MATHEMATICS HIGH SCHOOL

A box is shaped like an octagonal prism. Here is what the base of the prism looks like. If the height of the box is 7 inches, the volume of the box will be [1] cubic inches.

Answers

Answer 1

Answer:

Answer:

The volume of the box is 33.796 cubic inches

Step-by-step explanation:

Given

$Height = 7in$

See attachment for the base of the prism

Required

The volume of the box

From the attachment, we have:

$a = 1in$ -- side length of the octagon

The area is then calculated as:

$Area = 2 * (1 + \sqrt 2)a^2$

So, we have:

$Area = 2 * (1 + \sqrt 2)* 1^2$

$Area = 2 * (1 + \sqrt 2)* 1$

$Area = 2 * (1 + \sqrt 2)$

Evaluate the square root

$Area = 2 * (1 + 1.414)$

$Area = 2 * (2.414)$

$Area = 4.828$

The volume is then calculated as:

$Volume = Height * Base\ Area$

$Volume = 7 * 4.828$

$Volume = 33.796$

Answer 2

Answer:

The volume of the box is 100 cubic inches.

To find the volume of an octagonal prism, we need to know the area of the base and the height of the prism.

The area of an octagon can be calculated using the following formula:

Area of octagon = 1/2 * apothem * perimeter

where the apothem is the distance from the center of the octagon to one of its sides and the perimeter is the total length of all the sides of the octagon.

In this case, we don't know the apothem or the perimeter of the octagon, so we can't calculate the area of the base using the formula above. However, we can estimate the area of the base by drawing a square inside the octagon and a circle inside the square.

The square will have an area of 16 square inches and the circle will have an area of about 12.5 square inches. Therefore, the area of the octagon is somewhere between 12.5 and 16 square inches.

Since we are estimating the area of the base, we will use the average of 12.5 and 16 square inches, which is 14.25 square inches.

The volume of the box is calculated as follows:

Volume of box = Area of base * Height

Volume of box = 14.25 square inches * 7 inches = 100 cubic inches

Therefore, the volume of the box is 100 cubic inches.

For such more question on volume:

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The angle measures of triangle ABC are given• The measure of angle A is (2x – 10)
• The measure of angle B is 70°
• The measure of angle Cis (4x)
What is the value of x?

Answers

The measure of the value x of the triangle is x = 20.

Given data:

In a triangle, the sum of the angles is always 180 degrees. Therefore, we can set up an equation using the given angle measures:

Angle A + Angle B + Angle C = 180

Substitute the given angle measures:

(2x - 10) + 70 + 4x = 180

Combine like terms:

6x - 10 + 70 = 180

Simplify:

6x + 60 = 180

Now, subtract 60 from both sides of the equation:

6x = 120

Finally, divide both sides by 6 to solve for x:

x = 20

Hence, the value of x is 20 and the angles are solved.

To learn more about triangles, refer:

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x is equal to 20.

The angles of one triangle always add up to 180°, so we can add the measures of each angle together and make an equation.

equation —> 2x - 10 + 70 + 4x = 180

After combining like terms, we get 6x + 60 = 180.

Then we can subtract 60 from both sides to isolate the variable, and the equation becomes 6x = 120. Then we can divide both sides by 6 to get the value of x. The equation becomes x = 20.

Will mark as brainliest plz help

Answers

BC = BD

Step-by-step explanation:

AC = AD

because AB bisect ∠A or

∠CAB = ∠BAD

∴ So, BC = BD

What is the solution of the system? Use elimination.
3x - 4y = 9
-3x + 2y = 9

Answers

You add two equations together to eliminate a variable. This particular problem is nice, because it's already setup to eliminate X.

3x - 4y = 9
-3x + 2y = 9

When we add these two together, 3x - 3x cancels each other out, leaving us with 0x, or nothing.

We continue with -4y + 2y (leaves us with -2y) and 9+9 (18).

-2y = 18

18/-2 = -9.

Now we have y = -9, and we can go back into the problems to solve for x.

3x - 4(-9) = 9

3x + 36 = 9.

3x = -27

x = -9.

Confirm with the final equation:

-3(-9) + 2(-9) = 9
27 - 18 = 9
9 = 9 --- Confirmed.

Answer:

[-9, -9]

Step-by-step explanation:

Here is how the Eliminasyon Metòd is done:

{3x- 4y = 9

{-3x+ 2y = 9

--------------

-2y = 18; -9 = y [plug this back into both equations for y to get -9 = x]

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Factor the polynomial 6x^2+23x+7

Answers

(2x+7)(3x+1)
Hope this helps

On a coordinate plane, triangle A B C is shown. Point A is at (negative 2, negative 4), point B is at (2, negative 1), and point C is at (3, negative 4). Triangle ABC is an isosceles triangle in which side AB = AC. What is the perimeter of triangle ABC? 5 + StartRoot 10 EndRoot units 10 + StartRoot 10 EndRoot units 10 StartRoot 10 EndRoot units 50 units