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olga55 [171]
2 years ago
5

37x + 1/2 - ( x + 1/4 ) = 9(4x-7)+5

Mathematics
1 answer:
Ilya [14]2 years ago
3 0

For this case we have the following equation:

37x + \frac {1} {2} - (x + \frac {1} {4}) = 9 (4x-7) +5

We apply distributive property considering that:

- * + = -\\37x + \frac {1} {2} -x- \frac {1} {4} = 36x-63 + 5

We add similar terms taking into account that:

Equal signs are added and the same sign is placed

Different signs are subtracted and the major sign is placed.

36x + \frac {1} {4} = 36x-58\\\frac {1} {4} = - 58

Equality is not met, there are no "x" values that meet equality.

Answer:

The equation has no solution

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A rectangular box is to have a square base and a volume of 40 ft3. If the material for the base costs $0.36/ft2, the material fo
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Answer:

  • length: 2 ft
  • width: 2 ft
  • height: 10 ft

Step-by-step explanation:

The total cost of the top and bottom is $0.36 + 0.14 = $0.50 per square foot.

The total cost of a pair of opposite sides is $0.05 +0.05 = $0.10 per square foot.

A minimum-cost box will have the cost of any pair of opposite sides be the same. Here, that means the box will have a side area that is 5 times the area of the top or bottom.

Since the base is square, that means the box is the shape of 5 cubes stacked one on the other. Each of those would be 8 ft³, so would have edge dimensions of ∛8 = 2 feet. The height is 5 times that, or 10 ft.

The box is 2 feet square by 10 feet high:

  • length: 2 ft
  • width: 2 ft
  • height: 10 ft

_____

If you feel the need to write an equation, you can let x represent the edge length of the base. Then the cost of the top and bottom will be ...

  top&bottom cost = 0.50·x²

The height of the box is 40/x², so the cost of the four sides will be ...

  side cost = (0.05)(4x)(40/x²) = 8/x

This is minimized when the derivative of the sum of these costs is zero:

  cost = top&bottom cost + side cost

  cost = 0.50x² + 8/x

  d(cost)/dx = 1.00x -8/x² = 0

Multiplying by x², we get ...

  x³ -8 = 0

  x = ∛8 = 2 . . . . . . as above

  height = 40/x² = 40/4 = 10 . . . . . as above

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The area of a square notepad is 100 square centimeters. How long is each side?<br><br> ​
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Step-by-step explanation:

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