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Ierofanga [76]
4 years ago
15

A rectangular prism must have a base with an area of no more than 27 square meters. The width of the base must be 9 meters less

than the height of the prism. The length of the base must be 6 meters more than the width of the base. Find the maximum height of the prism.
Let x = the height of the prism
x – 9 = the width of the base
A rectangular prism must have a base with an area of no more than 27 square meters. The width of the base must be 9 meters less than the height of the prism. The length of the base must be 6 meters more than the width of the base. Find the maximum height of the prism.
Let x = the height of the prism
x – 9 = the width of the base
x -3 = the length of the prism

Select the inequality that represents the problem.

x2 – 3 x – 81 ≤ 0

x2 – 3 x – 27 ≤ 0

x2 – 12 x – 27 ≤ 0

x2 – 12 x ≤ 0
Mathematics
1 answer:
tatuchka [14]4 years ago
7 0

Answer: Choice D) x^2 - 12x \le 0

The base has length x-3 and width x-9 which multiplies out to (x-3)(x-9) = x^2-12x+27

This area must be 27 square meters or less, so we set that expression less than or equal to 27

x^2-12x+27 \le 27

then we subtract 27 from both sides to get the final answer

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Cammie can mow 1/2 acre in 25 minutes. If her rate is constant, Cammie says she can mow 1 1/4 acres in one hour. Is Cammie corre
wlad13 [49]

Answer: No, Cammie is not correct. She can mow  1\frac{1}{5}\ acres in one hour (See explanation).

Step-by-step explanation:

Convert the mixed number to an impoper fraction:

1. Multiply the whole number part by the denominator of the fraction and add the product to the numerator.

2. The denominator does not change.

Then:

1\frac{1}{4}=\frac{(1*4)+1}{4}=\frac{5}{4}

Let be "x" the acres Cammie can mow in one hour.

You know that she can mow \frac{1}{2}\ acre in 25 minutes, then you can set up the following proportion (Remember that 1 hour has 60 minutes):

\frac{\frac{1}{2}}{25}=\frac{x}{60}

Solving for "x", you get:

\frac{\frac{1}{2}}{25}=\frac{x}{60}\\\\(60)(\frac{1}{50})=x\\\\x=\frac{6}{5}

Convert from improper fraction to mixed number:

1. When you divide 6 by 5, the quotient is 1. This will be the whole number part.

2. The remainder is 1. This will be the numerator.

3. The denominator does not change.

Then:

x=1\frac{1}{5}

Therefore, she can mow  1\frac{1}{5}\ acres in one hour.

5 0
3 years ago
Let me know how to do this?
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440 - 354 = 86

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