∆abc is transformed with the center of dilation at the origin. pre-image: ∆abc with vertices a(−5, −4), b(−7, 3), c(3, −2) image: ∆a'b'c' with vertices a' (−3.75, −3), b' (−5.25, 2.25), c' (2.25, −1.5) what is the scale factor of the dilation that maps the pre-image to the image?

3/4

Step-by-step explanation:

We are to find the scale factor of the dilation that maps the pre-image of triangle ABC with vertices A(−5, −4), B(−7, 3) and C(3, −2) to the image triangle A'B'C' with vertices A' (−3.75, −3), B' (−5.25, 2.25) and C' (2.25, −1.5).

Center of dilation is at the origin.

To find the scale factor, we will divide the corresponding vertices of the image and pre-image.

A(−5, −4) ---> A' (−3.75, −3) =

B(−7, 3) ---> B' (−5.25, 2.25) =

C(3, −2) ---> C' (2.25, −1.5) =

Therefore, the scale factor of the dilation is 3/4.

it is b)

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step-by-step explanation:

hello,

b) 62.47% of the students are between 14 and 18 years old.

step-by-step explanation:

mean = 15 and standard deviation = 2

student between 14 to 18

formula used z-score

for age 14 , z score

using z-table , p(z> -0.5)=0.3085

for age 18 , z score

using z-table , p(z< 1.5)=0.9332

p(-0.5< z< 1.5)=0.9332-0.3085 = 0.6247

thus, 62.47% of the students are between 14 and 18 years old.

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