Answer
so there are 7 singing acts and 5 comedy acts.
Step-by-step explanation:
Let x= number of singing acts.
Let y= number of comedy acts.
We will take x+y=12 as our first equation, as there are 12 shows in total. We will take 5x+3y=50 as our second equation as there are 50 total minutes, and singing acts are 5 mins and comedy acts are 3 mins.
We solve x+y=12
Y=-x+12
We know y=-x+12, so we will substitute that for the y in the second equation.
1. Substitute 5x+3(-x+12)=50
2. Distribute 5x-3x+36=50
3. Solve 2x+36=50
2x=14
X=7
Now that we have found x, we will find y by substitute the x in 5x+3y=50 with the value, 7, that we found for x.
5(7)+3y=50
35+3y=50
3y=15
Y=5
Answer:
3x + 9 + 4x + x = 8x + 9
Step-by-step explanation:
combine like terms
Lets x = measure of the second angle, so m<2 = x
m<1 = 2x (<span>the measure of the first angle is twice the measure of the second angle)
</span>m<3 = x + 96 (<span>96 degrees more than the measure of the second angle)
</span>
x + 2x + x+ 96 = 180
4x + 96 = 180
4x = 84
x = 21
2x = 2(21) = 42
x + 96 = 21+96 = 117
answer
m<1 = 42
m<2 = 21
m<3 = 117
Double check
sum = 180
m<1 + m<2 +m<3 = 180
42+21+117=180
180=180
The definition of sine is "opposite / hypotenuse".
So, it is safe to assume that hypotenuse = 38.
