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Veseljchak [2.6K]
3 years ago
15

Cassandra calculated the total volume of the figure below. A rectangular prism has a length of 7 inches, width of 6 inches, and

height of 7 inches. A rectangular pyramid has a base of 6 inches by 7 inches and a height of 3 inches. Total volume = V of prism – V of pyramid       = Bh - Bh       = (7)(6) (7) – (7)(6)(3)       = 294 – 126       = 168 square inches What mistakes did Cassandra make? Check all that apply. She used square units instead of cubic units. In calculating the volume of the pyramid, she did not multiply by 1/3. She incorrectly identified the shapes composing the total figure. She subtracted the pyramid volume instead of adding it. She should have multiplied the dimensions of the prism by 1/3.
Mathematics
2 answers:
olga2289 [7]3 years ago
6 0
<h2><u><em>- She used square units instead of cubic units.</em></u></h2><h2><u><em>- In calculating the volume of the pyramid, she did not multiply by 1/3.</em></u></h2><h2><u><em>- She subtracted the pyramid volume instead of adding it.</em></u></h2>
RideAnS [48]3 years ago
4 0

Answer:

1,2,4

Step-by-step explanation:

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alekssr [168]

Answer:

\theta_{CAB}=128.316

\theta_{ABC}=25.842

\theta_{BCA}=25.842

Step-by-step explanation:

A = (-3,0) , B = (1,3) , and C = (1,-3)

We're going to use the distance formula to find the length of the sides:

r= \sqrt{(x_1-x_2)^2+(y_1-y_2)^2+(z_1-z_2)^2}

AB= \sqrt{(-3-1)^2+(0-3)^2}=5

BC= \sqrt{(1-1)^2+(3-(-3))^2}=9

CA= \sqrt{(1-(-3))^2+(-3-0)^2}=5

we can use the cosine law to find the angle:

it is to be noted that:

the angle CAB is opposite to the BC.

the angle ABC is opposite to the AC.

the angle BCA is opposite to the AB.

to find the CAB, we'll use:

BC^2 = AB^2+CA^2-(AB)(CA)\cos{\theta_{CAB}}

\dfrac{BC^2-(AB^2+CA^2)}{-2(AB)(CA)} =\cos{\theta_{CAB}}

\cos{\theta_{CAB}}=\dfrac{9^2-(5^2+5^2)}{-2(5)(5)}

\theta_{CAB}=\arccos{-\dfrac{0.62}}

\theta_{CAB}=128.316

Although we can use the same cosine law to find the other angles. but we can use sine law now too since we have one angle!

To find the angle ABC

\dfrac{\sin{\theta_{ABC}}}{AC}=\dfrac{\sin{CAB}}{BC}

\sin{\theta_{ABC}}=AC\left(\dfrac{\sin{CAB}}{BC}\right)

\sin{\theta_{ABC}}=5\left(\dfrac{\sin{128.316}}{9}\right)

\theta_{ABC}=\arcsin{0.4359}\right)

\theta_{ABC}=25.842

finally, we've seen that the triangle has two equal sides, AB = CA, this is an isosceles triangle. hence the angles ABC and BCA would also be the same.

\theta_{BCA}=25.842

this can also be checked using the fact the sum of all angles inside a triangle is 180

\theta_{ABC}+\theta_{BCA}+\theta_{CAB}=180

25.842+128.316+25.842

180

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3 years ago
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3 years ago
Which of the following is a proportional relationship?
Solnce55 [7]

The two equations represent the proportional relationship.

y=3x and y=12x are proportional relation ship equations

proportion equations can be defined as

If we change x the y will change in the same proportion.

<h3>What is the proportional relationship?</h3>

Proportional relationships are relationships between two variables where their ratios are equivalent.

Another way to think about them is that, in a proportional relationship, one variable is always a constant value time the other.

That constant is known as the constant of proportionality.

proportional relationship equation contain (0,0) points

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2 years ago
A car used 5 2/3 gallons of fuel on a 3 hour trip. How many gallons were used each hour?
mr_godi [17]

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Svetach [21]

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Step-by-step explanation:

Let 1st # = x

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Add up all the x: x + x +3 +2x =51

Subtract 3 from both sides: 4x + 3 - 3 = 51 - 3

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Your 1st number is x = 12

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For the 3rd # it is 2 times x so 2(12) = 24

Check your answers by adding up the numbers you solved: 12 + 15 +24 = 51

Does it equal to 51 as stated in the question? Yes, answers check out.

7 0
3 years ago
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