Answer:
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Step-by-step explanation:
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For this case we have the following functions:
h (x) = 2x - 5
t (x) = 6x + 4
Part A: (h + t) (x)
(h + t) (x) = h (x) + t (x)
(h + t) (x) = (2x - 5) + (6x + 4)
(h + t) (x) = 8x - 1
Part B: (h ⋅ t) (x)
(h ⋅ t) (x) = h (x) * t (x)
(h ⋅ t) (x) = (2x - 5) * (6x + 4)
(h ⋅ t) (x) = 12x ^ 2 + 8x - 30x - 20
(h ⋅ t) (x) = 12x ^ 2 - 22x - 20
Part C: h [t (x)]
h [t (x)] = 2 (6x + 4) - 5
h [t (x)] = 12x + 8 - 5
h [t (x)] = 12x + 3
<span>
4x^2-8x-12 =
(x -3) * (x +1)
4x^2-24x+32
</span><span>(x -4) * (x -2)
</span>Factored Form
(x -3) * (x +1) * <span>(x -4) * (x -2) = 0
x = 3
x = -1
x = 4
x = 2
All four roots are real numbers and so the graph crosses the x-axis four times. The graph of the equation would resemble a "W".
</span>
Solution is in the picture