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Degger [83]
2 years ago
6

The dimensions of a rectangular prism are shown below: Length 2 1/4 ft | width 1 ft | height 1 1/4 ft.

Mathematics
1 answer:
zysi [14]2 years ago
4 0

Answer:

  • See below

Step-by-step explanation:

<u>Dimensions given:</u>

  • l = 2 1/4 ft, w = 1 ft, h = 1 1/4 ft

A small cube has side of 1/4 ft

Find the number of small cubes can fit in each dimension of the prism.

<u>Length</u>

  • 2 1/4 : 1/4 = 9/4 * 4 = 9

<u>Width</u>

  • 1 : 1/4 = 1 *4 = 4

<u>Height</u>

  • 1 1/4 : 1/4 = 5/4 * 4 = 5

Part A

<u>Number of small cubes would be:</u>

  • 9*4*5 = 180

Part B

<u>Each small cube has volume:</u>

  • V = (1/4)³ = 1/64 ft³

The volume of the prism in terms of small cubes is 180 as we found above.

<u>The volume in terms of unit cube:</u>

  • V = 180*1/64 = 180/64 = 2 52/64 = 2 13/16 ft³ or 2.8125 ft³
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Answer:

B. \frac{67}{10} x + 9

Step-by-step explanation:

Simplify the expression. Remember to go by the order of operations, or PEMDAS.

1) First, distribute the numbers outside of the set of parentheses to the terms inside the set of parentheses next to them. Then, simplify the fractions.

3(\frac{7}{5} x + 4) -2 (\frac{3}{2} -\frac{5}{4} x)

\frac{21}{5}x + 12  - \frac{6}{2} + \frac{10}{4} x

\frac{21}{5} x + 12 - 3 + \frac{10}{4} x

2) Finally, combine like terms. (This means to add or subtract constants and to add or subtract terms with the same variables.) You may need to convert terms to the same denominator in order to do so easier. Then, reduce the fraction.

\frac{21}{5} x + 9 + \frac{10}{4}x \\\frac{84}{20}x + \frac{50}{20}x + 9 \\\frac{134}{20}x + 9 \\\frac{67}{10}x + 9

Thus, the answer is \frac{67}{10} x + 9.

8 0
3 years ago
Which of the following shows the true solution to the logarithmic equation 3 log Subscript 2 Baseline (2 x) = 3 x = negative 1 x
sineoko [7]

The equation which shows the true solution to the given logarithmic equation is,

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<h3>What is power rule of logarithmic function?</h3>

The power of the log rule says that the number written in the front of the logarithmic function can be raised to the power of the logarithmic function.

For example,

n\log_b(M)=\log_b(M)^n

Given information-

The logarithmic equation given in the problem is,

3\log_2(2x)=3

Using the power rule of the logarithmic function,

\log_2(2x)^3=3

Using the exponent rule of the logarithmic function the above equation can be written as,

(2x)^3=3

Solve it further,

8x^3=3\\x^3=1\\x=1

Hence, the equation which shows the true solution to the given logarithmic equation is,

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Learn more about the rules of logarithmic function here;

brainly.com/question/13473114

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Doctors can use radioactive chemicals to treat some forms of cancer. The half life of a certain chemical is 7 days. A patient re
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Answer:

5 millicuries

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2 years ago
Find f(−1) given that f(x)=x3+2x2+3x+4. <br>A. 10 <br>B. -2 <br>C. 2 <br>D. -10
Finger [1]

Answer:

The answer is option C

Step-by-step explanation:

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To find f(-1) substitute the value of x that's

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That's

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We have the final answer as

<h3>f( - 1) = 2</h3>

Hope this helps you

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3 years ago
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