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Sliva [168]
3 years ago
9

The measures of two complementary angles are m angle 1 = (10x+7) and m angle 2=(9x-12) find the measures of both angles

Mathematics
1 answer:
USPshnik [31]3 years ago
5 0

Answer:

m<1 = 57°

m<2 = 33°

Step-by-step explanation:

To find the numerical measure of both angles, let's come up with an equation to determine the value of x.

Given that m<1 = (10x +7)°, and m<2 = (9x - 12)°, where both are complementary angles, therefore, it means, both angles will add up to give us 90°.

Equation we can generate from this, is as follows:

(10x + 7)° + (9x - 12)° = 90°

Solve for x

10x + 7 + 9x - 12 = 90

Combine like terms

19x - 5 = 90

Add 5 to both sides

19x = 90 + 5 (addition property not equality)

19x = 95

Divide both sides by 19

x = 5

m<1 = (10x +7)°

Replace x with 5

m<1 = 10(5) + 7 = 50 + 7 = 57°

m<2 = (9x - 12)

Replace x with 5

m<2 = 9(5) - 12 = 45 - 12 = 33°

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Max makes and sells posters. The function p(x)= -10x^2 +200x -250, graphed below, indicates how much profit he makes in a month
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Here is our profit as a function of # of posters
p(x) =-10x² + 200x - 250
Here is our price per poster, as a function of the # of posters:
pr(x) = 20 - x
Since we want to find the optimum price and # of posters, let's plug our price function into our profit function, to find the optimum x, and then use that to find the optimum price:
p(x) = -10 (20-x)² + 200 (20 - x) - 250
p(x) = -10 (400 -40x + x²) + 4000 - 200x - 250
Take a look at our profit function. It is a normal trinomial square, with a negative sign on the squared term. This means the curve is a downward facing parabola, so our profit maximum will be the top of the curve.
By taking the derivative, we can find where p'(x) = 0 (where the slope of p(x) equals 0), to see where the top of profit function is.
p(x) = -4000 +400x -10x² + 4000 -200x -250
p'(x) = 400 - 20x -200
0 = 200 - 20x
20x = 200
x = 10                         
p'(x) = 0 at x=10. This is the peak of our profit function. To find the price per poster, plug x=10 into our price function:
price = 20 - x
price = 10
Now plug x=10 into our original profit function in order to find our maximum profit:
<span>p(x)= -10x^2 +200x -250
p(x) = -10 (10)</span>² +200 (10) - 250
<span>p(x) = -1000 + 2000 - 250
p(x) = 750

Correct answer is C)
</span>
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