Answer:
B. 3/2
Step-by-step explanation:
If f(x) and
are inverse, that means that if we switch the x and y for f(x) and solve for y, we will get the inverse function.
Knowing that f(x) = 2x + 5, let's write this as y = 2x + 5 and switch the x and y:
x = 2y + 5
Now, solve for y:
x = 2y + 5
x - 5 = 2y
y = (x - 5)/2
That's the
function: ![f^{-1}(x)=\frac{x-5}{2}](https://tex.z-dn.net/?f=f%5E%7B-1%7D%28x%29%3D%5Cfrac%7Bx-5%7D%7B2%7D)
Plug in 8 for x:
![f^{-1}(x)=\frac{x-5}{2}](https://tex.z-dn.net/?f=f%5E%7B-1%7D%28x%29%3D%5Cfrac%7Bx-5%7D%7B2%7D)
![f^{-1}(8)=\frac{8-5}{2}=3/2](https://tex.z-dn.net/?f=f%5E%7B-1%7D%288%29%3D%5Cfrac%7B8-5%7D%7B2%7D%3D3%2F2)
The answer is thus B.
<em>~ an aesthetics lover</em>
Answer:
3is the scale factor and it is similar
Step-by-step explanation:
Answer:
x = 10
Step-by-step explanation:
First look at the big overall triangle.
It has a right angle and another angle of 44; therefore the missing angle is (since the sum of angles inside a triangle is 180)
180 - 90 - 44 = missing angle
missing angle (top) = 46; now the angle of a straight line is 180 and they give you 56° which has a supplementary angle of 180 - 56 = 124°.
Now we know that the triangle that include the x has angles 46° (missing top angle), and supplementary angle of 124°. Therefore
x = 180 - 46 - 124
x = 10
To find the volume of a triangular pyramid, the formula is:
![V=\frac{1}{3}(Area\text{ }of\text{ }thebase)(height)](https://tex.z-dn.net/?f=V%3D%5Cfrac%7B1%7D%7B3%7D%28Area%5Ctext%7B%20%7Dof%5Ctext%7B%20%7Dthebase%29%28height%29)
So we start by finding the area of the base, which is in the shape of a right triangle in this case.
The area of a right triangle is equal to 1/2 x base x height.
![\begin{gathered} A=\frac{1}{2}bh \\ \\ A=\frac{1}{2}(5)(6) \\ \\ A=15\text{ square feet} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20A%3D%5Cfrac%7B1%7D%7B2%7Dbh%20%5C%5C%20%20%5C%5C%20A%3D%5Cfrac%7B1%7D%7B2%7D%285%29%286%29%20%5C%5C%20%20%5C%5C%20A%3D15%5Ctext%7B%20square%20feet%7D%20%5Cend%7Bgathered%7D)
We use this area to find the volume.
![\begin{gathered} V=\frac{1}{3}Ah \\ \\ V=\frac{1}{3}(15)(6) \\ \\ V=30\text{ cubic feet} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20V%3D%5Cfrac%7B1%7D%7B3%7DAh%20%5C%5C%20%20%5C%5C%20V%3D%5Cfrac%7B1%7D%7B3%7D%2815%29%286%29%20%5C%5C%20%20%5C%5C%20V%3D30%5Ctext%7B%20cubic%20feet%7D%20%5Cend%7Bgathered%7D)
The volume of the triangular pyramid is 30 cubic feet.
Answer:
D 12,000
Step-by-step explanation:
There is 1000 meters in every km