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weqwewe [10]
3 years ago
15

Ivan is painting 3 walls in his living room. Each wall measures 9 3/4 feet tall by 14 1/4 feet wide. Ivan needs to estimate the

total area he will paint in order to determine the amount of paint to purchase. Which expression best represents the estimated area in square feet that Ivan will paint?​
Mathematics
1 answer:
Alenkinab [10]3 years ago
4 0

Answer:

The estimated area is 416\frac{13}{16}\ ft^{2}

Step-by-step explanation:

we know that

To estimate the area that Ivan will paint , calculate the area of one wall and then multiply by 3

step 1

Convert the dimensions to an improper fractions

9\frac{3}{4}\ ft=\frac{9*4+3}{4}=\frac{39}{4}\ ft

14\frac{1}{4}\ ft=\frac{14*4+1}{4}=\frac{57}{4}\ ft

step 2

Find the area of one wall

(\frac{39}{4})*(\frac{57}{4})=\frac{2,223}{16}\ ft^{2}

step 3

Multiply the area of one wall by 3

(3)*\frac{2,223}{16}=\frac{6,669}{16}\ ft^{2}

step 4

Convert to mixed number

\frac{6,669}{16}=\frac{6,656}{16}+\frac{13}{16}=416\frac{13}{16}\ ft^{2}

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Which ordered pair (a,b) is a solution to the given system of linear equations.
egoroff_w [7]

Answer:

A. (-13,-3)

Step-by-step explanation:

Solve the system of two equations:

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From the second equation:

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Substitute it into the first equation:

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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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