Inversely proportional: z = k/r
k = 32 * 1.5 = 48
Plug that into equation
8 = 48/r
Multiply both sides by r
8r = 48
Divide by 8
r = 6
Is the third side the hypotenuse?
Answer:
Please check the explanation.
Step-by-step explanation:
Given the expression
![2\left(P\:+1\right)\:+\:3\left(P\:+\:2\:\right)\:>\:2](https://tex.z-dn.net/?f=2%5Cleft%28P%5C%3A%2B1%5Cright%29%5C%3A%2B%5C%3A3%5Cleft%28P%5C%3A%2B%5C%3A2%5C%3A%5Cright%29%5C%3A%3E%5C%3A2)
solving the expression
![2\left(P\:+1\right)\:+\:3\left(P\:+\:2\:\right)\:>\:2](https://tex.z-dn.net/?f=2%5Cleft%28P%5C%3A%2B1%5Cright%29%5C%3A%2B%5C%3A3%5Cleft%28P%5C%3A%2B%5C%3A2%5C%3A%5Cright%29%5C%3A%3E%5C%3A2)
as
so the expression becomes
![5P+8>2](https://tex.z-dn.net/?f=5P%2B8%3E2)
subtracting 8 from both sides
![5P+8-8>2-8](https://tex.z-dn.net/?f=5P%2B8-8%3E2-8)
![5P>-6](https://tex.z-dn.net/?f=5P%3E-6)
Dividing both sides by 5
![\frac{5P}{5}>\frac{-6}{5}](https://tex.z-dn.net/?f=%5Cfrac%7B5P%7D%7B5%7D%3E%5Cfrac%7B-6%7D%7B5%7D)
![P>-\frac{6}{5}](https://tex.z-dn.net/?f=P%3E-%5Cfrac%7B6%7D%7B5%7D)
Therefore,
![2\left(P+1\right)+3\left(P+2\right)>2\quad :\quad \begin{bmatrix}\mathrm{Solution:}\:&\:P>-\frac{6}{5}\:\\ \:\mathrm{Decimal:}&\:P>-1.2\\ \:\mathrm{Interval\:Notation:}&\:\left(-\frac{6}{5},\:\infty \:\right)\end{bmatrix}](https://tex.z-dn.net/?f=2%5Cleft%28P%2B1%5Cright%29%2B3%5Cleft%28P%2B2%5Cright%29%3E2%5Cquad%20%3A%5Cquad%20%5Cbegin%7Bbmatrix%7D%5Cmathrm%7BSolution%3A%7D%5C%3A%26%5C%3AP%3E-%5Cfrac%7B6%7D%7B5%7D%5C%3A%5C%5C%20%5C%3A%5Cmathrm%7BDecimal%3A%7D%26%5C%3AP%3E-1.2%5C%5C%20%5C%3A%5Cmathrm%7BInterval%5C%3ANotation%3A%7D%26%5C%3A%5Cleft%28-%5Cfrac%7B6%7D%7B5%7D%2C%5C%3A%5Cinfty%20%5C%3A%5Cright%29%5Cend%7Bbmatrix%7D)
The graph is also attached below.
All you have to do is multiply 12 times .20 when you get your answer you add that to 12 and that’s your answer