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3 years ago

15

Sheila is ordering pizzas for a party. Each plain pizza costs $9.00, and each topping costs $1.50. The delivery charge is $3.00.

Write a function rule to show the total cost of the pizzas if the pizza ordered has 2 toppings. How much will 5 pizzas cost?

2 answers:

monitta3 years ago

6 0

f(5)=$63.00 is the answer.

ivolga24 [154]3 years ago

4 0

F(5)=$63.00 is the correct answer

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Solve the system equation

den301095 [7]

<h2>Answer:</h2>

We will use substitution to solve this system for x.

$x - 2y = 27\\y = 5x\\\\x - 2(5x) = 27\\\\x - 10x = 27\\\\-9x = 27\\\\x = -3$

Now that we know what x is, we can determine y by pluging in -3 for x in one of the original equations. I will use the first one.

$-3 - 2y = 27\\\\-2y = 30\\\\y = -15\\$

We now have our solution.

D. $(-3, -15)$

We can check our answer by pluging the solution into one of the original equations to see if both sides equal each other. I will use the first equation.

$-3 - 2(-15) = 27\\\\-3 + 30 = 27\\\\27 = 27$

Since the equation checks out, our solution is correct.

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2 years ago

A Norman window has the shape of a semicircle atop a rectangle so that the diameter of the semicircle is equal to the width of t

Makovka662 [10]

Answer:

132.233 ft2

Step-by-step explanation:

Let's call the width of the rectangle 'w' and the length 'x'. So the area of the semicircle is:

$A_1 = \pi*radius^2/2$

$A_1 = \pi*(w/2)^2/2$

$A_1 = \pi/8*w^2$

And the area of the rectangle is:

$A_2 = w*x$

If the perimeter of the window is 41 feet, we have:

$Perimeter = length + 2*width + \pi*radius$

$41 = x + 2*w + \pi*w/2$

$x = 41 - w(2 + \pi/2)$

Now, the equation for the total area of the window is:

$A = A_1 + A_2 = \pi/8*w^2 + w*x$

$A = \pi/8*w^2 + w*(41 - w(2 + \pi/2))$

$A = (\pi/8-2 - \pi/2)*w^2 + 41w = -3.1781w^2 + 41w$

To find the maximum area, we can find the x-coordinate of the vertex of the quadratic equation:

$x\_vertex = -b / 2a = -41 / (-3.1781*2) = 6.45$

So the width that gives us the maximum area of the window is 6.45 feet, and the area will be:

$A = -3.1781w^2 + 41w = -3.1781*(6.45)^2 + 41*6.45 = 132.233\ ft^2$

3 0

2 years ago

Jake has a rectangular garden that measures 12 feet by 14 feet. He wants to increase the area by 50% and plans to increase each

emmasim [6.3K]

<em>In order to increase the area of a rectangular garden that measures 12 feet by 14 feet by 50% Jake must increase each dimension by equal lengths, x:</em>

$x\approx 2.9ft$

<h2>Explanation:</h2><h2 />

First of all, let's calculate the area of the original rectangular garden:

$A=b\times h \\ \\ b:base \\ \\ h:height \\ \\ \\ b=12ft \\ \\ h=14ft \\ \\ \\ A=12(14) \\ \\ A=168ft^2$

Jake wants to increase the area by 50%, so the new area would be:

$A'=168(1.5) \\ \\ A'=252ft^2$

He wants to increase the area by 50% and plans to increase each dimension by equal lengths, x, so this is represented by the figure below, therefore:

$(12+x)(14+x)=252 \\ \\ 168+12x+14x+x^2-252=0 \\ \\ x^2+26x-84=0 \\ \\ \\ Using \ quadratic \ formula: \\ \\ x=\frac{-b \pm \sqrt{b^2-4ac}}{2a} \\ \\ a=1 \\ \\ b=26 \\ \\ c=-84 \\ \\ \\ x=\frac{-26 \pm \sqrt{26^2-4(1)(-84)}}{2(1)} \\ \\ x=\frac{-26 \pm \sqrt{1012}}{2} \\ \\ \\ Two \ solutions: \\ \\ x_{1}=-13+\sqrt{253} \approx 2.9\\ \\ x_{2}=-13-\sqrt{253} \approx -28.9 \\ \\ x_{2} \ is \ discarded \ because \ it \ can't \ be \ negatives$

Finally:

<em>In order to increase the area of a rectangular garden that measures 12 feet by 14 feet by 50% Jake must increase each dimension by equal lengths, x:</em>

$x\approx 2.9ft$

<h2>Learn more:</h2>

Dilation: brainly.com/question/10945890

#LearnWithBrainly

6 0

2 years ago

An oil tank has to be drained for maintenance. The tank is shaped like a cylinder that is 3ft long with a diameter of 2.2 ft . S

Contact [7]

4 minutes 34 seconds will takes to empty the tank, if the starts completely full and oil drained at a rate of 2.5 $ft^{3}$ per minute.

Step-by-step explanation:

The given is,

Tank is shaped like a cylinder that is 3 ft long with a diameter of 2.2 ft.

Oil drained at a rate of 2.5 $ft^{3}$ per minute.

Step:1

Time taken to dry the oil tank is,

T = $\frac{Volume of oil}{Oil drain rate}$ ....................................(1)

Step:2

Volume of the oil is,

$V = \pi r^{2} h$ .................................................(2)

Where, r - Radius of Cylinder

$r = \frac{d}{2}$

$r = \frac{2.2}{2}$

r = 1.1 ft

From eqn (1),

V = $\pi$ × $1.1^{2}$ × 3

= 11.40398 $ft^{3}$

Step:3

From equation (1)

= $\frac{11.40398}{2.5}$

= 4.56

= 4.56 minutes

T = 4 minutes 34 seconds

Result:

Time taken to dry the oil tank is 4 minutes 34 seconds, if a cylinder is 3 ft long with a diameter of 2.2 ft and oil is drained at a rate of 2.5ft^3 per minute.

4 0

2 years ago

Describe the domain of this function d=4300x/x^2 +40

Mashcka [7]

Step-by-step explanation:

The domain would be all real numbers

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2 years ago