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Brilliant_brown [7]
3 years ago
13

a sales associate is given a $500 hiring bonus with a new job. she earns an average commision of $250 per week for the next twel

ve weeks. how much does she earn?
Mathematics
1 answer:
nevsk [136]3 years ago
8 0
She earns $250 per week for the next twelve weeks, so
250x12=3000

Plus she's given a $500 hiring bonus:
If: 250 x 12 = 3000

Add: 3000 + 500 = 3500

3500 is the answer. 



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Jeremy wants to construct an open box from an 18-inch square piece of aluminum. He plans to cut equal squares, with sides of x i
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a.

The volume of the box V = 4x³ - 72x² + 324x

Since the dimensions of the square piece of paper are 18 inches each, and we cut out a length x from each side to give a total length of 2x cut from each side. So, each dimension is L = 18 - 2x.

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= 324x - 72x² + 4x³

The volume of the box V = 4x³ - 72x² + 324x

b.

The minimum value of length of the sides of the squares cut from each corner is x = 3 inches.

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Since the volume of the box is 432 cubic inches,

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324x - 72x² + 4x³ = 432

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x³  - 18x² + 81x - 108 = 0

A factor of the expression is x - 3

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Factorizing the expression x² - 15x + 36 = 0

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So,  x³  - 18x² + 81x - 108 = (x - 3)(x - 3)(x - 12) = 0

So, (x - 3)²(x - 12) = 0

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x - 3 = √0 and x - 12 = 0

x - 3 = 0 and x - 12 = 0

x = 3 twice and x = 12

Since x = 3 is the minimum value, the minimum value of x = 3.

Since the length of the box, L = 18 - 2x

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= 12 inches

The width of the box = L = 12 inches

The height of the box = x = 3 inches.

So,

The minimum value of length of the sides of the squares cut from each corner is x = 3 inches.

  • the length of the box, L = 12 inches,
  • the width of the box = 12 inches
  • and the height of the box, x = 3 inches.

Learn more about volume of a box here:

brainly.com/question/13309609

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