C. The Triangle Inequality Theorem States that any two sides of a triangle must be greater than the third side. It cannot be A because 35+40= 75, which is not greater than 75. It cannot be B because 40+30= 70, which is not greater than 75. It cannot be D because 35+40= 75, which is not greater than 80. It is C because 40+30= 70, which is greater than 65.
-x/4-6>-8
Multiply both sides by 4
-x-24>-32
Move the constant to the right
-x>-32+24
-x>-8
Change the signs
x<8
Answer:
The answer is option A.
<h3>Power Property and Product </h3><h3>Property</h3>
Hope this helps you
![\qquad \qquad\huge \underline{\boxed{\sf Answer}}](https://tex.z-dn.net/?f=%5Cqquad%20%5Cqquad%5Chuge%20%5Cunderline%7B%5Cboxed%7B%5Csf%20Answer%7D%7D)
Here's the solution ~
Let's find the measure of hypotenuse first, by using Pythagoras theorem ;
![\qquad \sf \dashrightarrow \: h {}^{2} = {8}^{2} + {6}^{2}](https://tex.z-dn.net/?f=%5Cqquad%20%5Csf%20%20%5Cdashrightarrow%20%5C%3A%20h%20%7B%7D%5E%7B2%7D%20%20%3D%20%20%7B8%7D%5E%7B2%7D%20%20%2B%20%20%7B6%7D%5E%7B2%7D%20)
![\qquad \sf \dashrightarrow \: h {}^{2} = {36}^{} + {64}^{}](https://tex.z-dn.net/?f=%5Cqquad%20%5Csf%20%20%5Cdashrightarrow%20%5C%3A%20h%20%7B%7D%5E%7B2%7D%20%20%3D%20%20%7B36%7D%5E%7B%7D%20%20%2B%20%20%7B64%7D%5E%7B%7D%20)
![\qquad \sf \dashrightarrow \: h {}^{2} = 100](https://tex.z-dn.net/?f=%5Cqquad%20%5Csf%20%20%5Cdashrightarrow%20%5C%3A%20h%20%7B%7D%5E%7B2%7D%20%20%3D%20100)
![\qquad \sf \dashrightarrow \: h {}^{} = \sqrt{100}](https://tex.z-dn.net/?f=%5Cqquad%20%5Csf%20%20%5Cdashrightarrow%20%5C%3A%20h%20%7B%7D%5E%7B%7D%20%20%3D%20%20%5Csqrt%7B100%7D%20)
![\qquad \sf \dashrightarrow \: h {}^{} = {10}](https://tex.z-dn.net/?f=%5Cqquad%20%5Csf%20%20%5Cdashrightarrow%20%5C%3A%20h%20%7B%7D%5E%7B%7D%20%20%3D%20%20%7B10%7D%20)
Now, let's find the asked values ~
![\qquad \sf \dashrightarrow \: \sin(x) = \dfrac{opposite \: side}{hypotenuse}](https://tex.z-dn.net/?f=%5Cqquad%20%5Csf%20%20%5Cdashrightarrow%20%5C%3A%20%20%5Csin%28x%29%20%3D%20%20%5Cdfrac%7Bopposite%20%5C%3A%20side%7D%7Bhypotenuse%7D%20%20)
![\qquad \sf \dashrightarrow \: \sin(x) = \dfrac{6}{10}](https://tex.z-dn.net/?f=%5Cqquad%20%5Csf%20%20%5Cdashrightarrow%20%5C%3A%20%20%5Csin%28x%29%20%3D%20%20%5Cdfrac%7B6%7D%7B10%7D%20%20)
![\qquad \sf \dashrightarrow \: \sin(x) = \dfrac{3}{5} \: or \: 0.6 \: units](https://tex.z-dn.net/?f=%5Cqquad%20%5Csf%20%20%5Cdashrightarrow%20%5C%3A%20%20%5Csin%28x%29%20%3D%20%20%5Cdfrac%7B3%7D%7B5%7D%20%20%20%5C%3A%20or%20%5C%3A%200.6%20%5C%3A%20units)
For Cos y :
![\qquad \sf \dashrightarrow \: \cos(y) = \dfrac{adjcant \: side}{hypotenuse}](https://tex.z-dn.net/?f=%5Cqquad%20%5Csf%20%20%5Cdashrightarrow%20%5C%3A%20%20%5Ccos%28y%29%20%3D%20%20%5Cdfrac%7Badjcant%20%5C%3A%20side%7D%7Bhypotenuse%7D%20%20)
![\qquad \sf \dashrightarrow \: \cos(y) = \dfrac{6}{10}](https://tex.z-dn.net/?f=%5Cqquad%20%5Csf%20%20%5Cdashrightarrow%20%5C%3A%20%20%5Ccos%28y%29%20%20%20%3D%20%5Cdfrac%7B6%7D%7B10%7D%20)
![\qquad \sf \dashrightarrow \: \cos(y) = \dfrac{3}{5} \: or \: 0.6 \: units](https://tex.z-dn.net/?f=%5Cqquad%20%5Csf%20%20%5Cdashrightarrow%20%5C%3A%20%20%5Ccos%28y%29%20%20%20%3D%20%5Cdfrac%7B3%7D%7B5%7D%20%20%5C%3A%20or%20%5C%3A%200.6%20%5C%3A%20units)
As we can see that both sin x and Cos y have equal values, therefore The required relationships is equality.
I.e Sin x = Cos y
Hope it helps ~
Answer:
4 and -7
Step-by-step explanation:
a coefficient is a number that is being multiplied with a variable (ex:5a) in this case the coefficients are 4 and -7