we have:
[tex]V = 2\pi \int\limits^a_b {p(y)h(y)} \, dy[/tex]
[tex]V = 2\pi \int\limits^4_0 {p(y)h(y)} \, dy[/tex]
The volume of the solid becomes:
[tex]V = 2\pi \int\limits^4_0 {x(8 - x^{\frac{3}{2}}}) \, dx[/tex]
Open bracket
[tex]V = 2\pi \int\limits^4_0 {8x - x.x^{\frac{3}{2}}} \, dx[/tex]
[tex]V = 2\pi \int\limits^4_0 {8x - x^{\frac{2+3}{2}}} \, dx[/tex]
[tex]V = 2\pi \int\limits^4_0 {8x - x^{\frac{5}{2}}} \, dx[/tex]
Integrate
[tex]V = 2\pi * [{\frac{8x^2}{2} - \frac{x^{1+\frac{5}{2}}}{1+\frac{5}{2}}]\vert^4_0[/tex]
[tex]V = 2\pi * [{4x^2 - \frac{x^{\frac{2+5}{2}}}{\frac{2+5}{2}}]\vert^4_0[/tex]
[tex]V = 2\pi * [{4x^2 - \frac{x^{\frac{7}{2}}}{\frac{7}{2}}]\vert^4_0[/tex]
[tex]V = 2\pi * [{4x^2 - \frac{2}{7}x^{\frac{7}{2}}]\vert^4_0[/tex]
Substitute 4 and 0 for x
[tex]V = 2\pi * ([{4*4^2 - \frac{2}{7}*4^{\frac{7}{2}}] - [{4*0^2 - \frac{2}{7}*0^{\frac{7}{2}}])[/tex]
[tex]V = 2\pi * ([{4*4^2 - \frac{2}{7}*4^{\frac{7}{2}}] - [0])[/tex]
[tex]V = 2\pi * [{4*4^2 - \frac{2}{7}*4^{\frac{7}{2}}][/tex]
[tex]V = 2\pi * [{64 - \frac{2}{7}*2^2^{*\frac{7}{2}}][/tex]
[tex]V = 2\pi * [{64 - \frac{2}{7}*2^7][/tex]
[tex]V = 2\pi * [{64 - \frac{2}{7}*128][/tex]
[tex]V = 2\pi * [{64 - \frac{2*128}{7}][/tex]
[tex]V = 2\pi * [{64 - \frac{256}{7}][/tex]
Take LCM
[tex]V = 2\pi * [\frac{64*7-256}{7}][/tex]
[tex]V = 2\pi * [\frac{448-256}{7}][/tex]
[tex]V = 2\pi * [\frac{192}{7}][/tex]
[tex]V = [\frac{2\pi * 192}{7}][/tex]
[tex]V = \frac{\pi * 384}{7}[/tex]
[tex]V = \frac{384}{7}\pi[/tex]
Hence, the required volume is:
[tex]Volume = \frac{384}{7}\pi[/tex]
The volume of the solid of revolution generated by revolving the plane region about the y-axis is [tex]\frac{10240\pi}{3}[/tex] cubic units.
How to calculate the volume of a solid of revolution by shell method
Let be [tex]f(x) = x^{5/2}[/tex] and [tex]g(x) = 32[/tex], whose point of intersection is [tex](x,y) = (4, 32)[/tex]. Solid of revolution generated by revolving the plane region about the y-axis is defined by the following formula:
[tex]V = 2\pi\int\limits^{32}_0 {y\cdot g(y)} \, dy[/tex] (1)
If we know that [tex]g(y) = y^{2/5}[/tex], then the volume of the solid of revolution is:
[tex]V = 2\pi\int\limits^{32}_{0} {y^{7/5}} \, dy[/tex]
[tex]V = 2\pi\cdot \left(\frac{5}{12}\cdot y^{12/5}\right)\left|_{0}^{32}[/tex]
[tex]V = \frac{5\pi}{6} \cdot y^{12/5}|\limit_{0}^{32}[/tex]
[tex]V = \frac{5\pi}{6}\cdot 32^{12/5}[/tex]
[tex]V = \frac{10240\pi}{3}[/tex]
The volume of the solid of revolution generated by revolving the plane region about the y-axis is [tex]\frac{10240\pi}{3}[/tex] cubic units. [tex]\blacksquare[/tex]
Remark
The statement is incomplete. Complete form is shown below:
Use the shell method to write and evaluate the definite integral that represents the volume of the solid generated by revolving the plane region about the y-axis. [tex]y = x^{5/2}[/tex], [tex]y = 32[/tex], [tex]x = 0[/tex].
