Answer:
112
Step-by-step explanation:
A supplementary angle is 1 or more angles that add up to 180 degrees. So, the 2 angles we have are 2x and 3x + 10, and those add up to 180.
In order to make an equation for this, we need to add 2x and 3x + 10 and equal it to 180.
5x + 10 = 180
Now that we have our equation, the goal is to isolate the variable. The most immediate step I see is to subtract 10 from both sides so 5x will be alone on one side of the equation.
5x = 170
Now, to ultimately isolate the variable, we must divide both sides by 5 so that x will be alone.
170 / 5 is 34
5x / 5 is x
x = 34
Now, we plug in our value of x into 3x + 10 to find out what the measurement is equal to.
3(34) + 10 = y
102 + 10 = y
112 = y
3x + 10 is equal to 112.
Answer:f(x) = x becomes g(x) = (1/5)x through vertical compression by a factor of 5.
Step-by-step explanation:
Answer: -34
Step-by-step explanation:
4x-7=-28
-28-6=-34
If the points are scattered it’s no correlation
initial volume of balloon =
![\frac{4}{3} \times \frac{22}{7} \times r^{3} \\ \frac{4}{3} \times \frac{22}{7} \times {3}^{3} \\ 113.14](https://tex.z-dn.net/?f=%20%5Cfrac%7B4%7D%7B3%7D%20%20%5Ctimes%20%20%5Cfrac%7B22%7D%7B7%7D%20%20%5Ctimes%20r%5E%7B3%7D%20%20%5C%5C%20%20%5Cfrac%7B4%7D%7B3%7D%20%20%5Ctimes%20%20%5Cfrac%7B22%7D%7B7%7D%20%5Ctimes%20%20%7B3%7D%5E%7B3%7D%20%20%20%5C%5C%20113.14)
so intial volume is 113.14 cubic inches
volume after one hour will be 113.14 - 2 = 111.14 inches
new radius
![111.14 = \frac{4}{3} \times \frac{22}{7} \times {x}^{3} \\ \frac{2333.94}{88} = {x}^{3} \\ 26.52 = {x}^{3} \\ x = 2.98](https://tex.z-dn.net/?f=111.14%20%3D%20%20%20%5Cfrac%7B4%7D%7B3%7D%20%20%20%5Ctimes%20%20%5Cfrac%7B22%7D%7B7%7D%20%20%5Ctimes%20%20%7Bx%7D%5E%7B3%7D%20%20%5C%5C%20%20%5Cfrac%7B2333.94%7D%7B88%7D%20%20%3D%20%20%7Bx%7D%5E%7B3%7D%20%20%5C%5C%2026.52%20%3D%20%20%7Bx%7D%5E%7B3%7D%20%20%5C%5C%20x%20%3D%202.98)
Rate change of radius is
![\frac{2.98}{3} \times 100 \\ \frac{298}{3} \\ 99.93\%](https://tex.z-dn.net/?f=%20%5Cfrac%7B2.98%7D%7B3%7D%20%20%5Ctimes%20100%20%5C%5C%20%20%5Cfrac%7B298%7D%7B3%7D%20%20%5C%5C%2099.93%5C%25)
Rate change is 0.7% per hour the radius is decreasing