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r-ruslan [8.4K]
2 years ago
13

A company makes gift boxes in different sizes following the pattern shown below. What is the volume of the fourth gift box to th

e nearest cubic inch? - see attachment :)

Mathematics
1 answer:
AVprozaik [17]2 years ago
4 0

The volume of the fourth box is of 410.1 cubic inches.

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

The volume of a rectangular prism is given by the <u>base area multiplied by the height,</u> that is:

V = A_bh

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

  • For the first three boxes, the height is constant at 9 inches.
  • At the base, the <u>edge length is multiplied by 1.5</u> each time, as \frac{4.5}{3} = \frac{3}{2} = 1.5, thus, for the fourth box, the edge length, in inches, will be of 4.5 \times 1.5 = 6.75

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

  • Square base, of<u> length 6.75 inches</u>, thus:

A_b = 6.75^2 = 45.5625

  • Height of <u>9 inches</u>, thus h = 9 and:

V = A_bh = 45.5625(9) = 410.1

The volume of the fourth gift box will be of 410.1 cubic inches.

A similar problem is given at brainly.com/question/23756783

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7n+2 = 4n+17 solve the equation
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Answer:

n = -5

Step-by-step explanation:

Solve for n:

n + 2 = 4 n + 17

Hint: | Move terms with n to the left hand side.

Subtract 4 n from both sides:

(n - 4 n) + 2 = (4 n - 4 n) + 17

Hint: | Combine like terms in n - 4 n.

n - 4 n = -3 n:

-3 n + 2 = (4 n - 4 n) + 17

Hint: | Look for the difference of two identical terms.

4 n - 4 n = 0:

2 - 3 n = 17

Hint: | Isolate terms with n to the left hand side.

Subtract 2 from both sides:

(2 - 2) - 3 n = 17 - 2

Hint: | Look for the difference of two identical terms.

2 - 2 = 0:

-3 n = 17 - 2

Hint: | Evaluate 17 - 2.

17 - 2 = 15:

-3 n = 15

Hint: | Divide both sides by a constant to simplify the equation.

Divide both sides of -3 n = 15 by -3:

(-3 n)/(-3) = 15/(-3)

Hint: | Any nonzero number divided by itself is one.

(-3)/(-3) = 1:

n = 15/(-3)

Hint: | Reduce 15/(-3) to lowest terms. Start by finding the GCD of 15 and -3.

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n = 5/(-1)

Hint: | Simplify the sign of 5/(-1).

Multiply numerator and denominator of 5/(-1) by -1:

Answer: n = -5

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Step-by-step explanation:

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