In class, julie was asked to create a scenario for the linear function shown. she came up with the following:

joe planned a hiking trip from where he parked his car to the mountain cabin he had rented. joe parked 12 miles away from the cabin. after one hour, he was still 7 miles from the cabin. joe’s hike from his car to the cabin can be modeled by the function f(x)=-3x+12.

does julie’s scenario match the linear function graphed? if not, where does she go wrong? how can she correct her mistake and match scenario to the function?

The linear function that matches Julie's scenario is

Step-by-step explanation:

see the attached figure to better understand the problem

Let

x -----> the time in hours

y ----> the distance in miles from the cabin

we know that

After one hour, he was still 7 miles from the cabin.

so

For x=1 h, y=7 mi

Observing the graph

For x=1 h, y=9 mi

therefore

Julie's scenario does not match the graphed linear function.

Find the correct linear equation that match Julie’s scenario

we have the points

(0,12) and (1,7)

Find the slope

Find the linear equation in slope intercept form

we have

----> the y-intercept is the point (0,12)

substitute

therefore

The linear function that matches Julie's scenario is

second option

step-by-step explanation:

the measures of a triangle equal 180. use that to find x.

2x+3x+4x=180

9x=180

9x/9=180/9

x=20

now you know x, you know angle a is 40°, angle b is 60°, angle c is 80°.

because angle a is 40°, the first option doesn't work.

because angle b is 60°, the second option does work.

when you add angle a and b, you get 100°. complementary means it equals 90°, so the third option doesn't work.

when you add angle a and c, you get 120°, which is not 100.

dilation scale factor 2: starting with δabc, draw the dilation image of the triangle with a center at the origin and a scale factor of two. notice that every coordinate of the original triangle has been multiplied by the scale factor (x2). dilation with scale factor 2, multiply by 2.