1=5-4 because you have to substitute x and y (x,y) or (5,1)
Answer:
116 cm²
Step-by-step explanation:
The area of a circle = πr² ← r is the radius
shaded area = external area - internal area
= π × 6.5² - π × 2.3²
= π( 42.25 - 5.29)
= π × 36.96 ≈ 116 cm²
The graph of a quadratic function does not cross the x-axis if the discriminant has negative value.
Answers:
C ) -25
D ) -7
Answer:
-87
Step-by-step explanation:
-(-7^2) + 6(-7) + 4
-49 -42 + 4
-87
Notice that we have common denominator 2, so we can split the denominator to express the function in the form
![f(x)=mx+b](https://tex.z-dn.net/?f=f%28x%29%3Dmx%2Bb)
where
![m](https://tex.z-dn.net/?f=m)
is the slope
![b](https://tex.z-dn.net/?f=b)
is the y-intercept
![f(x)= \frac{3x-1}{2}](https://tex.z-dn.net/?f=f%28x%29%3D%20%5Cfrac%7B3x-1%7D%7B2%7D%20)
![f(x)= \frac{3}{2} x- \frac{1}{2}](https://tex.z-dn.net/?f=f%28x%29%3D%20%5Cfrac%7B3%7D%7B2%7D%20x-%20%5Cfrac%7B1%7D%7B2%7D%20)
Look what we have here, a linear function! We know that the domain and range of linear functions is the real numbers.
We can conclude that:
the domain of the function is
all the real numbers
the range of the function
is all the real numbers
Now, to find the inverse of our function, we are going to replace
![f(x)](https://tex.z-dn.net/?f=f%28x%29)
with
![y](https://tex.z-dn.net/?f=y)
; then, we are going to interchange
![x](https://tex.z-dn.net/?f=x)
and
![y](https://tex.z-dn.net/?f=y)
and solve for
![y](https://tex.z-dn.net/?f=y)
:
![f(x)= \frac{3}{2} x- \frac{1}{2}](https://tex.z-dn.net/?f=f%28x%29%3D%20%5Cfrac%7B3%7D%7B2%7D%20x-%20%5Cfrac%7B1%7D%7B2%7D%20)
![y= \frac{3}{2} x- \frac{1}{2}](https://tex.z-dn.net/?f=y%3D%20%5Cfrac%7B3%7D%7B2%7D%20x-%20%5Cfrac%7B1%7D%7B2%7D%20)
![x=\frac{3}{2} y- \frac{1}{2}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B3%7D%7B2%7D%20y-%20%5Cfrac%7B1%7D%7B2%7D)
![\frac{3}{2} y=x+ \frac{1}{2}](https://tex.z-dn.net/?f=%20%5Cfrac%7B3%7D%7B2%7D%20y%3Dx%2B%20%5Cfrac%7B1%7D%7B2%7D%20)
![3y=2x+1](https://tex.z-dn.net/?f=3y%3D2x%2B1)
![y= \frac{2}{3} x+ \frac{1}{3}](https://tex.z-dn.net/?f=y%3D%20%5Cfrac%7B2%7D%7B3%7D%20x%2B%20%5Cfrac%7B1%7D%7B3%7D%20)
![f^{-1}(x)=\frac{2}{3} x+ \frac{1}{3}](https://tex.z-dn.net/?f=f%5E%7B-1%7D%28x%29%3D%5Cfrac%7B2%7D%7B3%7D%20x%2B%20%5Cfrac%7B1%7D%7B3%7D)
The inverse of our linear function, is another linear function, so we can conclude that:
the domain of the inverse function is
all the real numbers
the range of the inverse function
is all the real numbers