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ruslelena [56]
2 years ago
14

If 12 keychains cost $9 then how much does 20 keychains cost? $________ Also if you could may you provide steps on how you got t

he answer​

Mathematics
2 answers:
AleksandrR [38]2 years ago
5 0

Answer:

Step-by-step explanation:

12k=9

12k*5/3=9*5/3

20k=15

Jlenok [28]2 years ago
5 0

Answer:

20 keychains will be $15

Step-by-step explanation:

i did 9 divided by 12 equals 0.75 so thats how much each keychain costs. 0.75x20=15

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Can you see an easy way to work out the value of <img src="https://tex.z-dn.net/?f=%5Csqrt%7B%201%5E3%20%2B%202%5E3%20%2B%203%5E
Lina20 [59]

We have the sum of cubes identity

a^3 + b^3 = (a + b) (a^2 - ab + b^2)

and observing that 1 + 4 = 2 + 3, we have

1^3 + 4^3 = (1 + 4) (1^2 - 4 + 4^2) = 5 \times 13

and

2^3 + 3^3 = (2 + 3) (2^2 - 6 + 3^2) = 5 \times 7

Then

\sqrt{1^3+2^3+3^3+4^3+5^3} = \sqrt{5\times13 + 5\times7 + 5\times5^2} = \sqrt{5 \times (20 + 25)} \\\\ ~~~~~~~~ = \sqrt{5^2 \times (4 + 5)} = \sqrt{5^2\times9} = \sqrt{5^2\times3^2} = 5\times3 = \boxed{15}

Alternatively, we have the well-known sum of cubes formula

\displaystyle \sum_{i=1}^n i^3 = \frac{n^2(n+1)^2}4

The sum under the square root is this sum with n=5. Then

1^3+2^3+3^3+4^3+5^3 = \dfrac{5^2\times6^2}4 = 225 = 15^2

and so the square root again reduces to 15.

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1 year ago
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ruslelena [56]
Hello there, have a nice day
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