Answer:
Step-by-step explanation:
![a) \dfrac{3x}{2}-5=4](https://tex.z-dn.net/?f=a%29%20%5Cdfrac%7B3x%7D%7B2%7D-5%3D4)
Add 5 to both sides
![\dfrac{3x}{2}-5 +5 = 4 + 5\\\\\dfrac{3x}{2} = 9 \\\\Now \ multiply \ both \ sides \ by \ 2 \\\\\dfrac{3x}{2}*2 = 9*2\\\\3x = 18\\Now \ divide \ both \ sides \ by \ 3\\\\x =\dfrac{18}{3}\\\\](https://tex.z-dn.net/?f=%5Cdfrac%7B3x%7D%7B2%7D-5%20%2B5%20%3D%204%20%2B%205%5C%5C%5C%5C%5Cdfrac%7B3x%7D%7B2%7D%20%3D%209%20%5C%5C%5C%5CNow%20%5C%20multiply%20%5C%20both%20%5C%20sides%20%20%5C%20by%20%20%5C%20%202%20%5C%5C%5C%5C%5Cdfrac%7B3x%7D%7B2%7D%2A2%20%3D%209%2A2%5C%5C%5C%5C3x%20%3D%2018%5C%5CNow%20%5C%20divide%20%5C%20both%20%5C%20sides%20%20%5C%20by%20%5C%203%5C%5C%5C%5Cx%20%3D%5Cdfrac%7B18%7D%7B3%7D%5C%5C%5C%5C)
x = 6
![b) \dfrac{x-3}{5} + 1 = -2\\\\\\Subtract \ 1 \ from \ both \ sides\\\\\dfrac{x-3}{5} = -2 -1\\\\\dfrac{x-3}{5} = -3\\\\Multiply \ both \ side \ by \ 5\\\\x - 3 = -3*5\\\\x -3 = -15\\\\](https://tex.z-dn.net/?f=b%29%20%5Cdfrac%7Bx-3%7D%7B5%7D%20%2B%201%20%3D%20-2%5C%5C%5C%5C%5C%5CSubtract%20%5C%201%20%5C%20from%20%20%5C%20both%20%5C%20sides%5C%5C%5C%5C%5Cdfrac%7Bx-3%7D%7B5%7D%20%3D%20-2%20-1%5C%5C%5C%5C%5Cdfrac%7Bx-3%7D%7B5%7D%20%3D%20-3%5C%5C%5C%5CMultiply%20%5C%20both%20%5C%20side%20%5C%20by%20%5C%205%5C%5C%5C%5Cx%20-%203%20%3D%20-3%2A5%5C%5C%5C%5Cx%20-3%20%3D%20-15%5C%5C%5C%5C)
Add 3 to both sides
x = -15 +3
x = -12
Answer:
A
Step-by-step explanation:
We want to solve the equation:
![5\sin(2x)=3\cos(x)](https://tex.z-dn.net/?f=5%5Csin%282x%29%3D3%5Ccos%28x%29)
To do so, we can rewrite the equation.
Recall the double-angle for sine:
![\sin(2x)=2\sin(x)\cos(x)](https://tex.z-dn.net/?f=%5Csin%282x%29%3D2%5Csin%28x%29%5Ccos%28x%29)
By substitution:
![5\left(2\sin(x)\cos(x)\right)=3\cos(x)](https://tex.z-dn.net/?f=5%5Cleft%282%5Csin%28x%29%5Ccos%28x%29%5Cright%29%3D3%5Ccos%28x%29)
Distribute:
![10\sin(x)\cos(x)=3\cos(x)](https://tex.z-dn.net/?f=10%5Csin%28x%29%5Ccos%28x%29%3D3%5Ccos%28x%29)
We can subtract 3cos(x) from both sides:
![10\sin(x)\cos(x)-3\cos(x)=0](https://tex.z-dn.net/?f=10%5Csin%28x%29%5Ccos%28x%29-3%5Ccos%28x%29%3D0)
And factor:
![\cos(x)\left(10\sin(x)-3\right)=0](https://tex.z-dn.net/?f=%5Ccos%28x%29%5Cleft%2810%5Csin%28x%29-3%5Cright%29%3D0)
Hence, our answer is A.
*It is important to note that we should not divide both sides by cos(x) to acquire 10sin(x) = 3. This is because we need to find the values of x, and one or more may result in cos(x) = 0, and we cannot divide by 0. Hence, we should subtract and then factor.
See those lines that are pependicular
meanins that those lines are same legnth
in triangle, if 2 sides are same measure legnth then the angles oposite those sides are same measure
therefor top right and top left angle is 42
remember that vertical angles are congruent
remmeber all angles ad to 180 in a triangle
so therefor look at top triangle
top right angle is 42
top left is 42
bottom must be x
total is 180 so
42+42+x=180
84+x=180
minus 84 fromboth sides
x=96
answer is 96 degrees
Answer:
y=-2x-7
Step-by-step explanation:
Hope this helps, have a nice night! (^-^)
O.6 easy because of the answer that is why