6x + 3 = 3(2x+3) Which statement correctly explains whether the equation is true or not?

A Norman window is rectangular on three sides with a semi-circular top. You decide to install a Norman window in your family roo

sergiy2304 [10]

Given that the window is rectangular on three sides with semi-circular top and with the following dimensions: 4 as the length and 3 as the width. We can calculate the perimeter using the given values, and it gives us the perimeter of 15.71 feet.

8 0

2 years ago

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A sports company wants to package a ball with a 1.5-inch radius in sets of two. They have two options: a cylinder or a square pr

guajiro [1.7K]

Step 1

Find the Volume of the two balls

we know that

the Volume of a sphere is equal to

$V=\frac{4}{3} \pi r^{3}$

In this problem we have

$r=1.5\ in$

Substitute

$V=\frac{4}{3} \pi 1.5^{3}=4.5\pi\ in^{3}$

so

the volume of the two balls is equal

$V=2*4.5\pi=9 \pi\ in^{3}$

Step 2

Find the volume of a cylinder

we know that

The Volume of a cylinder is equal to

$V=\pi r^{2}h$

In this problem we have

$r=1.5\ in$

$h=4*r=4*1.5=6\ in$

Substitute

$V=\pi (1.5^{2})(6)=13.5 \pi\ in^{3}$

Step 3

Find the amount of wasted space in the cylinder

Subtract the volume of the two balls from the volume of the cylinder

$13.5\pi\ in^{3}-9\pi\ in^{3}=4.5\pi\ in^{3}=14.14\ in^{3}$

Step 4

Find the volume of the square prism

The volume of the prism is equal to

$V=Bh$

where

B is the area of the base of the prism

h is the height of the prism

In this problem we have

$B=(2*1.5)^{2}=9\ in^{2}$ -----> the base is equal to the diameter

$h=4*r=4*1.5=6\ in$

Substitute

$V=9*6=54\ in^{3}$

Step 5

Find the amount of wasted space in the prism

Subtract the volume of the two balls from the volume of the prism

$54\ in^{3}-9\pi\ in^{3}=25.73\ in^{3}$

Step 6

Compare the amount of wasted space

the amount of wasted space in the cylinder is $14.14\ in^{3}$

the amount of wasted space in the prism is $25.73\ in^{3}$

Find the difference

$25.73\ in^{3}-14.14\ in^{3}=11.59\ in^{3}=11.6\ in^{3}$

The package that has the least amount of wasted space is the cylinder

therefore

<u>the answer is the option</u>

the cylinder because it has approximately 11.6 in.3 less wasted space than the prism

5 0

2 years ago

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I ordered some books online for myself and friends. Each book costs \$ 13$13 and the store charges a flat rate for shipping of

Sonbull [250]

Answer: 13n + 20

Step-by-step explanation:

The cost of each book is $13. That means that if you end up buying "n" books, cost would be:

= Cost of each book * number of books

= 13 * n

= 13n

You would also get charged a flat rate for shipping of $20 which would be added to the above cost to bring a total of:

= 13n + 20

8 0

2 years ago

Write the equation 2x 2 - 4x + 6 = 1 in standard form and then choose the value of "c."

Karolina [17]

It is 5
2x2 -4x +6-1= 0 is the standard form

6 0

2 years ago

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HELP PLZ ASAP!!!!!!!!!

Anon25 [30]

Use the quadratic formula, the second, the 6th answers are correct.

3 0

2 years ago