Answer:
9
Step-by-step explanation:
f(3) = 2(3) + 3
= 9
Answer:
, x>=0
Step-by-step explanation:
![f(x)=(x+6)^2](https://tex.z-dn.net/?f=f%28x%29%3D%28x%2B6%29%5E2)
To find the inverse function , replace f(x) by y
![y=(x+6)^2](https://tex.z-dn.net/?f=y%3D%28x%2B6%29%5E2)
Replace x with y and y with x
![x=(y+6)^2](https://tex.z-dn.net/?f=x%3D%28y%2B6%29%5E2)
Solve the equation for y
take square root on both sides
![+\sqrt{x} =y+6](https://tex.z-dn.net/?f=%2B%5Csqrt%7Bx%7D%20%3Dy%2B6)
Now subtract 6 from both sides
![+\sqrt{x}-6=y](https://tex.z-dn.net/?f=%2B%5Csqrt%7Bx%7D-6%3Dy)
replace y with g(x)
![g(x)=\sqrt{x}-6](https://tex.z-dn.net/?f=g%28x%29%3D%5Csqrt%7Bx%7D-6)
There will be excactly 400 fiction books. The ratio of fiction to all is 4 to 9, or 4 to 900.
We will have to use the formula for the area of a trapezoid on this problem, which is (
and
are the bases of the trapezoid and
is the height):
![\dfrac{b_1 + b_2}{2} \cdot h](https://tex.z-dn.net/?f=%20%5Cdfrac%7Bb_1%20%2B%20b_2%7D%7B2%7D%20%5Ccdot%20h%20)
All we need to do is substitute the information we are given into our formula:
![\dfrac{21 + b_2}{2} \cdot 4 = 68](https://tex.z-dn.net/?f=%20%5Cdfrac%7B21%20%2B%20b_2%7D%7B2%7D%20%5Ccdot%204%20%3D%2068%20)
Now, let's just simplify the equation:
![\dfrac{21 + b_2}{2} \cdot 4 = 68](https://tex.z-dn.net/?f=%20%5Cdfrac%7B21%20%2B%20b_2%7D%7B2%7D%20%5Ccdot%204%20%3D%2068%20)
![\dfrac{21 + b_2}{2} = 17](https://tex.z-dn.net/?f=%20%5Cdfrac%7B21%20%2B%20b_2%7D%7B2%7D%20%3D%2017%20)
![21 + b_2 = 34](https://tex.z-dn.net/?f=%2021%20%2B%20b_2%20%3D%2034%20)
![b_2 = 13](https://tex.z-dn.net/?f=%20b_2%20%3D%2013%20)
The missing base has a length of 13 units.