(90 ! and brainliest) answer these math problems

see explanation

Step-by-step explanation:

(2)

(f • g)(x) = f(x) × g(x), that is

(4x - 1)(x² - 5x + 3)

= 4x(x² - 5x + 3) - 1 (x² - 5x + 3) ← distribute parenthesis

= 4x³ - 20x² + 12x - x² + 5x - 3 ← collect like terms

= 4x³ - 21x² + 17x - 3

(3)

Factor both g(x) and f(x)

g(x) = 3x - 12 = 3(x - 4) ← common factor of 3

f(x) = x² + x - 20 = (x + 5)(x - 4), thus

=

Cancel the factor (x - 4) on the numerator and denominator

=

The denominator cannot be zero as this would make rational function undefined, thus

domain is x ∈ R , x ≠ - 5

(4)

To evaluate (g ￮ h)(7), evaluate h(7) then use this result to evaluate g(x)

h(7) = 7 - 2 = 5, then

g(5) = 5² + 3 = 25 + 3 = 28

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240