Answer:
D
Step-by-step explanation:
The equation of a parabola in vertex form is
f(x) = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
To obtain this form using the method of completing the square.
Given
f(x) = 3x² - 24x + 10
We require the coefficient of the x² term to be 1 , thus factor out 3
3(x² - 8x) + 10
To complete the square
add/subtract ( half the coefficient of the x- term )² to x² - 8x
= 3(x² + 2(- 4)x + 16 - 16) + 10
= 3(x - 4)² + (3 × - 16) + 10
= 3(x - 4)² - 48 + 10
= 3(x - 4)² - 38, thus
f(x) = 3(x - 4)² - 38 ← in vertex form
Answer:
-27
Step-by-step explanation:
substitute x for 5
multiply -5 and 5
subtract 2 from -25
Answer:
1/2
Step-by-step explanation:
First square area = 4cm^2, thus the side length is 2cm
Second square area = 16cm^2, thus the side length is 4cm
This gives a ratio of 2/4, simplifying yields 1/2
<span>3780
If you consider every letter in the word "tennessee" to be unique there is 9!, or 362880 different ways to arrange the letters. So let's use that as a starting point.
Now there's 4 e's, which we really don't care how they're arranged. So divide by 4!, or 24. Giving us 362880/24 = 15120 different ways to arrange the letters.
There's also 2 n's. So divide by 2!, giving us 15120/2 = 7560 different ways.
Don't forget the s's either. So another division by 2!, giving 7560/2 = 3780 different ways.
And there's no more duplicate letters, so the final figure is 3780 different ways to arrange the letters in the word "tennessee".</span>
