2400 x 0.03 = $72
500 x 0.03 = $15
Total commission = $87
Answer:
11.54°
Step-by-step explanation:
This is a right triangle with the hypotenuse of 60 and the opposite side of 12
We can use sin theta
sin theta = opp/ hypotenuse
sin theta = 12/60
Taking the inverse of each side
sin ^-1 sin theta = sin^-1 (12/60)
theta = 11.53695903
to the nearest hundredth
theta = 11.54
Answer:
![2x(x^2-3)(x^2+9)](https://tex.z-dn.net/?f=2x%28x%5E2-3%29%28x%5E2%2B9%29)
Step-by-step explanation:
Given polynomial:
![2x^5+12x^3-54x](https://tex.z-dn.net/?f=2x%5E5%2B12x%5E3-54x)
Factor out the common term
:
![\implies 2x(x^4+6x^2-27)](https://tex.z-dn.net/?f=%5Cimplies%202x%28x%5E4%2B6x%5E2-27%29)
To factor the trinomial
:
![\textsf{Let }u=x^2 \implies u^2+6u-27](https://tex.z-dn.net/?f=%5Ctextsf%7BLet%20%7Du%3Dx%5E2%20%5Cimplies%20u%5E2%2B6u-27)
Factor the quadratic by finding two numbers that multiply to -27 and sum to 6: 9 and -3
Rewrite the middle term as the sum of these two numbers:
![\implies u^2+9u-3u-27](https://tex.z-dn.net/?f=%5Cimplies%20u%5E2%2B9u-3u-27)
Factorize the first two terms and the last two terms separately:
![\implies u(u+9)-3(u+9)](https://tex.z-dn.net/?f=%5Cimplies%20u%28u%2B9%29-3%28u%2B9%29)
Factor out the common term (u + 9):
![\implies (u-3)(u+9)](https://tex.z-dn.net/?f=%5Cimplies%20%28u-3%29%28u%2B9%29)
Substitute back
:
![\implies (x^2-3)(x^2+9)](https://tex.z-dn.net/?f=%5Cimplies%20%28x%5E2-3%29%28x%5E2%2B9%29)
Therefore, the factored form of the given polynomial is:
![\implies 2x(x^2-3)(x^2+9)](https://tex.z-dn.net/?f=%5Cimplies%202x%28x%5E2-3%29%28x%5E2%2B9%29)
Answer:
7
Step-by-step explanation:
Well, the best way to solve this would involve the Pythagorean theorem.
First, take the length of the hypotenuse (the string in this case) and square it. Do the same to the side length we are given (the kites height above the ground).
We then subtract the squared height from the squared hypotenuse. We should be left with 1,781m.
All we have to do now is find the square root of 1,781m.
Your answer for b is 42.20189569m.