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FromTheMoon [43]
3 years ago
8

A dump truck brought 1⁄3 of a ton of rock on the first trip, 5⁄6 of a ton on the second trip, and 5⁄12 of a ton on the third tri

p. What was the total weight of the rock?
Mathematics
2 answers:
ludmilkaskok [199]3 years ago
8 0
First convert the numbers to get the same denominator
1/3=4/12
5/6=10/12
5/12
Then add them all together
4/12+10/12+5/12= 19/12
Then reduce
1 7/12
Your answer is 1 ton and 7/12 of a ton
leonid [27]3 years ago
4 0

Answer:

Weight = 1 and \frac{7}{12} Ton

Step-by-step explanation:

The total weight of the rock is calculated by adding the three fractions.

Weight = \frac{1}{3}+\frac{5}{6}+\frac{5}{12}

As they are different denominators, we look for a common denominator that is the Least Common Multiple (LCM).

Then, for each term, the LCM is divided by the denominator of the original fraction and multiplied by the numerator.

Weight = \frac{1}{3}+\frac{5}{6}+\frac{5}{12}

Weight = \frac{(12/3*1) + (12/6*5) + (12/12*5)}{12}

Weight = \frac{4+10+5}{12}

Weight = \frac{19}{12}=1.5833 Ton

Or

Weight = \frac{19}{12}

Weight = \frac{12+7}{12}

Weight = \frac{12}{12}+\frac{7}{12}

Weight = 1+\frac{7}{12}

Weight = 1 and \frac{7}{12} Ton

Hope this helps!

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2 years ago
2(2x + 3) = -6(x + 9)
sergeinik [125]

Answer:

Your answer is -6.

Step-by-step explanation:

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6 0
2 years ago
Examine the following steps. Which do you think you might use to prove the identity Tangent (x) = StartFraction tangent (x) + ta
Over [174]

Answer:

The correct options are;

1) Write tan(x + y) as sin(x + y) over cos(x + y)

2) Use the sum identity for sine to rewrite the numerator

3) Use the sum identity for cosine to rewrite the denominator

4) Divide both the numerator and denominator by cos(x)·cos(y)

5) Simplify fractions by dividing out common factors or using the tangent quotient identity

Step-by-step explanation:

Given that the required identity is Tangent (x + y) = (tangent (x) + tangent (y))/(1 - tangent(x) × tangent (y)), we have;

tan(x + y) = sin(x + y)/(cos(x + y))

sin(x + y)/(cos(x + y)) = (Sin(x)·cos(y) + cos(x)·sin(y))/(cos(x)·cos(y) - sin(x)·sin(y))

(Sin(x)·cos(y) + cos(x)·sin(y))/(cos(x)·cos(y) - sin(x)·sin(y)) = (Sin(x)·cos(y) + cos(x)·sin(y))/(cos(x)·cos(y))/(cos(x)·cos(y) - sin(x)·sin(y))/(cos(x)·cos(y))

(Sin(x)·cos(y) + cos(x)·sin(y))/(cos(x)·cos(y))/(cos(x)·cos(y) - sin(x)·sin(y))/(cos(x)·cos(y)) = (tan(x) + tan(y))(1 - tan(x)·tan(y)

∴ tan(x + y) = (tan(x) + tan(y))(1 - tan(x)·tan(y)

6 0
3 years ago
Read 2 more answers
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