Answer:
C. R = 17.9 degrees
Step-by-step explanation:
We have a rectangle triangle with the adjacent side and the opposite side (neither of which are the hypotenuse).
The relation between those elements is the tangent:
![tan(angle) = \frac{Opposite side}{Adjacent side}](https://tex.z-dn.net/?f=tan%28angle%29%20%3D%20%5Cfrac%7BOpposite%20side%7D%7BAdjacent%20side%7D)
So, to isolate the angle, we modify the formula as such:
![angle = arctan(\frac{Opposite side}{Adjacent side}) = arctan(\frac{10}{31}) = arctan(0.3225) = 17.87](https://tex.z-dn.net/?f=angle%20%3D%20arctan%28%5Cfrac%7BOpposite%20side%7D%7BAdjacent%20side%7D%29%20%3D%20arctan%28%5Cfrac%7B10%7D%7B31%7D%29%20%3D%20arctan%280.3225%29%20%3D%2017.87)
If we round 17.87 degrees to the tenth... we get 17.9 degrees.
Answer:
![\frac{125x^3 - 8}{5x - 2} = 25x^2 + 10x +4](https://tex.z-dn.net/?f=%5Cfrac%7B125x%5E3%20-%208%7D%7B5x%20-%202%7D%20%3D%2025x%5E2%20%2B%2010x%20%2B4)
Step-by-step explanation:
Given
![Dividend = 125x^3 - 8](https://tex.z-dn.net/?f=Dividend%20%3D%20125x%5E3%20-%208)
![Divisor = 5x - 2](https://tex.z-dn.net/?f=Divisor%20%3D%205x%20-%202)
Required
Determine the quotient
See attachment for complete process.
First, divide 125x^3 by 5x
![\frac{125x^3}{5x} =25x^2](https://tex.z-dn.net/?f=%5Cfrac%7B125x%5E3%7D%7B5x%7D%20%3D25x%5E2)
Write
at the top
Multiply
by ![25x^2](https://tex.z-dn.net/?f=25x%5E2)
![= 125x^3 - 50x^2](https://tex.z-dn.net/?f=%3D%20125x%5E3%20-%2050x%5E2)
Subtract from 125x^3 - 8
i.e.
![125x^3 - 8 - (125x^3 - 50x^2) = 50x^2 - 8](https://tex.z-dn.net/?f=125x%5E3%20-%208%20-%20%28125x%5E3%20-%2050x%5E2%29%20%3D%2050x%5E2%20-%208)
Step 2:
Divide 50x^2 by 5x
![\frac{50x^2}{5x} = 10x](https://tex.z-dn.net/?f=%5Cfrac%7B50x%5E2%7D%7B5x%7D%20%3D%2010x)
Write
at the top
Multiply
by ![10x](https://tex.z-dn.net/?f=10x)
![= 50x^2 - 20x](https://tex.z-dn.net/?f=%3D%2050x%5E2%20-%2020x)
Subtract from 50x^2 - 8
i.e.
![50x^2 - 8 - (50x^2 - 20x) = 20x - 8](https://tex.z-dn.net/?f=50x%5E2%20-%208%20-%20%2850x%5E2%20-%2020x%29%20%3D%2020x%20-%208)
Step 3:
Divide 20x by 5x
![\frac{20x}{5x} = 4](https://tex.z-dn.net/?f=%5Cfrac%7B20x%7D%7B5x%7D%20%3D%204)
Write
at the top
Multiply
by ![4](https://tex.z-dn.net/?f=4)
![= 20x - 8](https://tex.z-dn.net/?f=%3D%2020x%20-%208)
Subtract from 20x - 8
i.e.
![20x - 8 - (20x - 8) = 0](https://tex.z-dn.net/?f=20x%20-%208%20-%20%2820x%20-%208%29%20%3D%200)
Hence:
![\frac{125x^3 - 8}{5x - 2} = 25x^2 + 10x +4](https://tex.z-dn.net/?f=%5Cfrac%7B125x%5E3%20-%208%7D%7B5x%20-%202%7D%20%3D%2025x%5E2%20%2B%2010x%20%2B4)
Answer:
(2, 2) states x=2 and y=2
Considering the inequality:
![y\leq 4x-6](https://tex.z-dn.net/?f=y%5Cleq%204x-6)
Is y less than or equal to 2 when x = 2?
![2\leq 4(2)-6\\2\leq 8-6\\2\leq 2\\](https://tex.z-dn.net/?f=2%5Cleq%204%282%29-6%5C%5C2%5Cleq%208-6%5C%5C2%5Cleq%202%5C%5C)
Yes, (2, 2) is a solution for the inequality.
Step-by-step explanation:
Here, we'll need to multiply these two values together. I'll use the expansion formula, which goes as follows:
![(a+b)(c+d)](https://tex.z-dn.net/?f=%28a%2Bb%29%28c%2Bd%29)
![ac + ad + bc + bd](https://tex.z-dn.net/?f=ac%20%2B%20ad%20%2B%20bc%20%2B%20bd)
Lets apply this to the following equation:
![(x+3) (x+7)](https://tex.z-dn.net/?f=%28x%2B3%29%20%28x%2B7%29)
![(x*x) + (x * 7) + (3 * x) + (3 * 7)](https://tex.z-dn.net/?f=%28x%2Ax%29%20%2B%20%28x%20%2A%207%29%20%2B%20%283%20%2A%20x%29%20%2B%20%283%20%2A%207%29)
![(x^2) + (7x) + (3x) + (21)](https://tex.z-dn.net/?f=%28x%5E2%29%20%2B%20%287x%29%20%2B%20%283x%29%20%2B%20%2821%29)
- Remove parenthesis and add.
![x^2+10x+21](https://tex.z-dn.net/?f=x%5E2%2B10x%2B21)
Answer:
x^2+10x+21
Answer:
Step-by-step explanation:
ans is c) f(x) is a polynominal function. The degree is 5 and the leading coefficient is -7.
x -> ∞, f(x) -> ∞; x -> -∞, f(x) -> -∞
the only ans that follows the above is a) f(x)=7x^9-3x^2-6
correct statments are: c) (1, 6.08) and (3, 0.75) are local extrema for the function and d) (-2, -9.67) is the global minimum for the function.