All are correct except these 2:
The graph has one x-intercept:
No, the graph does not cut at the x-axis at all, there is no x-intercept.
The graph as a y-intercept at (5,0):
No, the y-intercept is at (0,5)
<u>Answer:</u>
1/4
<u>Step-by-step explanation:</u>
We are to find the scale factor of the dilation that maps the pre-image of triangle ABC with vertices A(2, 5), B(6, 10) and C(9, −1) to the image triangle A'B'C' with vertices A' (0.5, 1.25), B' (1.5, 2.5), C' (2.25, −0.25).
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(2, 5) ---> A' (0.5, 1.25) = ![\frac{0.5}{2} , \frac{1.25}{5}=(\frac{1}{4} , \frac{1}{4})](https://tex.z-dn.net/?f=%5Cfrac%7B0.5%7D%7B2%7D%20%2C%20%5Cfrac%7B1.25%7D%7B5%7D%3D%28%5Cfrac%7B1%7D%7B4%7D%20%2C%20%5Cfrac%7B1%7D%7B4%7D%29)
B(6, 10) ---> B' (1.5, 2.5) = ![\frac{1.5}{6} , \frac{2.5}{10}=(\frac{1}{4} , \frac{1}{4})](https://tex.z-dn.net/?f=%5Cfrac%7B1.5%7D%7B6%7D%20%2C%20%5Cfrac%7B2.5%7D%7B10%7D%3D%28%5Cfrac%7B1%7D%7B4%7D%20%2C%20%5Cfrac%7B1%7D%7B4%7D%29)
C(9, −1) ---> C' (2.25, −0.25) = ![\frac{2.25}{9} , \frac{-0.25}{-1}=(\frac{1}{4} , \frac{1}{4})](https://tex.z-dn.net/?f=%5Cfrac%7B2.25%7D%7B9%7D%20%2C%20%5Cfrac%7B-0.25%7D%7B-1%7D%3D%28%5Cfrac%7B1%7D%7B4%7D%20%2C%20%5Cfrac%7B1%7D%7B4%7D%29)
Therefore, the scale factor of the dilation is 1/4.
Answer:
21
Step-by-step explanation:
I wil call the length l and the width w in the following. We are given these informations:
The area of the rectangle is 105. That means l * w = 105. (1)
The length is 16 inches longer that the width. That means l = w + 16. (2)
If we plug the information we get from (2) into the equation (1), we get:
(w + 16) * w = 105
Simplify and you get
w² + 16 w - 105 = 0
With the the quadratic formula we get the results w = 5 and w = -21. The negative result doesn't make sense for our task, we are only interested in positive length and width :).
If we now plug w = 5 back into our infromation (2), we get:
l = 5 + 16 = 21
(To confirm the result plug w = 5 and l = 21 into (1))
Step 1: Find the slope:
To find the slope, find two points on the graph and count the “rise over run” between the points.
Two points here are (0,-1) and (2,1). To get from (0,-1) to the other point, you need to go “up 2” and then “right 2”. This means your slope is 2/2 or 1.
Step 2: Find the y-intercept:
We can see the y-intercept is (0,-1) on the graph. We’ll use the “-1” from that point for our equation.
Step 3: Put it all together:
The slope-intercept form is y=mx+b, where m is the slope and b is from the y-intercept.
Putting Step 1 and Step 2 into play, we have:
y = x - 1
Note: since m=1, we don’t need to write y = 1x -1. That 1 on the 1x is unnecessary.
Answer :use the less than one