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guapka [62]
2 years ago
13

Help me please with an explanation/work, thank you!!

Mathematics
1 answer:
kiruha [24]2 years ago
8 0

Answer:

1. 3

Step-by-step explanation:

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Find the linear equation in slope intercept form that passes through the points (5,3) and (2,-1)
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\bf (\stackrel{x_1}{5}~,~\stackrel{y_1}{3})\qquad  (\stackrel{x_2}{2}~,~\stackrel{y_2}{-1}) \\\\\\ slope =  m\implies  \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{-1-3}{2-5}\implies \cfrac{-4}{-3}\implies \cfrac{4}{3} \\\\\\ \stackrel{\textit{point-slope form}}{y- y_1= m(x- x_1)}\implies y-3=\cfrac{4}{3}(x-5)\implies y-3=\cfrac{4}{3}x-\cfrac{20}{3} \\\\\\ y=\cfrac{4}{3}x-\cfrac{20}{3}+3\implies y=\cfrac{4}{3}x-\cfrac{11}{3}

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The profit function p(x) of a tour operator is modeled by p(x) = −2x2 + 900x − 40000, where x is the average number of tours he
shtirl [24]

Solving the quadratic function, it is found that the range is of:

between 200 and 250; inclusive

The profit for x tours is modeled by the following equation:

p(x) = -2x^2 + 900x - 40000

It is concave down, so the monthly profit will be of at least $60,000 between the two roots when p(x) = 60000. Thus:

60000 = -2x^2 + 900x - 40000

2x^2 - 900x + 10000 = 0

Simplifying by 2:

x^2 - 450x + 50000 = 0

Which has a = 1, b = -450, c = 50000

Then:

\Delta = (-450)^2 - 4(1)(50000) = 2500

x_{1} = \frac{-(-450) + \sqrt{2500}}{2} = 250

x_{2} = \frac{-(-450) - \sqrt{2500}}{2} = 200  

At least $60,000 includes $60,000, thus the interval is inclusive, and the correct option is:

between 200 and 250; inclusive

A similar problem is given at brainly.com/question/25181401

3 0
2 years ago
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