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Shkiper50 [21]
3 years ago
14

Use the substitution method to solve the system of equation.choose the correct ordered pair. y=3x+2 y=x+12

Mathematics
1 answer:
Travka [436]3 years ago
4 0

y = 3x + 2 \\ y = x + 12 \\ 3x + 2 = x + 12 \\ 3x - x = 12 - 2 \\ 2x = 10 \\ x = 5
I hope this would help
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PLS help I will give brainliest​
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Answer: 1= X = 8

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House of Mohammed sells packaged lunches, where their finance department has established a
blagie [28]

The revenue function is a quadratic equation and the graph of the function

has the shape of a parabola that is concave downwards.

The correct responses are;

  • (a) <u>R = -x² + 82·x</u>
  • (b) <u>$1,645</u>
  • (c) The graph of <em>R</em> has a maximum because the <u>leading coefficient </u>of the quadratic function for <em>R</em> is negative.
  • (d)  <u>R = -1·(x - 41)² + 1,681</u>
  • (e) <u>41</u>
  • (f) <u>$1,681</u>

Reasons:

The given function that gives the weekly revenue is; R = x·(82 - x)

Where;

R = The revenue in dollars

x = The number of lunches

(a) The revenue can be written in the form R = a·x² + b·x + c by expansion of the given function as follows;

R = x·(82 - x) = 82·x - x²

Which gives;

  • <u>R = -x² + 82·x </u>

<em>Where, the constant term, c = 0</em>

(b) When 35 launches are sold, we have;

x = 35

Which by plugging in the value of x = 35, gives;

R = 35 × (82 - 35) = 1,645

  • The revenue when 35 lunches are sold, <em>R</em> = <u>$1,645</u>

(c) The given function for <em>R</em> is R = x·(82 - x) = -x² + 82·x

Given that the leading coefficient is negative, the shape of graph of the

function <em>R</em> is concave downward, and therefore, the graph has only a

maximum point.

(d) The form a·(x - h)² + k is the vertex form of quadratic equation, where;

(h, k) = The vertex of the equation

a = The leading coefficient

The function, R = x·(82 - x), can be expressed in the form a·(x - h)² + k, as follows;

R = x·(82 - x) = -x² + 82·x

At the vertex, of the equation; f(x) = a·x² + b·x + c,  we have;

\displaystyle x = \mathbf{-\frac{b}{2 \cdot a}}

Therefore, for the revenue function, the x-value of the vertex, is; \displaystyle x = -\frac{82}{2 \times (-1)} = \mathbf{41}

The revenue at the vertex is; R_{max} = 41×(82 - 41) = 1,681

Which gives;

(h, k) = (41, 1,681)

a = -1 (The coefficient of x² in -x² + 82·x)

  • The revenue equation in the form, a·(x - h)² + k is; <u>R = -1·(x - 41)² + 1,681</u>

(e) The number of lunches that must be sold to achieve the maximum revenue is given by the x-value at the vertex, which is; x = 41

Therefore;

  • The number of lunches that must be sold for the maximum revenue to be achieved is<u> 41 lunches</u>

(f) The maximum revenue is given by the revenue at the vertex point where x = 41, which is; R = $1,681

  • <u>The maximum revenue of the company is $1,681</u>

Learn more about the quadratic function here:

brainly.com/question/2814100

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Compare and contrast an extinct species and an endangered species​
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Extinct species are species that do not exist anymore today whilst endangered species are species which there are few left of and the main causes are habitat destruction or are being hunted
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