To learn more on solids of revolution, we kindly invite to check this verified question: https://brainly.com/question/338504
5 more than the product of 12 and 8 as a numerical expression.
Answers
Answer:
(12x8) + 5
Step-by-step explanation:
The product of 12 and 8 would be multiplication, so you can represent that as
(12x8) or 12x8
"5 more" simply means addition
So if you were to put all that together as a numerical expression it would be
(12x8) + 5
Hope this helps!
The answer is 12x8+5
Please I need help haha it’s for math
Answers
Answer:
1600
Step-by-step explanation:
pls brainliest
Answer:
hope it helped have a good day mate
What is the answer
5+7+9+8=
Answers
Answer:
29
Step-by-step explanation:
Middle school students were asked how they got to school each morning. There were 375 students who said they rode the bus. This number represents 60 percent of the school enrollment. How many students are enrolled?
Answers
Answer:
give me 1 second to answer with the correct answer
Consider the following sets of sample data:
A: $28,200, $34,300, $32,300, $20,800, $36,900, $20,600, $20,000, $29,600, $35,400, $20,200, $20,200, $38,100, $31,300, $38,600
B: 4.77, 3.46, 4.62, 3.30, 3.13, 3.01, 4.69,3.55, 3.57, 4.59, 3.65
Step 1 of 2: For each of the above sets of sample data, calculate the coefficient of variation, CV. Round to one decimal place.
Answers
Answer:
25.3% and 17.6%
Step-by-step explanation:
hey anyone mind helping out
Answers
Answer:
The answer is A
Step-by-step explanation:
Find the mean, median, mode, and range for each set of data 21.5, 35.5, 49.5, 16.3, 35.5
Answers
Answer:
Mean :31.66
Median:35.5
Mode:35.5
Step-by-step explanation:
(hope this helps can i plz have brainlist :D hehe)
D
Angles that have the same
_________________
are called
__________________
angles.
Answers
Answer:
Can’t trust anyone these days fake is becoming the new trend.
Here are the ingredients needed to make 8 pancakes
250ml milk
140 g flour
5 g butter
a) Simon makes 4 pancakes.
Answers
Answer: To make 4 pancakes, Simon will need 125 ml milk, 70 grams flour, and 2.5 grams of butter.
Step-by-step explanation:
If that is the recipe to make 8 pancakes, and Simon has 4 pancakes, then Simon needs to cut the recipe in half. So we can multiply each ingredient by 1/2.
250 x 1/2 = 125.
140 x 1/2 = 70.
5 x 1/2 = 2.5
In conclusion, to make 4 pancakes, Simon will need 125 ml milk, 70 grams of flour, and 2.5 grams of butter.
my REAL FINAL LAST 100 points, pls do me well this time... show work pls :(
Answers
Im not sure how to explain how to do a graph, but I hope this helps at least a bit!
~Direct Variation When two variables are related in such a way that the ratio of their values always remains the same, the two variables are said to be in direct variation. In simpler terms, that means if A is always twice as much as B, then they directly vary. If a gallon of milk costs $3, and I buy 1 gallon, the total cost is $3.~
2. 7 2/6 + 1/12 = M
A.7 3/18
B.7/18
C.7 2/12
D.7 5/12
3. 1 6/10 + 1 4/5 = ?
A. 2 10/15
B. 2 10/50
C. 3 4/10
D. 3 10/10
4. 5/8 + 1/2 = Z
A. 9/8
B. 6/8
C. 1
D. 1 5/8
5. 2/12 + 2/4 = R *
A. 4/16
B. 8/16
C. 4/12
D. 8/12
Answers
Answer:
2 a 3 d 4 c 5 b
Step-by-step explanation:
At a gourmet coffee shop. 3 pounds of dark-roast coffee beans cost $56 and 7 pounds of the same coffee cost $112. On the grid below, graph a line that shows how the cost of these coffee
beans varies proportionally with the number of pounds purchased. Use your graph to identify the unit rate for these coffee beans.
PLEASE ITS DUE IN A HOUR
Answers
Answer:
In the question, it says that this is a proportional relationship.
A proportional relationship is something like:
y = k*x
So when we have x = 0, we also need to have y = 0.
