A triangle has vertices A (-5, -4), B (2, 6), and C (4, -3). The center of dilation is the origin and (x, y) changes to (3x, 3y). What are the vertices of the dilated image?

(-15,12),(6,18)(12,-9)

Step-by-step explanation:

Given

A (-5, -4), B (2, 6), and C (4, -3)

Dilated from (x,y) to (3x,3y)

Required

Vertices of the dilated image

First, the scale factor has to be calculated

This is calculated as thus;

Dilation = Original * Scale Factor;

In case of (x,y) to (3x,3y)

So, we have

Simplify brackets

Divide both sides by (x,y)

Now, the vertices of the new image can be calculated;

Using the formula: Dilation = Original * Scale Factor;

At vertex A(-5,4)

Dilation = (-5,4) * 3

Dilation = (-5*3 ,4*3)

Dilation = (-15,12)

At vertex B(2,6)

Dilation = (2,6) * 3

Dilation = (2*3 ,6*3)

Dilation = (6,18)

At vertex C(4,-3)

Dilation = (4,-3) * 3

Dilation = (4*3 ,-3*3)

Dilation = (12,-9)

Hence, the vertices of the dilated image are (-15,12),(6,18)(12,-9)

47

step-by-step explanation:

the given growth  function for the length of the fish (cm) is

f(m) = 5(1.07)m = 5.35m

where 

m = months

at the end of the study, the length is 9.19 cm. the  time for conducting the study is determined as

5.35m = 9.19

m = 1.7178 months

part a.

the study was performed over a time period  of about 1.72 months. therefore  the domain for  plotting the function is 0 < = m < = 1.72.

note:

if growth  continues at this rate for up to m months, then the domain would be 0< =m< =m.

part b.

the growth function is a linear function.

when m=0, f=0.

therefore the initial growth is zero, which represents the y-intercept.

part c.

assume that the growth function is valid for 0< =m< =9.

the average rate of change of the function is the slope of the linear function, which is 5.35 cm/month.