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3 years ago

A store uses the expression -2p+ 50 to model the number of backpacks it sells per day, where the price, p, can be anywhere

Mathematics

1 answer:

Ivan3 years ago

3 0

Answer:

B: $12.00 per backpack gives the maximum revenue; the maximum revenue is $312.00.

Step-by-step explanation:

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Solve x2 + 2x = 4 for x by completing the square. x equals plus or minus square root of 5 plus 1 x equals plus or minus square r

steposvetlana [31]

Answer:

x equals plus or minus square root of 5 minus 1

Step-by-step explanation:

we have

$x^{2} +2x=4$

Divide by 2 the coefficient of the x-term

$2/2=1$

squared the number

$1^2=1$

Adds both sides

$x^{2} +2x+1=4+1$

$x^{2} +2x+1=5$

Rewrite as perfect squares

$(x+1)^{2}=5$

take the square root both sides

$x+1=(+/-)\sqrt{5}$

$x=(+/-)\sqrt{5}-1$

therefore

x equals plus or minus square root of 5 minus 1

4 0

3 years ago

Alex wants to fence in an area for a dog park. He has plotted three sides of the fenced area at the points E (1, 5), F (3, 5), a

hram777 [196]

Answer:

$(1,1)$

Step-by-step explanation:

Given: E, F, G, H denote the three coordinates of the area fenced

To find: coordinates of point H

Solution:

According to distance formula,

length of side joining points $(x_1,y_1)\,,\,(x_2,y_2)$ is equal to $\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

So,

$EF=\sqrt{(3-1)^2+(5-5)^2}=2\,\,units\\FG=\sqrt{(6-3)^2+(1-5)^2}=\sqrt{9+16}=5\,\,units\\GH=\sqrt{(x-6)^2+(y-1)^2}\\EH=\sqrt{(x-1)^2+(y-5)^2}$

Perimeter of a figure is the length of its outline.

$EF+FG+GH+EH=16\\2+5+\sqrt{(x-6)^2+(y-1)^2}+\sqrt{(x-1)^2+(y-5)^2}=16\\\sqrt{(x-6)^2+(y-1)^2}+\sqrt{(x-1)^2+(y-5)^2}=16-2-5\\\sqrt{(x-6)^2+(y-1)^2}+\sqrt{(x-1)^2+(y-5)^2}=9$

Put $(x,y)=(1,1)$

$\sqrt{(1-6)^2+(1-1)^2}+\sqrt{(1-1)^2+(1-5)^2}=9\\\sqrt{25}+\sqrt{16}=9\\5+4=9\\9=9$

This is true.

So, the point $(1,1)$ satisfies the equation $\sqrt{(x-6)^2+(y-1)^2}+\sqrt{(x-1)^2+(y-5)^2}=9$

So, point H is $(1,1)$ .

7 0

3 years ago

The length, with, and height of a rectangular prism can be represented by the expressions (x+3),(x+7),and(x-1). Write an express

joja [24]

Answer: 6x² + 36x + 22

Step-by-step explanation:2 faces (x + 3) by (x + 7), area of both these faces 2(x+3)*(x + 7)

2 faces (x + 3) by (x - 1), area of both these faces 2(x+3)*(x - 1)

2 faces (x -1 ) by (x + 7), area of both these faces 2(x-1)*(x + 7)

Whole surface area is

2(x+3)*(x + 7) + 2(x+3)*(x - 1) + 2(x-1)*(x + 7) =

=2(x² + 3x +7x +21) + 2(x² +3x -x - 3) + 2(x² - x +7x -7)=

=2x² + 20x +42 + 2x² + 4x - 6 + 2x² + 12x -14 =

= 6x² + 36x + 22

5 0

2 years ago

Read 2 more answers

a total of 1500 raffle tickets were collected during the school fair. if you have 30 raffle tickets, what is the probability tha

hammer [34]

Answer: 1/50 or 0.02

Step-by-step explanation:

30 / 1500 = 1/50

1/50 or 0.02

3 0

3 years ago

the height of a triangle is 4 meters less than the base. if the area of the triangle is 6 m^2 what is the height of the triangle

inna [77]

Answer:

$2m$

Step-by-step explanation:

Alrighty let's do this.

We know that formula for the Area of a triangle is:

$A = \frac{1}{2}bh$

They give us the area as $6m^2$ , so let's include it in the equation.

$6 = \frac{1}{2}bh$

Now we reach a stage where we have 2 unknown variables! That means we can't solve it in its current state. So the idea you should have in cases like these where you have 2 or more unknown variables is, "Can I represent this one variable in terms of another variable?" In this case you can do exactly that. You can represent height in terms of length of the base. We are told the height of the triangle is 4 meters less than the base. That is telling us that $h = b-4$

So replace $h$ in the equation with $b-4$ .

You will now get:

$6 = \frac{1}{2}b(b-4)$

Now we can work towards solving. Let's get simplifying.

$12 = b(b-4)\\12 = b^2 - 4b\\$

bring everything to one side so we can make a quadratic and factor:

$0 = b^2 - 4b - 12\\0 = (b-6)(b+2)\\\\b = 6\\b\neq -2$

We get that $b=6$ .

Since we need the height of the triangle we'll need to call back on what h is. We found earlier that $h = b - 4$ , so to find h, we just sub in our b value into that.

$h = (6) - 4 = 2$

We find that $h=2$

7 0

2 years ago