Answer:
see below the first three problems
Step-by-step explanation:
f(g(-2))
First, find g(-2) using function g(x). Then use that value as input for function f(x).
g(x) = -2x + 1
g(-2) = -2(-2) + 1
g(-2) = 5
f(x) = 5x
f(5) = 5(5)
f(5) = 25
f(g(-2)) = 25
g(h(3))
First, find h(3) using function h(x). Then use that value as input for function g(x).
h(x) = x^2 + 6x + 8
h(3) = 3^2 + 6(3) + 8 = 9 + 18 + 8
h(3) = 35
g(x) = -2x + 1
g(35) = -2(35) + 1 = -70 + 1
g(35) = -69
g(h(3)) = -69
f(g(3a))
First, find g(3a) using function g(x). Then use that value as input for function f(x).
g(x) = -2x + 1
g(3a) = -2(3a) + 1
g(3a) = -6a + 1
f(x) = 5x
f(-6a + 1) = 5(-6a + 1)
f(-6a + 1) = -30a + 5
f(g(3a)) = -30a + 5
The blank answers are 340 and 0.34
Answer: t = 6 s
Step-by-step explanation:
When Rose hit the water, the height of the jump is 0, so: h(t) = 0.
Resolving it, we have:
-16t² + 16t + 480 = 0
To simplify the second degree equation, divided it by 16:
-t² + t + 30 = 0
Now, solve the equation using Bhaskara:
Δ = 1² - 4. (-1) . 30
Δ = 1 + 120
Δ = 121
t = 
t₁ =
= - 5
t₂ =
= 6
Since time can be negative, it took t = 6s for Rose to hit the water.
x = -2
function value at x = -2 is intersection of the x value and graph
which is, 3
Hope it is clear:)
Equation: x² - (x - y)² * y
Substitute values for x and y into equation.
-> (-5)² - ( (-5) - (-8) )² * (-8)
-> 25 - (-5 + 8)² * (-8)
-> 25 - (3)² * (-8)
-> 25 - 9 * (-8)
-> 25 - (-72)
-> 25 + 72
-> 97