If three-quarters of a gallon of ice cream was shared equally among the 5 people, what fraction of a whole gallon did each perso
2 answers:
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Answer:
Step-by-step explanation:
First let us evaluate the value of both the expressions.
a) Hence, Larry's claim that both the expressions are equivalent is wrong.
The evaluation of the expressions have been shown above. The second expression was obtained by swapping the addition and multiplication order and that created the difference.
b) Clearly,
520 > 264
Therefore,
is greater by the expression
by a value of 520 - 264 = 256.
These are 10 questions and 10 answers
1)![\sqrt[3]{24} . \sqrt[3]{45}](https://tex.z-dn.net/?f=%20%5Csqrt%5B3%5D%7B24%7D%20%20.%20%5Csqrt%5B3%5D%7B45%7D%20)
Answer: third option 6∛5
Explanation:
24 = 2^3 * 3
45 = 3^2 * 5
=> 24 * 45 = 2^3 * 3^3 * 5
=> (∛24).(∛45) = ∛[ (2^3).(3^3).5 ] = (2)(3)∛5 = 6∛5
2)![\sqrt[5]{4x^2} . \sqrt[5]{4x^2}](https://tex.z-dn.net/?f=%20%5Csqrt%5B5%5D%7B4x%5E2%7D%20.%20%5Csqrt%5B5%5D%7B4x%5E2%7D%20)
Answer: second option.
Demostration:
![\sqrt[5]{4x^2} . \sqrt[5]{4x^2} = \sqrt[5]{4^2x^4} = \sqrt[5]{2^4x^4} = \sqrt[5]{16x^2}](https://tex.z-dn.net/?f=%20%5Csqrt%5B5%5D%7B4x%5E2%7D%20.%20%5Csqrt%5B5%5D%7B4x%5E2%7D%20%3D%20%20%5Csqrt%5B5%5D%7B4%5E2x%5E4%7D%20%3D%20%5Csqrt%5B5%5D%7B2%5E4x%5E4%7D%20%3D%20%5Csqrt%5B5%5D%7B16x%5E2%7D%20)
3)
Answer: first option 10
Justification:
√10 . √10 = (√10)^2 = √(10^2) = √100 = 10
4)![\sqrt[4]{7} . \sqrt[4]{7} . \sqrt[4]{7} . \sqrt[4]{7}](https://tex.z-dn.net/?f=%20%5Csqrt%5B4%5D%7B7%7D%20.%20%5Csqrt%5B4%5D%7B7%7D%20.%20%5Csqrt%5B4%5D%7B7%7D%20.%20%5Csqrt%5B4%5D%7B7%7D%20)
Answer: fourth option: 7
Explanation:
![\sqrt[4]{7} . \sqrt[4]{7} . \sqrt[4]{7} . \sqrt[4]{7}= (\sqrt[4]{7^})^4= \sqrt[4]{7^4}=7 ^{4/4}=7^1=7](https://tex.z-dn.net/?f=%20%5Csqrt%5B4%5D%7B7%7D%20.%20%5Csqrt%5B4%5D%7B7%7D%20.%20%5Csqrt%5B4%5D%7B7%7D%20.%20%5Csqrt%5B4%5D%7B7%7D%3D%20%28%5Csqrt%5B4%5D%7B7%5E%7D%29%5E4%3D%20%5Csqrt%5B4%5D%7B7%5E4%7D%3D7%20%5E%7B4%2F4%7D%3D7%5E1%3D7)
5)
Answer: the third option: 7x^2 - 12x√14 + 72
Solution:
Notice that it is the two factors are identical, so this is a perfect square binomial:
(x√7 - 3√8)^2 = (x√7)^2 - 2*(x√7)(3√8) + (3√8)^2 = 7x^2 - 6√(56)x + 72 =
= 7x^2 -(6)(2)x√14 + 72 = 7x^2 - 12x√14 + 72
6) √12 . √18
Answer: the fourth option 6√6
Explanation:
√12 . √18 = √ (2 . 2 . 3 . 2 . 3 . 3) = √ [( 2^3) . (3^3)] = 2 . 3 √6 = 6√6
7)
Answer: first option y^3
Justification:
8) ∛d . ∛d . ∛d
Answer: first option: d
Explanation:
∛d . ∛d . ∛d =![( \sqrt[3]{d}) ^3 = d{3/3}=d^1=d](https://tex.z-dn.net/?f=%28%20%5Csqrt%5B3%5D%7Bd%7D%29%20%5E3%20%3D%20d%7B3%2F3%7D%3Dd%5E1%3Dd)
9)
Answer: second option
Explanation:
10) (∛4) . √3
Answer: third option![\sqrt[6]{432}](https://tex.z-dn.net/?f=%20%5Csqrt%5B6%5D%7B432%7D%20)
Explanation:
![\sqrt[3]{4} . \sqrt{3} = \sqrt[6]{4^2} . \sqrt[6]{3^3} = \sqrt[6]{16.27} = \sqrt[6]{432}](https://tex.z-dn.net/?f=%20%5Csqrt%5B3%5D%7B4%7D%20.%20%5Csqrt%7B3%7D%20%3D%20%5Csqrt%5B6%5D%7B4%5E2%7D%20.%20%5Csqrt%5B6%5D%7B3%5E3%7D%20%3D%20%5Csqrt%5B6%5D%7B16.27%7D%20%3D%20%5Csqrt%5B6%5D%7B432%7D%20)
1)
Answer: third option 6∛5
Explanation:
24 = 2^3 * 3
45 = 3^2 * 5
=> 24 * 45 = 2^3 * 3^3 * 5
=> (∛24).(∛45) = ∛[ (2^3).(3^3).5 ] = (2)(3)∛5 = 6∛5
2)
Answer: second option.
Demostration:
3)
Answer: first option 10
Justification:
√10 . √10 = (√10)^2 = √(10^2) = √100 = 10
4)
Answer: fourth option: 7
Explanation:
5)
Answer: the third option: 7x^2 - 12x√14 + 72
Solution:
Notice that it is the two factors are identical, so this is a perfect square binomial:
(x√7 - 3√8)^2 = (x√7)^2 - 2*(x√7)(3√8) + (3√8)^2 = 7x^2 - 6√(56)x + 72 =
= 7x^2 -(6)(2)x√14 + 72 = 7x^2 - 12x√14 + 72
6) √12 . √18
Answer: the fourth option 6√6
Explanation:
√12 . √18 = √ (2 . 2 . 3 . 2 . 3 . 3) = √ [( 2^3) . (3^3)] = 2 . 3 √6 = 6√6
7)
Answer: first option y^3
Justification:
8) ∛d . ∛d . ∛d
Answer: first option: d
Explanation:
∛d . ∛d . ∛d =
9)
Answer: second option
Explanation:
10) (∛4) . √3
Answer: third option
Explanation: