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3 years ago

What is the volume of a rectangular prism whose length is 2x+1 units, width is x-2 units, and whose height is 3x units?

Mathematics

1 answer:

Helen [10]3 years ago

4 0

Answer:

V = 6x^3 - 9x^2 - 6x (which matches the third answer choice)

Step-by-step explanation:

The volume of a rectangular prism of length L, depth W and height H is

V = L * W * H.

Thus,

in this case,

V = (2x + 1)(x - 2)(3x).

The order in which we multiply these quantities together is immaterial.

Working from left to right, we get:

V = (2x^2 - 3x - 2)(3x), and then:

V = 6x^3 - 9x^2 - 6x (which matches the third answer choice)

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Evaluate and match each expression.

avanturin [10]

Answer:

12+x=12+4=16

3x+y=3*4+7=12+7=19

4y-10=4*7-10=28-10=18

1/2xy=1/2*4*7=28/2=14

Step-by-step explanation:

5 0

3 years ago

Drag each expression to the correct location on the model. Not all will be used

grandymaker [24]

Answer: $\dfrac{x^{2}+2x+1 }{\mathbf {x-1}} \cdot \dfrac{\mathbf {5x^{2} +15x-20} }{7x^{2} +7x}$

Step-by-step explanation:

$\dfrac{\dfrac{5x^{2} +25x+20}{7x} }{\dfrac{x^{2} +2x+1}{7x^{2} +7x} } =\dfrac{5x^{2} +25x+20}{7x} \times \dfrac{7x^{2} +7x}{x^{2} +2x+1}=\dfrac{5x^{2} +25x+20}{7x} \times \dfrac{7x(x +1)}{(x+1)^{2} }=\\\\=\dfrac{5x^{2} +25x+20}{x+1} =\dfrac{{5(x+1)(x+4)}}{x+1}=5(x+4)$

$5(x+4)=\dfrac{5(x-1) \cdot (x+4)}{x-1}=\dfrac{5x^{2} +15x-20}{x-1}$

<em>Thus, the expressions will be used: (5x² + 15x - 20) and (x + 4).</em>

<em>Let's check:</em>

$\dfrac{x^{2}+2x+1 }{\mathbf {x-1}} \cdot \dfrac{\mathbf {5x^{2} +15x-20} }{7x^{2} +7x} =\dfrac{(x+1)^{2} }{x-1} \cdot \dfrac{5(x-1) \cdot (x+4)}{7x(x+1)} =\\\\=\dfrac{(x+1) \cdot 5 \cdot (x+4)}{7x} =\dfrac{5x^{2} +25x+20}{7x}$

5 0

3 years ago

Solve!!!!!!!!!!!! Please

frozen [14]

Begin by multiplying everything by 3 to get rid of the fraction. That gives us $-2n \leq 48$ . The rule is when you divide by a negative, the direction of the sign changes, so we will end up with $n \geq -24$ . Because there is a line under the inequality sign, the circle is closed. So your choices are the second, fourth, and sixth.

6 0

4 years ago

Matt started doing extra chores around the house and his allowance changed from $30 per week to $40 per week. What is the percen

slega [8]

Answer:

33.3%

Step-by-step explanation:

Let's say the percent change is x%. Then the equation is:

30 + x% * 30 = 40

Subtract 30 from both sides:

x% * 30 = 10

Divide by 30:

x% = 10/30 = 1/3

Remember that % simply means "out of 100", so:

x/100 = 1/3

Multiply both sides by 100:

x = (1/3) * 100 = 33.3%

3 0

3 years ago

Read 2 more answers

Which is the product or 11/12 and 4? A 1 1/4 B 3 2/3 C 4 1/3 D 33

bazaltina [42]

Answer:

Step-by-step explanation:

11/12 × 4 = 11/3 = 3⅔

8 0

3 years ago