Select the correct answer from each drop-down menu.
1 answer:
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Answer:
B. is greater than
Step-by-step explanation:
As the graph of function f(x) is a parabola, so that the equation of function f(x) is: f(x) =
As it can be seen in thee figure, the graph of function f(x) cross points (0;8) ;(-2; 0) and (4;0)
=> f(0) = 8; f(-2) = 0; f(4) = 0
We have:
- f(x=0) = a x 0 + b x 0 + c = 8 => c = 8
- f (x=-2) =
= 4a -2b + 8 = 0
- f (x=4) =
= 16a + 4b + 8 = 0
We have:
+) 4a -2b + 8 = 0 => 2 x (4a -2b + 8) = 8a - 4b + 16 = 0 (1)
+) 16a + 4b + 8 = 0 (2)
We take (2) minus (1)
=> (16a + 4b + 8) - (8a - 4b + 16) = 0
=> 8a - 8 = 0 => a = 1
Replace a = 1 into (1)
=> 8 x 1 - 4b + 16 = 0 => b = 6
So that:
f (2) = 2^2 + 6 x 2 + 8 = 24
g (2) = 3 -2 + 2 = 3
<em>=> f(2) is greater than g(2)</em>
Answer:
8 and 10
Step-by-step explanation:
Given
+
=
← combine the fractions on the left side
=
=
( cross- multiply )
9(x² + 2x) = 40(2x + 2) ← distribute both sides
9x² + 18x = 80x + 80 ( subtract 80x + 80 from both sides )
9x² - 62x - 80 = 0
Consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term.
product = 9 × - 80 = - 720 and sum = - 62
The factors are - 72 and + 10
Use these factors to split the x- term
9x² - 72x + 10x - 80 = 0 ( factor the first/second and third/fourth terms )
9x(x - 8) + 10(x - 8) = 0 ← factor out (x - 8) from each term
(x - 8)(9x + 10) = 0
Equate each factor to zero and solve for x
x - 8 = 0 ⇒ x = 8
9x + 10 = 0 ⇒ 9x = - 10 ⇒ x = -
x is an integer , then x = 8 and x + 2 = 8 + 2 = 10
The integers are 8 and 10