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kati45 [8]
3 years ago
5

5/6, 1/4, and 2/3 yard. Needs 1 yd of cable

Mathematics
1 answer:
mixer [17]3 years ago
3 0
1. So first of all we have to divide the 3 fractions into decimals to get a decimal to compare. So 5/6 is the same as 5 divided by 6 which is .83 bar and so on...

5/6= .83 bar
1/4= .25
2/3= .66 bar

So 5/6 and 2/3 are closer to one.




2. The two shortest pieces are 2/3 and 1/4 so you se 1/4 + 2/3. Let’s get a common denominator for these fractions. The common denominator is 12. So multiply 1/4 • 3 to get 3/12 and multiply 2/3 by • 4 to get 8/12. Add them together and you get 11/12. So he would need 1/12 more cable or 0.083 bar.


3. Now we have to find a common denominator for all of them. The common denominator is 12 again. Multiply 5/6•2 and then you get 10/12, then add 10/12 +2/12(from 1/4) and then you get leftover with 9/12 or 3/4 more wire.
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<img src="https://tex.z-dn.net/?f=%20%5Cfrac%7B%20%7B2%7D%5E%7Bx%20%2B%202%7D%20-%20%20%7B2%7D%5E%7B%20x%20%2B%203%7D%20%7D%7B%2
weeeeeb [17]

I suppose you just have to simplify this expression.

(2ˣ⁺² - 2ˣ⁺³) / (2ˣ⁺¹ - 2ˣ⁺²)

Divide through every term by the lowest power of 2, which would be <em>x</em> + 1 :

… = (2ˣ⁺²/2ˣ⁺¹ - 2ˣ⁺³/2ˣ⁺¹) / (2ˣ⁺¹/2ˣ⁺¹ - 2ˣ⁺²/2ˣ⁺¹)

Recall that <em>n</em>ª / <em>n</em>ᵇ = <em>n</em>ª⁻ᵇ, so that we have

… = (2⁽ˣ⁺²⁾ ⁻ ⁽ˣ⁺¹⁾ - 2⁽ˣ⁺³⁾ ⁻ ⁽ˣ⁺¹⁾) / (2⁽ˣ⁺¹⁾ ⁻ ⁽ˣ⁺¹⁾ - 2⁽ˣ⁺²⁾ ⁻ ⁽ˣ⁺¹⁾)

… = (2¹ - 2²) / (2⁰ - 2¹)

… = (2 - 4) / (1 - 2)

… = (-2) / (-1)

… = 2

Another way to get the same result: rewrite every term as a multiple of <em>y</em> = 2ˣ :

… = (2²×2ˣ - 2³×2ˣ) / (2×2ˣ - 2²×2ˣ)

… = (4×2ˣ - 8×2ˣ) / (2×2ˣ - 4×2ˣ)

… = (4<em>y</em> - 8<em>y</em>) / (2<em>y</em> - 4<em>y</em>)

… = (-4<em>y</em>) / (-2<em>y</em>)

… = 2

8 0
3 years ago
There are 2112 people in a concert.
nadya68 [22]

Answer:

75% of 352 children are boys

Step-by-step explanation:

If 5/6 of the people participaticipants to a concert are adults then 1 out of 6 prople are children so we may reach a number of 2112:6=352 children

if 25% of the children are girls then 75% are boys

88×3=264 boys

7 0
3 years ago
Rewrite the following without an exponent.<br> (-5)-2 (the -2 is the exponent)
yuradex [85]

Answer: -5 x -5

The exponent two means the other number multiplied 2 times, so the equation is -5 x -5. The answer to the equation is -25.

Hope this helped you out!

3 0
3 years ago
What is 2/3 x 9/8 as a fraction in simplest form
tresset_1 [31]

Answer: \frac{3}{4}

Have attached the picture for explanation...

7 0
3 years ago
I have 24 golf clubs. i have 3 bags. how many clubs do i have in each bag.
NeX [460]

Answer:

8

Step-by-step explanation:

24/3 = 8

6 0
3 years ago
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