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Anvisha [2.4K]
3 years ago
15

A rectangle is 12m longer than it is wide. Its perimeter is 68m. Write and equation and show steps to find its length and width.

Mathematics
1 answer:
Galina-37 [17]3 years ago
4 0

Answer:

  length: 23 m; width: 11 m.

Step-by-step explanation:

The perimeter of a rectangle is twice the sum of its length and width, so that sum is 34 m. Then you can write two equations in length and width:

  l + w = 34

  l - w = 12

Adding these together gives you ...

  2l = 46

  l = 23 . . . . . . divide by 2

Then the width is

  w = 23 -12 = 11

The length and width are 23 m and 11 m, respectively.

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Answer:

Each monthly payment is $ 49.05, and in total Tom paid $ 648.60.

Step-by-step explanation:

Given that Tom buys a DVD player on 12 monthly payments, whose cash price is $ 600, and he pays a 10% deposit and the store charges 9% interest, to determine how much is each payment and the total amount Tom pays for the DVD player the following calculations must be performed:

600 - 600 x 0.1 = 540

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True or False:
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2 years ago
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The sum of four consecutive odd integers is -72. Write an equation to model this situation, and ind the values of the four integ
Nutka1998 [239]

Answer:

  • equation: (x-3) +(x-1) +(x+1) +(x+3) = -72
  • values: -21, -19, -17, -15

Step-by-step explanation:

When dealing with consecutive integers, it often simplifies the problem to work with their average value. We know the average value of the integers in this problem is the even integer between the middle two. We can call it x, and write the equation ...

  (x-3) +(x-1) +(x+1) +(x+3) = -72

This simplifies to ...

  4x = -72 . . . . . . . we knew this before we wrote the above equation, since the sum of 4 numbers is 4 times their average.

  x = -18 . . . . . . . . the middle number of the sequence

So, the numbers are:

  • -18-3 = -21
  • -18-1 = -19
  • -18+1 = -17
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_____

A more conventional approach is to define the variable as the integer at one end or the other of the sequence. If we make it be the lowest number, then the equation is ...

  (x) +(x +2) +(x +4) +(x +6) = -72

and that simplifies to ...

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  4x = -84 . . . . . . . . subtract 12

  x = -21 . . . . . . . . . . divide by 4

Now, the other three numbers are found by adding 2, 4, and 6 to this one.

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