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navik [9.2K]
3 years ago
5

What is the scale factor of two similar pyramids with volume of 13824 cubic feel and 216 cubic feet?

Mathematics
1 answer:
velikii [3]3 years ago
3 0

Answer: The scale factor is 4

Step-by-step explanation:

We know that the pyramids are similar. The volume of one of these pyramids is  13,824 cubic feet and the volume of the other one is 216 cubic feet. Then:

V_1=13,824ft^3\\V_2=216ft^3

By Similar solids theorem, if two similar solids have a scale factor of \frac{a}{b}, then corresponding volumes have a ratio of \frac{a^3}{b^3}

Then:

\frac{V_1}{V_2}=\frac{a^3}{b^3}

Knowing this, we can find the scale factor. This is:

\frac{13,824}{216}=\frac{a^3}{b^3}\\\\\frac{13,824}{216}=(\frac{a}{b})^3\\\\\frac{a}{b}=\sqrt[3]{\frac{13,824}{216}}\\\\scale\ factor=\frac{a}{b}=4

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Two parallel lines are cut by a transversal. Which statements are true for all such cases? Select three that apply.
Rudiy27

Answer:

Step-by-step explanation:

Each pair of vertically opposite angles are equal. If you mean vertical angles as in 90 degrees, you should qualify the question

Each pair of alternate interior angles is congruent (think it should be are congruent).

Each pair of corresponding angles is congruent

8 0
2 years ago
A loan of $900 will be repaid in 36 installment of $30.22 each .what is the finance charge for the loan
Marat540 [252]

i hope this is what you are looking for but 36 times 30.22 equals 1087.92 subtract from 900 which is $187.92

<h2>$187.92 for finance charge for loan</h2>
8 0
3 years ago
Amy wants to sell at most 25 cookies and at least 10 sprites
Inga [223]

Answer:

x\leq 25\\y\geq 10\\.50x + y\geq 30

Step-by-step explanation:

It is given that,

Amy wants to sell at most 25 cookies ,

Let number of cookies be 'x' , then x should be less than or equal to 25

Which is represented by  x\leq 25 ,

Further,

Let number of sprites be 'y', then 'y' should be greater than or equal to  10

Which is represented by y\geq 10

Also,

Given,

she profits $.50 on every cookie

and $1.00 on every  sprite.

So total profit on selling cookies would be

= Profit on each cookie times the number of cookies

=.50\times x

=.5x

Similarly, total profit on selling sprites would be

=profit on each sprite times the number of sprites

=1.00\times y

=y

Now, combining these two should be greater than or equal to $30

representing this through an equation,

.50x+y\geq 30

Thus the sysytem of equations is given as:

x\leq 25\\y\geq 10\\.50x + y\geq 30

6 0
3 years ago
On his drive from Montpelier, Vermont, to Columbia, South Carolina, Arthur averaged 51 mph. If he had been able to average 60 mp
Llana [10]

Answer:

Distance between Montpelier and Columbia is 1020

Step-by-step explanation:

51 mi/hr average:

d = 51 t  

60 mi/hr average:

d t = 60*(t-3)

Substitute (1) into (2)  

   51 t =  60*(t-3)

   51 t =  60 t + 180

   9 t  =  180

   t    =   20

d = 51 t

   = 51 (20)

   = 1020

let see distance is 1020 lets check

51 t = 60 * (t-3)

51 (20)= 60* (20-3)

1020   = 60*17

1020 = 1020

4 0
3 years ago
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tester [92]

Answer:

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6 0
3 years ago
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