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emmasim [6.3K]
3 years ago
8

The volume of a box is 80 cubic feet with length x-3 and width x-1 and height x+5. What are the possible values of x? What are t

he possible dimensions?

Mathematics
1 answer:
Kryger [21]3 years ago
4 0

Answer:

  • the only possible value of x is 5
  • the dimensions are 2 × 4 × 10

Step-by-step explanation:

The cubic equation ...

  (x -3)(x -1)(x +5) = 80

has one real root: x = 5. Using that value for x, the dimensions become ...

  length = 5 - 3 = 2

  width = 5 - 1 = 4

  height = 5 + 5 = 10

The dimensions are (length, width, height) = (2, 4, 10).

_____

We cannot tell the thrust of the problem, since it has only one solution. Perhaps you're supposed to write the cubic in standard form and use the <em>Rational Root theorem</em> to find <em>possible values of x</em>. That form can be found to be ...

  (x -3)(x -1)(x +5) -80 = 0

  x³ +x² -17x -65 = 0

Descartes' rule of signs tells you there is one positive real root. The rational root theorem tells you possible rational roots are factors of 65:

  1, 5, 13, 65

We know that x must be greater than 3 (so all dimensions are positive). Thus <em>possible values of x are 5, 13, 65</em>, and we're pretty sure that 65 is way too large.

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Answer:

The correct option is;

A. A set of nine data pairs with a correlation coefficient r = -0.4

Step-by-step explanation:

In statistical analysis, it is important to make use of an adequate sample size in order to arrive at a valid result. An analysis with a very small sample size can provide misleading results

When performing regression analysis it is generally accepted by researchers that each variable should have at least 10 observations.

Therefore, the data set having nine data pairs with a negative correlation of -0.4 will provide the most valid result that can then be used for generalization about the larger statistical population.

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By looking at the calculation below, write down a multiplication fact using the same numbers.
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Answer:

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Step-by-step explanation:

Since 294 divided by 3 is 98, that means 294 is 3 times 98. So, we can say:

3 x 98 = 294

We can also say that 98 x 3 = 294 since it doesn't matter in which order you multiply.

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The volume of a rectangular prism is (x4 + 4x3 + 3x2 + 8x + 4), and the area of its base is (x3 + 3x2 + 8). If the volume of a r
muminat

x + 1 minus StartFraction 4 Over x cubed + 3 x squared + 8

Step-by-step explanation:

Volume of the prism is given by the product of its base area and height. To get the height, divide the volume by the base area

Perform long division of the volume polynomial by the polynomial for base area to get the polynomial for height

x³+3x²+8 √x⁴+4x³+3x²+8x+4

                -x⁴+3x³+8x

                ---------------------------

                       1x³+3x²+0+4

                     - 1x³+3x²+8

                   ------------------------

                                     -4

The answer will be : x+1 + -4/(x³+3x²+8)

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3 years ago
The length of a rectangle is 8feet less than the width. The perimeter is 64 feet. Find the length and the width
nataly862011 [7]

Answer:

Length = 4 feet

Width = 4 feet

Step-by-step explanation:

The perimeter of a rectangle formula = 2L + 2W

Where L = Length

W = Width

The length of a rectangle is 8feet less than the width.

Hence,

L = 8 - W

The perimeter is 64 feet.

Hence,

64 = 2(8 - W) × 2W

64 =( 16 - 2W )2W

64 = -4W² + 32W

4W² - 32W + 64 = 0

Factorise

4W² - 16W - 16W + 64 = 0

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W = 4

Width = 4

Solving for L

L = 8 - W

L = 8 - 4

L = 4

Therefore,

Length = 4 feet

Width = 4 feet

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3 years ago
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