Segment AB is dilated from the origin to create segment A prime B prime at A' (0, 4) and B' (4, 6). What scale factor was segment AB dilated by?
Answer choices:
A. 1/2
B. 2
C. 3
D.4
Answers
Given:
Endpoint of segment AB are A(0,2), B(2,3).
Segment AB is dilated from the origin to create segment A prime B prime at A' (0, 4) and B' (4, 6).
To find:
The scale factor of dilation.
Solution:
If a figure is dilated about the origin with factor k, then
[tex](x,y)\to (kx,ky)[/tex]
Using this rule, we get
[tex]A(0,2)\to A'(k(0),k(2))[/tex]
[tex]A(0,2)\to A'(0,2k)[/tex]
So, the image of A is A'(0,2k).
It is given that image of A is A'(0,4). So,
[tex]A'(0,2k)=A'(0,4)[/tex]
On comparing the y-coordinates from both sides, we get
[tex]2k=4[/tex]
[tex]k=\dfrac{4}{2}[/tex]
[tex]k=2[/tex]
Therefore, the scale factor is 2 and the correct option is B.
Dilation involves changing the size of a line
The scale factor is 2.
From the graph, the coordinates of AB are:
[tex]\mathbf{A = (0,2)}[/tex]
[tex]\mathbf{B = (2,3)}[/tex]
The coordinates of AB are:
[tex]\mathbf{A' = (0,4)}[/tex]
[tex]\mathbf{B' = (4,6)}[/tex]
Divide A' by A or B' by B to calculate the scale ratio (k)
[tex]\mathbf{k = \frac{A'}{A}}[/tex]
So, we have:
[tex]\mathbf{k = \frac{(0,4)}{(0,2)}}[/tex]
Expand
[tex]\mathbf{k = \frac{2(0,2)}{(0,2)}}\\[/tex]
Divide
[tex]\mathbf{k = 2}\\\\\\\\[/tex]
Hence, the scale factor is 2.
Read more about scale factors at:
https://brainly.com/question/16713785
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[tex]3^2+x^2=12^2\\9+x^2=144\\x=\sqrt{135}[/tex]
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[tex]x=3\sqrt{15}[/tex] meters or 11.62 meters
7 1/3 : 2 4/9= what does it equal?
Answers
Answer:
3/1 or 3
Step-by-step explanation:
7 1/3 = 7x3 + 1/3 =21 + 1/3 =22/3
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-------------------------------------------------
2 4/9 2x9 + 4/9 = 18 + 4 /9= 22/9
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1, 1, 1, 1, 4, 4, 7, 7, 7, 7
1, 1, 1, 4, 4, 4, 4, 7, 7, 7
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Answers
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Step-by-step explanation:
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Days Hours
Sunday 0
Monday 1.5
Tuesday 2.5
Wednesday 2.5
Thursday 3
Friday 0
Sunday N
Answers
Answer:
1 hour
Step-by-step explanation:
We are given that
Day Hours
Sunday 0
Monday 1.5
Tuesday 2.5
Wednesday 2.5
Thursday 3
Friday 0
Saturday n
Mean number of hours of study per day=1.5
Mean=[tex]\frac{sum\;of\;data\;}{total\;number\;of\;data\;points}[/tex]
Total number of days=7
Using the formula
[tex]1.5=\frac{0+1.5+2.5+2.5+3+0+n}{7}[/tex]
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Answer:
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Step-by-step explanation:
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Answer:
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Step-by-step explanation:
Please let me know if you want me to add an explanation.
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Answers
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Step-by-step explanation:
Given
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Required
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Answer:
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Answer:
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Answer:
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Step-by-step explanation:
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50% off makes the new price half of the original, then another 50 % would be half off the discounted price, so they actually end up paying 25 % of the original price:
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Answers
100% - 0.5% = 99.5% or 0.995
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A quantity with an initial value of 9800 decays exponentially at a rate such that the quantity cuts in half every 6 days. What is the value of the quantity after 138 hours, to the nearest hundredth?
