Question

directions: show all your work to receive full credit. make sure to answer all parts of the question.

1. the graph below models the height of sam’s kite over a period of time. state the time intervals over which the height of the kite is increasing
2. express (4x - 5)(x + 6) as a trinomial in standard form.

Explanation:

Step1: Simplify the monomial product

$\frac{3x^3 \cdot 2x^2}{6x^3} = \frac{6x^{3+2}}{6x^3} = \frac{6x^5}{6x^3}$

Step2: Cancel common factors

$\frac{6x^5}{6x^3} = x^{5-3}$

Step3: State increasing intervals from graph

Observe upward-trending segments on the time axis.

Step4: Expand the binomial product

$(4x-5)(x+6) = 4x(x+6) -5(x+6)$

Step5: Distribute and combine like terms

$4x^2 +24x -5x -30 = 4x^2 +19x -30$

Answer:

1. Simplified monomial: $x^2$
2. Increasing time intervals: $0 < t < 0.5$ minutes and $1 < t < 2$ minutes
3. Trinomial in standard form: $4x^2 + 19x - 30$