Answer:
20 units²
Step-by-step explanation:
The x-intercepts are symmetrically located around the x-coordinate of the vertex, so are at
1.5 ± 5/2 = {-1, 4}
Using one of these we can find the unknown parameter "a" in the parabola's equation (in vertex form) ...
0 = a(4 -1.5)² +12.5
0 = 6.25a +12.5 . . . . . simplify
0 = a +2 . . . . . . . . . . . divide by 6.25
-2 = a
Then the standard-form equation of the parabola is ...
y = -2(x -1.5)² +12.5 = -2(x² -3x +2.25) +12.5
y = -2x² +6x +8
This tells us the y-intercept is 8. Then the relevant triangle has a base of 5 units and a height of 8. Its area is given by the formula ...
A = (1/2)bh = (1/2)(5)(8) = 20 . . . . units²
(a) The measure of the indicated angle for figure 1 is 48⁰.
(b) The measure of the indicated angle for figure 2 is 42⁰.
<h3>Measure of the indicated angle</h3>
The measure of the indicated angles can be calculated as follows;
<h3>Figure 1</h3>
sinθ = opp/hypo
sinθ = 72/97
sinθ = 0.7423
θ = sin⁻¹(0.7423)
θ = 47.9⁰ ≈ 48⁰
<h3>Figure 2</h3>
sinθ = 65/97
sinθ = 0.6701
θ = sin⁻¹(0.6701)
θ = 42.1⁰ ≈ 42⁰
Learn more about angles here: brainly.com/question/25770607
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Answer: The answer is 
Step-by-step explanation: Given that a school wants to put on a dance recital. The programs of Middle school dancer will be short of 4 minutes each and programmes of High school performers will be long of 7 minutes each.
Number of middle school dances is "M" and number od high school dances is "H".
Since there cannot be more than 10 dances all together, so fisrt inequality can be written as
Also, the entire recital must take maximum 90 minutes, so the second inequality can be written as
Thus, the pair of inequalities is
