If g left parenthesis x right parenthesis equals 36 x squared minus 36 and h left parenthesis x right parenthesis equals 65 x,
then solve g left parenthesis x right parenthesis greater than h left parenthesis x right parenthesis .
1 answer:
Given
g(x) = 36x² -36
h(x) = 65x
Find
x such that g(x) > h(x)
Solution
We can start by substituting the given information into the required relation.
36x² -36 > 65x
Subtracting the right side and factoring gives
36x² -65x -36 > 0
(9x +4)(4x -9) > 0
The product of these factors will be greater than zero when both factors are negative or both are positive. They change sign at x = -4/9 and x = 9/4. Hence, the solution is
x < -4/9 or 9/4 < x
g(x) = 36x² -36
h(x) = 65x
Find
x such that g(x) > h(x)
Solution
We can start by substituting the given information into the required relation.
36x² -36 > 65x
Subtracting the right side and factoring gives
36x² -65x -36 > 0
(9x +4)(4x -9) > 0
The product of these factors will be greater than zero when both factors are negative or both are positive. They change sign at x = -4/9 and x = 9/4. Hence, the solution is
x < -4/9 or 9/4 < x
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Answer:
AE = 4
Step-by-step explanation:
Use the formula
AE*EC = DE*EB
Since we don't know AE or EC, let AE = x and then EC will = 16 - x. The formula then becomes
x(16 - x) = 8(6)
Getting everything on one side and setting it equal to 0 will allow us to factor for x:
Factoring that gives you that
x = 4 and x = 12. That means that one of those sements has a length of 4 and the other has a length of 12. AE is shorter so it's 4 and EC = 12