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Zielflug [23.3K]
3 years ago
15

Solve by completing the square 4x^2-30=12+10x

Mathematics
1 answer:
natali 33 [55]3 years ago
5 0
16x - 30 = 12 + 10

6x = 42

x = 7
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Solve for x.<br> 21x + 11 - 5 = 5
Reil [10]

Answer:

x= -1/21

Step-by-step explanation:

21x + 11 - 5 = 5

21x + 6 = 5

(-6 each side)

21x = -1

(divide 21 each side)

x= -1/21

3 0
3 years ago
Read 2 more answers
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

6 0
2 years ago
Azul went snorkeling and he noticed That is the ratio of parrotfish to clown fish what is 4:3 He saw a 20 parrot fish how many C
skelet666 [1.2K]
\frac{4}{3} = \frac{20}{?}

\frac{3 \times 20}{4} = 15
8 0
3 years ago
Analyze the diagram below and complete the instructions that follow. <br> Find sin 60 degree
MaRussiya [10]

Answer:

sin 60° = 0.9

Step-by-step explanation:

sin 60° = cos 30°

cos 30° = 0.866025403

0.866025403 to one significant figure

0.866025403 ~ 0.9

~. means approximately.

therefore sin 60° = cos 30°

sin 60° = 0.9

4 0
2 years ago
What is the slope of the line that contains these points?
nikdorinn [45]

Answer:

Slope = 6

Step-by-step explanation:

Find the difference of the y's over/divided by the difference of the x's.

i.e 8-2 / 14 - 13 = 6 / 1 = 6

8 0
3 years ago
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