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icang [17]
4 years ago
6

Cora has 1/2 hour to do 5chores. She palns to spend the same fraction of an hour on each chore. She wants to use the number line

to help her determine what fraction of an hour she can spend on each chore
Mathematics
2 answers:
kiruha [24]4 years ago
4 0
Hi! So to find this answer, you could do it two ways. Firstly, you could spend a major amount of time doing this in your head. Or second, you could use a calculator and do 30/5. This would give you 6. So 6 minutes on each chore.
Free_Kalibri [48]4 years ago
4 0
If you want to use a number line create a number line going up to 30 (1/2 an hour). Then, divide it by 5 and then you can see that each section is 6 units.
So, she spends 6 min. on each chore.
6/60=1/10
She spends 1/10 of an hour on each chore.

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These are 10 questions and 10 answers

1) \sqrt[3]{24}  . \sqrt[3]{45}


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}

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}

3) \sqrt{10} . \sqrt{10}

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}

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

5) (x \sqrt{7} -3 \sqrt{8}).(x \sqrt{7}-3 \sqrt{8})

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) \sqrt{y^3} . \sqrt{y^3}

Answer: first option y^3

Justification:

\sqrt{y^3} . \sqrt{y^3} =( \sqrt{y^3} )^2 =(y^3)^{2/2}=y^3

8) ∛d . ∛d . ∛d

Answer: first option: d

Explanation:

∛d . ∛d . ∛d =     ( \sqrt[3]{d}) ^3 = d{3/3}=d^1=d

9) \sqrt{5x^8y^2} . \sqrt{10x^3} . \sqrt{12y}

Answer: second option

Explanation:

\sqrt{5x^8y^2} . \sqrt{10x^3} . \sqrt{12y} = \sqrt{(5.10.12)x^8y^2x^3y}= \sqrt{600x^{11}y^3} =

=10x^5y \sqrt{6xy}

10) (∛4) . √3

Answer: third option     \sqrt[6]{432}

Explanation:

\sqrt[3]{4} . \sqrt{3} = \sqrt[6]{4^2} . \sqrt[6]{3^3} = \sqrt[6]{16.27} = \sqrt[6]{432}
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