Answer:
(x,y)=(-2,-5)
Step-by-step explanation:
y=1/2x-4
y=-2x-9
(y=) 1/2x-4=-2x-9
1/2x +2x=-9+4
1/2x +4/2x=-5
5/2x=-5
5x=-5*2
5x=-10
x=-2
x=-2
y=-2x-9=-2*(-2)-9=4-9=-5
(x,y)=(-2,-5)
Answer:
D. m∠A=43, m∠B=55, a=20
Step-by-step explanation:
Given:
∆ABC,
m<C = 82°
AB = c = 29
AC = b = 24
Required:
m<A, m<C, and a (BC)
SOLUTION:
Find m<B using the law of sines:
![\frac{sin(B)}{b} = \frac{sin(C)}{c}](https://tex.z-dn.net/?f=%20%5Cfrac%7Bsin%28B%29%7D%7Bb%7D%20%3D%20%5Cfrac%7Bsin%28C%29%7D%7Bc%7D%20)
![\frac{sin(B)}{24} = \frac{sin(82)}{29}](https://tex.z-dn.net/?f=%20%5Cfrac%7Bsin%28B%29%7D%7B24%7D%20%3D%20%5Cfrac%7Bsin%2882%29%7D%7B29%7D%20)
![sin(B)*29 = sin(82)*24](https://tex.z-dn.net/?f=%20sin%28B%29%2A29%20%3D%20sin%2882%29%2A24%20)
![\frac{sin(B)*29}{29} = \frac{sin(82)*24}{29}](https://tex.z-dn.net/?f=%20%5Cfrac%7Bsin%28B%29%2A29%7D%7B29%7D%20%3D%20%5Cfrac%7Bsin%2882%29%2A24%7D%7B29%7D%20)
![sin(B) = \frac{sin(82)*24}{29}](https://tex.z-dn.net/?f=%20sin%28B%29%20%3D%20%5Cfrac%7Bsin%2882%29%2A24%7D%7B29%7D%20)
![sin(B) = 0.8195](https://tex.z-dn.net/?f=%20sin%28B%29%20%3D%200.8195%20)
![B = sin^{-1}(0.8195)](https://tex.z-dn.net/?f=%20B%20%3D%20sin%5E%7B-1%7D%280.8195%29%20)
![B = 55.0](https://tex.z-dn.net/?f=%20B%20%3D%2055.0%20)
m<B = 55°
Find m<A:
m<A = 180 - (82 + 55) => sum of angles in a triangle.
= 180 - 137
m<A = 43°
Find a using the law of sines:
![\frac{a}{sin(A)} = \frac{b}{sin(B)}](https://tex.z-dn.net/?f=%20%5Cfrac%7Ba%7D%7Bsin%28A%29%7D%20%3D%20%5Cfrac%7Bb%7D%7Bsin%28B%29%7D%20)
![\frac{a}{sin(43)43} = \frac{24}{sin(55)}](https://tex.z-dn.net/?f=%20%5Cfrac%7Ba%7D%7Bsin%2843%2943%7D%20%3D%20%5Cfrac%7B24%7D%7Bsin%2855%29%7D%20)
Cross multiply
![a*sin(55) = 25*sin(43)](https://tex.z-dn.net/?f=%20%20a%2Asin%2855%29%20%3D%2025%2Asin%2843%29%20)
![a = \frac{25*sin(43)}{sin(53)}](https://tex.z-dn.net/?f=%20%20a%20%3D%20%5Cfrac%7B25%2Asin%2843%29%7D%7Bsin%2853%29%7D%20)
(approximated)
Megan has $5,621 to give to charity. She wanrs to give the money to 23 different charities. Each charity will get the same amount. How much money will each charity get? How much will be left over? Answer: 22r9
Answer:
36 inches
Step-by-step explanation:
12 inches equals 1 foot
There is 3 feet in a yard
2 yards equals 6 feet
1 yard equals 36 inches