Answer:
The vertex is (0, -5) and the axis of symmetry is x = 0.
Step-by-step explanation:
In order to find the axis of symmetry, we look for the x value of the vertex. We can find this using the equation -b/2a, in which a is equal to the coefficient of the x^2 term and b is the coefficient of the x term.
x = -b/2a
x = 0/2(1)
x = 0/2
x = 0
So the axis of symmetry is 0 as is the x value of the vertex. Now we can find the y value by plugging in the x value into the equation.
f(x) = x^2 - 5
f(x) = 0^2 - 5
f(x) = 0 -5
f(x) = -5
This gives us a vertex of (0,-5)
Answer:
The inverse of the function is
.
Step-by-step explanation:
The function provided is:

Let
.
Then the value of <em>x</em> is:

For the inverse of the function,
.
⇒ 
Compute the value of
as follows:
![f[f^{-1}(x)]=f[\frac{x-5}{3}]](https://tex.z-dn.net/?f=f%5Bf%5E%7B-1%7D%28x%29%5D%3Df%5B%5Cfrac%7Bx-5%7D%7B3%7D%5D)
![=3[\frac{x-5}{3}]+5\\\\=x-5+5\\\\=x](https://tex.z-dn.net/?f=%3D3%5B%5Cfrac%7Bx-5%7D%7B3%7D%5D%2B5%5C%5C%5C%5C%3Dx-5%2B5%5C%5C%5C%5C%3Dx)
Hence proved that
.
Compute the value of
as follows:
![f^{-1}[f(x)]=f^{-1}[3x+5]](https://tex.z-dn.net/?f=f%5E%7B-1%7D%5Bf%28x%29%5D%3Df%5E%7B-1%7D%5B3x%2B5%5D)

Hence proved that
.
The shorter side is 40 in and the longer side is 64 in
Let's take the difference between the old and new (70 - 60) to get 10 and then divide this by the old (70) amount...10/70 = .142857 convert to a percent by moving the decimal 2 spaces to the right... 14.29 %
Answer:
The correct options are 1, 2 and 4.
Step-by-step explanation:
The given triangle is an equilateral triangle. All the sides of an equilateral triangle are same. All interior angles are equal with measure 60 degree.
The distance from the center of an equilateral triangle to the midpoint of a side is known as apothem. In the given figure letter a represents the apothem.
Point D is the midpoint of BC,

Use Pythagorean theorem in triangle COD. So, option 1 is correct.





The distance can not be negative, so the length of the apothem is approximately 2.5 cm. Option 4 is correct.
The line OC bisects the angle C.



Therefore option 2 is correct.
The perimeter of an equality triangle is

Option 3 is incorrect.

Option 5 is incorrect.
Therefore options 1, 2 and 4 are correct.