Answers
Answer:
About 5043.58
Step-by-step explanation:
The standard form for an exponential decay after t time is:
[tex]\displaystyle f(t)=a(r)^{t/d}[/tex]
Where a is the initial value, r is the rate decay, t is the time that has passed, and d is the amount of time it takes for 1 cycle.
The initial value is 9800. So a = 9800.
The quantity cuts in half. So, r = 1/2.
And it cuts in half every 6 days. For this question, we will convert this to hours. 6 days = 144 hours. So, we can let d = 144, where t will be in hours.
Therefore, our function is:
[tex]\displaystyle f(t)=9800\Big(\frac{1}{2}\Big)^{t/144}[/tex]
Where t is the amount of time that has passed, in hours.
Then the quantity left after 138 hours will be:
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Answer:
i think it is y=15x-6
Step-by-step explanation:
if it is correct plz plz mark as brainliest
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19NBoli
Answer:
y = 2x-6
Step-by-step explanation:
Slope intercept form:
y = mx+b
m = slope
In this case the slope is 2/1 or 2.b = The point where the line crosses the y-axis
In this case -6 is the exact point the line crosses the y-axisSo if you put it all together you get the answer of:
y = 2x-6
I hope this helped!
P.S. I am so sorry I couldn't respond earlier :(
Sincerely,
Rekifromsk8theinfinity
:D
Kyla sold her laptop to Fely in a condition that Fely should give he a downpayment of Php8,000 and Fely will pay her Php1,000 every month for 1 year .if the money ears 0.5% compound monthly what is the market value of Fely's offer?
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The median household income in the US grew linearly from approximately $30, 000 in 1990 to $48, 000 in 2006. Let x be the number of years since 1990. Express the median income as a function of x. Use this function to approximate the median income in 2030. What is the significance of the slope of this function
Answers
Answer:
[tex]y = 1125x+30000[/tex] --- The equation
The median income in 2030 is $75000
Step-by-step explanation:
Given
Represent years since 1990 with x and the income with y.
So, we have:
[tex](x_1,y_1) = (0,30000)[/tex] --- In 1990
[tex](x_2,y_2) = (16,48000)[/tex] --- In 2006
Solving (a): Express as a function.
First, we calculate the slope
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
[tex]m = \frac{48000-30000}{16-0}[/tex]
[tex]m = \frac{18000}{16}[/tex]
[tex]m = 1125[/tex]
The equation is then calculated as:
[tex]y = m(x-x_1)+y_1[/tex]
This gives:
[tex]y = 1125(x-0)+30000[/tex]
Open bracket
[tex]y = 1125x-0+30000[/tex]
[tex]y = 1125x+30000[/tex]
Solving (b): Income in 2030.
In 2030, x = 40.
Substitute 40 for x in [tex]y = 1125x+30000[/tex]
[tex]y = 1125*40 +30000[/tex]
[tex]y = 45000 +30000[/tex]
[tex]y = 75000[/tex]
Solving (c): The significance of the slope.
In (a), the slope is calculated as 1125.
This implies that the yearly rate is $1125
Find the curved surface area of a cylinder if it's base circumference is 36 cm and it's height is 4 cm
Answers
Answer:
CSA of a cylinder = 144cm²
Step-by-step explanation:
Given the following data;
Base circumference = 36cm
Height = 4cm
To find the curved surface area (CSA) of the cylinder;
CSA of a cylinder = 2πr * h
But 2πr = 36cm
Substituting the values into the equation, we have;
CSA of a cylinder = 36 * 4
CSA of a cylinder = 144cm²
0.3 - 0.04 = i need it ASAP
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A motor cyclist completes a journey at an average speed of 65 mph in 3½ hours. Calculate the distance travelled.
Answers
Answer:
227.5
Step-by-step explanation:
65 mhp
after 3.5 h
Just multiply
65 x 3.5 = 227.5
Answer:
227.5
Step-by-step explanation:
multiply 65 mph to 3 1/2 [3.5 (estimated)] to calculate the distanbce travelled