For the case in the question, this does not happen, so i guess that the actual question is:
"At a gourmet coffee shop. 3.5 pounds of dark-roast coffee beans cost $56 and 7 pounds of the same coffee cost $112."
We can define:
x = amount of coffee
y = price of that coffee
Now we have two pairs:
$56 to get 3.5lb
$112 to get 7lb
Then we have two points:
(3.5lb, $56)
(7lb, $112)
We can draw these two points and then connect them with a line, this line will represent the proportional relationship.
Now we need to look at the value 1 in the x-axis, then draw a vertical line
At the point where this vertical line intersects the graph, we draw a horizontal line, and the value of y is the value at which this horizontal line intersects the y-axis.
(you can see a rough sketch of this in the image below)
The solution is 1lb of coffee costs $16.
The product of two consecutive room numbers is 210. Find the room numbers.
Answers
Answer:
104.5 and 105.5
Step-by-step explanation:
Unless there are such things are 1/2 room numbers, there is no answer. But algebraically, x + x + 1 = 2x + 1 = 210
2x + 1 = 210
2x = 209
x = 104.5
When Brandon went bowling, it cost $4.95 per game, plus a one-time fee to rent the shoes. Brandon played 5 games and paid $32. Write and solve a linear equation to find the cost to rent the shoes. Enter just the equation in slope-intercept form on this question.
Use the equation from the previous question to find the cost of renting the shoes.
Answers
Answer:
$7.25.
Step-by-step explanation:
Given that, when Brandon went bowling, it cost $ 4.95 per game, plus a one-time fee to rent the shoes, and knowing that Brandon played 5 games and paid $ 32, to find the cost to rent the shoes the following equation must be performed :
4.95 x 5 + X = 32
24.75 + X = 32
X = 32 - 24.75
X = 7.25
Thus, the cost of renting the shoes was $ 7.25.
please help mee with this thing
Answers
Please help me with this thank you!
Answers
Answer:
y = -x + 1
Step-by-step explanation:
y=mx+b
m:slope= rise/run, the line goes down 1 and over 1 so it would be -1/1 which is -1
b:y-intercept: the line crosses the y-axis at 1
plug in m=-1 and b=1 into y=mx+b
y=-1x+1
y=-x+1
what is the answer of this question?
Answers
Answer:
Its B.
Step-by-step explanation:
Because [tex]11^{2}[/tex] + [tex]12^{2}[/tex] does not equal [tex]15^{2}[/tex]
121 + 144 [tex]\neq[/tex] 225
265 [tex]\neq[/tex] 225
help me please i don’t understand
Answers
Answer:(If you need the slope)
y=3x+6.5
Step-by-step explanation:
HELP ME PLEASEEE ASAPPP
Answers
Line EF intersects the parallel lines AB and CD.
What is the measure of angle J in the figure below?
Answers
Answer:
d, 125
Step-by-step explanation:
Answer:
d)125
Step-by-step explanation:
HELP ME NOW ASAPPP UnU
Answers
Answer:
56.757 and if u divide it : 676.75
Step-by-step explanation:
uwu
how would I do linear expression
Answers
Answer:
Linear expression is linear equations
Step-by-step explanation:
Which function rule represents the data in the table below ?
y = 4 + 5 x
y = 3 + 6x
y= 5 + 4x
y = 6 + 3x
Answers
I need an answer for 5/6x4. I appreciate the effort in helping. Sorry im not very good at fractions
Answers
Answer:
3.33
Step-by-step explanation:
Answer:
3 1/3
Step-by-step explanation:
5/6 x 4 = 3 1/3
Please help! I need by tomorrow!
Answers
Answer:
-1 = -6
-5 = 2
2 = 4
or it could be
-1,-1
-5, -1
2,2
Step-by-step explanation:
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PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!!PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!!
PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!!PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!!
PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!!PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!!
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PLS SHOW THE WORK!!!!!!!!
Answers
Now im not 100% sure, but this is what i got (for number one).
y=2x−1
Swap sides so that all variable terms are on the left hand side.
2x−1=y
Add 1 to both sides.
2x=y+1
Divide both sides by 2.
2x/2 = y+1/2
Dividing by 2 undoes the multiplication by 2.
So therefore, X = Y+1/2.
(i couldnt explain that very well im sorry, i dont know the 2nd answer im very bad at these)
Answer:
I need 1 Brainliest before I can become Virtuoso
Step-by-step explanation:
