Answer:
32
Step-by-step explanation:
Step 1: Define
f(x) = 3x² - 5x - 4
g(x) = -4x - 12
Step 2: Find f(g(x))
f(g(x)) = 3(-4x - 12)² - 5(-4x - 12) - 4
f(g(x)) = 3(16x² + 96x + 144) + 20x + 60 + 4
f(g(x)) = 48x² + 288x + 432 + 20x + 64
f(g(x)) = 48x² + 308x + 496
Step 3: Find f(g(-4))
f(g(-4)) = 48(-4)² + 308(-4) + 496
f(g(-4)) = 48(16) - 1232 + 496
f(g(-4)) = 768 - 736
f(g(-4)) = 32
Answer:
20 units²
Step-by-step explanation:
The x-intercepts are symmetrically located around the x-coordinate of the vertex, so are at
1.5 ± 5/2 = {-1, 4}
Using one of these we can find the unknown parameter "a" in the parabola's equation (in vertex form) ...
0 = a(4 -1.5)² +12.5
0 = 6.25a +12.5 . . . . . simplify
0 = a +2 . . . . . . . . . . . divide by 6.25
-2 = a
Then the standard-form equation of the parabola is ...
y = -2(x -1.5)² +12.5 = -2(x² -3x +2.25) +12.5
y = -2x² +6x +8
This tells us the y-intercept is 8. Then the relevant triangle has a base of 5 units and a height of 8. Its area is given by the formula ...
A = (1/2)bh = (1/2)(5)(8) = 20 . . . . units²
Answer:
Set up the equation. On a piece of paper, write the number being divided on the right, under the division symbol, and the number doing the division to the left on the outside. ...
Divide the first digit. ...
Divide the first two digits. ...
Enter the first digit of the quotient.
hope this helps :)
Answer:
5m-n-4p
4a^2+6x-3
Step-by-step explanation:
3m-4n +7p
-5m +9n -6p
+7m -6n -5p
----------------------
Combine like terms
3m-4n +7p
-5m +9n -6p
+7m -6n -5p
----------------------
(3-5+7)m +(-4+9-6)n +(7-6-5)p
5m-n-4p
a^2 -3x +1
a^2 +9x -6
2a^2 +0x +2
----------------------
Combine like terms
a^2 -3x +1
a^2 +9x -6
2a^2 +0x +2
----------------------
(1+1+2)a^2 +(-3+9+0)x +(1-6+2)
4a^2+6x-3
