Answer:
-25
Step-by-step explanation:
g(f(3))= g(-5)
=4(-5)-5
= -20-5
=-25
The perimeter of a rectangle:P = 2 L + 2 W
L ( length ) = 5.50 mW ( width ) = 12.0 mP = 2 * 5.50 + 2 * 12.0 = 11 + 24 = 35 mThe area of a rectangle:A = L x W
A = 5.50 * 12.0 = 66 m²Answer: 35, 66
Answer:
![y = \frac{32}{3}](https://tex.z-dn.net/?f=y%20%3D%20%5Cfrac%7B32%7D%7B3%7D)
Step-by-step explanation:
Firstly, move over the negative 3/4 fraction (don't forget to swap the operation i.e subtract to add):
![\frac{y}{8} = \frac{7}{12} + \frac{3}{4}](https://tex.z-dn.net/?f=%5Cfrac%7By%7D%7B8%7D%20%3D%20%5Cfrac%7B7%7D%7B12%7D%20%20%2B%20%5Cfrac%7B3%7D%7B4%7D)
Now, to add the two fractions, simply multiply the numerator and denominator by 3:
![\frac{3*3}{4*3} = \frac{9}{12}](https://tex.z-dn.net/?f=%5Cfrac%7B3%2A3%7D%7B4%2A3%7D%20%3D%20%5Cfrac%7B9%7D%7B12%7D)
Now add this to the other fraction:
![\frac{9}{12} + \frac{7}{12} = \frac{16}{12}](https://tex.z-dn.net/?f=%5Cfrac%7B9%7D%7B12%7D%20%2B%20%5Cfrac%7B7%7D%7B12%7D%20%3D%20%5Cfrac%7B16%7D%7B12%7D)
This can be simplified down by dividing both the numerator and denominator by 4:
![\frac{4}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B4%7D%7B3%7D)
Which now simplifies the original equation to:
![\frac{y}{8} = \frac{4}{3}](https://tex.z-dn.net/?f=%5Cfrac%7By%7D%7B8%7D%20%20%3D%20%5Cfrac%7B4%7D%7B3%7D)
Remove the y out of the fraction:
![\frac{1}{8}y = \frac{4}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B8%7Dy%20%3D%20%5Cfrac%7B4%7D%7B3%7D)
Now multiply both sides by 8:
![(\frac{1}{8}y) * 8 = (\frac{4}{3}) * 8](https://tex.z-dn.net/?f=%28%5Cfrac%7B1%7D%7B8%7Dy%29%20%2A%208%20%3D%20%28%5Cfrac%7B4%7D%7B3%7D%29%20%2A%208)
![y = \frac{4*8}{3}](https://tex.z-dn.net/?f=y%20%3D%20%5Cfrac%7B4%2A8%7D%7B3%7D)
![y = \frac{32}{3}](https://tex.z-dn.net/?f=y%20%3D%20%5Cfrac%7B32%7D%7B3%7D)
Hope this helps!
Answer:
D
Step-by-step explanation:
So we want to find<em> θ. </em>We are already given the hypotenuse and the side length opposite to <em>θ. </em>Therefore, we can use the trig function sine to find <em>θ. </em>
Recall that:
![\sin(\theta)=opp/hyp](https://tex.z-dn.net/?f=%5Csin%28%5Ctheta%29%3Dopp%2Fhyp)
Plug in 10.2 for the opposite side and 15 for the hypotenuse:
![\sin(\theta)=10.2/15](https://tex.z-dn.net/?f=%5Csin%28%5Ctheta%29%3D10.2%2F15)
Solve for <em>θ. </em>Use a calculator:
![\theta=\sin^{-1}(10.2/15)\\\theta\approx42.8436\textdegree](https://tex.z-dn.net/?f=%5Ctheta%3D%5Csin%5E%7B-1%7D%2810.2%2F15%29%5C%5C%5Ctheta%5Capprox42.8436%5Ctextdegree)
The answer is D.
Replace all the variables with their values. In this case, we know the value of the variable p.
Now the expressions p + 5 becomes 2 + 5.
2 + 5 = 7
So, C. 7 is the answer.