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sdas [7]
3 years ago
14

The length between any two consecutive bases of a baseball diamond is 90 feet. how much shorter is it for the catcher to walk al

ong the diagonal from home plate to second base than the runner running from second to home?
Mathematics
1 answer:
Schach [20]3 years ago
7 0
The diagonal is the hypotenuse of a triangle with legs 90

2*90² = c²
16200=c²
c=√16200= 127.3
walking the diagonal is 180

he saves 52.7 feet

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A wallet contains $460 in $5, $10, and $20 bills. The number of $5 bills exceeds twice the number of $10 bills by 4, and the num
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Number of $5 bills = 32

Number of $10 bills = 14

Number of $20 bills = 8

Step-by-step explanation:

Let x number of $5, y number of $10 and z number of $20

The number of $5 bills exceeds twice the number of $10 bills by 4.

Therefore, x = 2y + 4

The number of $20 bills is 6 fewer than the number of $10 bills.

Therefore, z = y - 6

A wallet contains $460 in $5, $10, and $20 bills.

Therefore,

5x + 10y + 20z = 460

Substitute x and y into equation

    5(2y+4) + 10y + 20(y-6) = 460

10y + 20 + 10y + 20y - 120 = 460

                           40y - 100 = 460

                                    40y = 460 + 100

                                    40y = 560

                                      y = 14

  • Put the value of y into x = 2y + 4 and solve for x

                                      x = 2(14) + 4

                                      x = 32

  • Put the value of y into z = y - 6 and solve for z

                                      z = 14 - 6

                                      z = 8

Hence, the each type of bills,

Number of $5 bills = 32

Number of $10 bills = 14

Number of $20 bills = 8

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