Answer:
a. x=-17, y=27
b. x=0, y=-6
c. x=9, y=-1
d. undefined
e. x=4, y=-6
f. x=4, y=0
Step-by-step explanation:
a. 3x+y=24
y=3x+24
-x+3x+24=-10
2x=-34
x=-17
-(-17)-y=-10
17-y=-10
-y=-27
y=27
b. 3y=-18
y=-6
-6=-x-6
0=x
c. -2x+17=8-x
9=x
y=8-9
y=-1
d. x-7=x+7
x-14=x
-14=0
e. -4x+10+2x=2
-2=-8
x=4
y=-4(4)+10
y=-16+10
y=-6
f. x+2y=4
x=4-2y
-4(4-2y)-3y=16
-16+8y-3y=16
-16+5y=16
5y=0
y=0
x+2(0)=4
x=4
Answer:
![y = 0.35x + 35](https://tex.z-dn.net/?f=y%20%3D%200.35x%20%2B%2035)
Step-by-step explanation:
Linear equation:
A linear equation has the following format:
![y = mx + b](https://tex.z-dn.net/?f=y%20%3D%20mx%20%2B%20b)
In which m is the slope and b is the y-intercept.
Finding the slope:
We have two points: (110, 73.5) and (760, 301).
The slope is given by the change in y divided by the change in x. So
Change in y: 301 - 73.5 = 227.5
Change in x: 760 - 110 = 650
Slope: ![m = \frac{227.5}{650} = 0.35](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7B227.5%7D%7B650%7D%20%3D%200.35)
So
![y = 0.35x + b](https://tex.z-dn.net/?f=y%20%3D%200.35x%20%2B%20b)
Finding the y-intercept:
(760, 301) means that when
. So
![301 = 0.35(760) + b](https://tex.z-dn.net/?f=301%20%3D%200.35%28760%29%20%2B%20b)
![b = 301 - 0.35(760)](https://tex.z-dn.net/?f=b%20%3D%20301%20-%200.35%28760%29)
![b = 35](https://tex.z-dn.net/?f=b%20%3D%2035)
So
![y = 0.35x + 35](https://tex.z-dn.net/?f=y%20%3D%200.35x%20%2B%2035)
If the pentagon is rotated 360° about the origin, that means the new figure will be exactly in the same position as the original image, because a rotation of 360° about the origin doesn't change the figure position or orientation.
So, if the vertex was located at (10, -8), the new figure will also have a vertex located at (10, -8).
Therefore the correct option is the fourth one.
Answer:
-6
Step-by-step explanation:
To find the sum of the roots, find the roots by factoring the equation and solving for x.
![x^2 + 6x-55=0\\(x+11)(x-5) = 0\\x=-11, 5](https://tex.z-dn.net/?f=x%5E2%20%2B%206x-55%3D0%5C%5C%28x%2B11%29%28x-5%29%20%3D%200%5C%5Cx%3D-11%2C%205)
Find the sum by adding -11 + 5 = -6.