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Bogdan [553]
3 years ago
5

1. The prism below measures 6 inches x 3 inches x 10 inches. A diagonal

Mathematics
1 answer:
12345 [234]3 years ago
3 0

9514 1404 393

Answer:

  √145 ≈ 12.04

Step-by-step explanation:

The length of the space diagonal is the root of the sum of the squares of the prism edge lengths:

  d² = a² +b² +c² = 6² +3² +10² = 145

  d = √145 ≈ 12.04 . . . inches

__

The face diagonal is found using the Pythagorean theorem in the usual way:

  f² = a² + b²

The space diagonal is the hypotenuse of the right triangle whose sides are the face diagonal and the remaining edge:

  d² = f² +c²

  d² = a² +b² +c²

__

Here is a diagram.

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Using a system of equations, it is found that there are 5 dimes and 9 quarters in his pocket.

<h3>What is a system of equations?</h3>

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

In this problem, the variables are given as follows:

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  • Variable y: number of quarters in his pocket.

He has a total of 14 coins, hence:

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Since y = 14 - x:

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x = 5.

y = 14 - x = 14 - 5 = 9.

There are 5 dimes and 9 quarters in his pocket.

More can be learned about a system of equations at brainly.com/question/24342899

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