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andrezito [222]
3 years ago
10

SSIGNMENTS ASSIGNMENT - Solve the equation for x. 6(4x - 10) = 84

Mathematics
1 answer:
scZoUnD [109]3 years ago
4 0

Answer:Simplifying

6(4x + 10) = 84

Reorder the terms:

6(10 + 4x) = 84

(10 * 6 + 4x * 6) = 84

(60 + 24x) = 84

Solving

60 + 24x = 84

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-60' to each side of the equation.

60 + -60 + 24x = 84 + -60

Combine like terms: 60 + -60 = 0

0 + 24x = 84 + -60

24x = 84 + -60

Combine like terms: 84 + -60 = 24

24x = 24

Divide each side by '24'.

x = 1

Simplifying

x = 1

Step-by-step explanation:

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Graph the image of square CDEF after a reflection across the x-axis​
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So we only change the sign of the y-component.

Now, if we do a reflection across the x-axis of a whole figure, then we apply the reflection to all the points that make the figure.

Then, we could just apply the reflection to the vertices of the square, then graph the new vertices, and then connect them, that is equivalent to graph the image of the square after the reflection.

The original vertices are:

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E = (0, 10)

F = (-3, 10)

Now we apply the reflection, remember that this only changes the sign of the y-component, then the new vertices are:

C' = (-3, -7)

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E' = (0, - 10)

F' = (0, - 10)

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5 0
2 years ago
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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2 years ago
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Answer:

X = \frac{L}{6\pi r } - \frac{5r}{6}  

Step-by-step explanation:

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3 years ago
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