Answer:
The y-coordinate of their intersection point is 3
That is y=3
Step-by-step explanation:
Given two lines are y=6x+15 and y=mx+4
Given that the two lines intersect at x=-2
To find the y coordinate of their intersection point :
Equating the two lines
6x+15=mx+4
6x+15-mx-4=0
6x-mx+11=0
(6-m)x+11=0
At x=-2 (6-m)x+11=0
(6-m)(-2)+11=0
(6-m)(-2)=-11
![6-m=\frac{11}{2}](https://tex.z-dn.net/?f=6-m%3D%5Cfrac%7B11%7D%7B2%7D)
![-m=\frac{11}{2}-6](https://tex.z-dn.net/?f=-m%3D%5Cfrac%7B11%7D%7B2%7D-6)
![-m=\frac{11-12}{2}](https://tex.z-dn.net/?f=-m%3D%5Cfrac%7B11-12%7D%7B2%7D)
![-m=\frac{-1}{2}](https://tex.z-dn.net/?f=-m%3D%5Cfrac%7B-1%7D%7B2%7D)
![m=\frac{1}{2}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B1%7D%7B2%7D)
Substitute the value
in y=mx+4 we get
![y=\frac{1}{2}x+4](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B1%7D%7B2%7Dx%2B4)
At x=-2 ![y=\frac{1}{2}(-2)+4](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B1%7D%7B2%7D%28-2%29%2B4)
![=-1+4](https://tex.z-dn.net/?f=%3D-1%2B4)
![=3](https://tex.z-dn.net/?f=%3D3)
Therefore y=3
Therefore the y-coordinate of their intersection point is 3
Pythagorean Theorem: a^2 + b^2 = c^2
-A and B are legs of the triangle
-C is the hypotenuse
#1.
6^2 + 8^2 = c^2
36 + 64 = c^2
100 = c^2
c = 10
#2.
5^2 + 12^2 = c^2
25 + 144 = c^2
169 = c^2
c = 13
#4.
10^2 + 4^2 = c^2
100 + 16 = c^2
116 = c^2
c = ![4\sqrt{29}](https://tex.z-dn.net/?f=4%5Csqrt%7B29%7D)
#5.
15^2 + 9^2 = c^2
225 + 81 = c^2
306 = c^2
c = ![3\sqrt{34}](https://tex.z-dn.net/?f=3%5Csqrt%7B34%7D)
#6.
120^2 + b^2 = 150^2
14400 + b^2 = 22500
b^2 = 8100
b = 90
#7.
144^2 + b^2 = 194^2
20736 + b^2 = 37636
b^2 = 16900
b = 130
Hope this helps!! :)
Fasle,2nd degree(^2)polynomials are called quadratics, 3rd degree are called cubics
d
^3
+
d^
2
+
12
d
+
18
Step-by-step explanation:
She should have added 2 to both sides of the equation instead of subtracting 2.
2x -2 = 14
Add 2 to both sides:
2x = 16
Divide both sides by 2:
x = 8