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Lelu [443]
3 years ago
11

The equation p = −5x2 + 100x − 250 models the profit p in dollars from selling pizza, where x is the price per pizza in dollars.

What is the highest price you can charge per pizza to profit $100?
Mathematics
1 answer:
sattari [20]3 years ago
7 0

Answer:

$23.0384

Step-by-step explanation:

p = −5x2 + 100x − 250

Where,

P = profits in dollars

x = price in dollars

Find x when p = $100

p = −5x2 + 100x − 250

100 = −5x² + 100x − 250

100 + 250 = -5x² + 100x

350 = -5x² + 100x

-5x² + 100x - 350 = 0

x = -b ± √(b² - 4ac) / 2a

= -100 ± √(100² - 4*-5*-350) / 2*-5

= -100 ± √10000 - (-7000) / -10

= -100 ± √ 10000 + 7000 / -10

= -100 ± √ 17,000 / -10

= -100 ± 10√170 / -10

= -100/-10 ± 10√170/-10

x = 10 ± √170

x = 10 + √170 or 10 - √170

x = 23.0384 or -3.0384

Price of pizza can't be negative

Therefore, the highest price you can charge per pizza to profit $100 is $23.0384

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Vanyuwa [196]

Answer:

(i) the other two sides are 6 and  6\sqrt{2}

(ii) the other two sides are   \frac{4}{3} and                                         \frac{8}{3}

Step-by-step explanation:

(i)  Sine: sin(θ) = Opposite ÷ Hypotenuse

    Cosine: cos(θ) = Adjacent  ÷ Hypotenuse

    Tangent: tan(θ) = Opposite ÷ Adjacent

Here adjacent side = 6

opposite side = d

angle = 45°

other angles are 90° and 45°

tan (45) = Opposite ÷ Adjacent

 1 = d ÷ 6

∴ d = 6 × 1 = 6

so opposite side = 6

Hypotenuse ² = opposite side ² + adjacent side²

                      =  6² + 6²

                      = 36 + 36

                       = 72

hypotenuse = \sqrt{72}

                     = 6\sqrt{2}

the other two sides are 6 and  6\sqrt{2}

(ii) here adjacent side = 4√3

angle = 30°

other angles are 90° and 60°

opposite side = d

tan ( 30) = opposite ÷ adjacent

 \frac{1}{\sqrt{3}} = d ÷ 4√3

\frac{1}{\sqrt{3}} = d × (\frac{\sqrt{3}}{4})

                       3 d = 4

therefore d = \frac{4}{3}

therefore opposite side = \frac{4}{3}

Hypotenuse ² = opposite side ² + adjacent side²

                        =( \frac{4}{3})² +( \frac{4}{\sqrt{3}})²

                        = \frac{64}{9}

therefore hypotenuse = \sqrt{\frac{64}{9}}

                                     =\frac{8}{3}

the other two sides are   \frac{4}{3} and                                    \frac{8}{3}

7 0
4 years ago
The slope of the line that contains the points (2, -7) and (-2, 5) is -3. What is the y-intercept?
kramer

Answer:

C. -1

Step-by-step explanation:

Find the y intercept by plugging in the slope and a given point into the equation y = mx + b. Then, solve for b:

y = mx + b

-7 = -3(2) + b

-7 = -6 + b

-1 = b

So, the y intercept is -1.

The correct answer is C. -1

4 0
3 years ago
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4 years ago
In 1 and 2, use the table below that shows information about squares.
frutty [35]

1. The table has a constant of proportionality of 4, therefore, the perimeter and side length of squares are proportional.

2. Equation for the proportion is, y = 4x.

Perimeter = 48 cm.

<h3>What is the Equation of a Proportional Relationship?</h3>

The equation that defines a proportional relationship is, y = kx, where k is the constant of proportionality between variables x and y.

1. For the table given:

y = perimeter

x = side length

k = constant of proportionality = 8/2 = 16/4 = 24/6 = 4.

Since k is the same all through, the equation can be modelled as y = 4x, which means the perimeter and side length of squares are proportional.

2. Using the equation, y = 4x,the perimeter (y) of a square when its side length is 12 (x) is:

y = 4(12)

y = 48 cm.

The perimeter (y) of the square is: 48 cm.

Learn more about proportional relationship on:

brainly.com/question/15618632

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What is the value of (8 – 5)!?
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<span>(8-5)!=3!=6</span>
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