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NeX [460]
2 years ago
13

ac%7B10%7D%7B3%7D%20" id="TexFormula1" title=" \frac{1 }{4 } \times \frac{3}{4} \div \frac{10}{3} " alt=" \frac{1 }{4 } \times \frac{3}{4} \div \frac{10}{3} " align="absmiddle" class="latex-formula">
What is the answer to the above equation?
​
Mathematics
2 answers:
loris [4]2 years ago
6 0

Answer:

Step-by-step explanation:

Solution

This (after combining the top 2 fractions, is a 4 tier fraction.

1/4*3/4 = 3/16

So the question now becomes 3/16 ÷ 10/3

The rule for such a question is invert (turn up side down) the second fraction and multiply.

3/16 * 3/10                   Combine

(3*3)/(16* 10)          

9 / 160

0.05625

____ [38]2 years ago
4 0

\bf{\dfrac{1}{4}\times\dfrac{3}{4}\div\dfrac{10}{3}    }

Multiply 1/4 by 3/4 (to do this, multiply the numerator by the numerator and the denominator by the denominator).

\bf{\dfrac{1\times3}{4\times4}\div\dfrac{10}{3} \ \ \to \ \ \ Multiply.}

Do the multiplications in the fraction 1 × 3 / 4 × 4.

\bf{\dfrac{3}{16}\div\dfrac{10}{3}   }

Divide 3/16 by 10/3 by multiplying 3/16 by the reciprocal of 10/3.

\bf{\dfrac{3}{16}\times\left(\dfrac{3}{10}\right)   }

Multiply 3/16 by 3/10 (to do this, multiply the numerator by the numerator and the denominator by the denominator).

\bf{\dfrac{3\times3}{16\times10 } \ \ \to \ \ \ Multiply  }

Do the multiplications in the fraction 3 × 3 / 16 × 10

\bf{\dfrac{9}{160} \ \ \to \ \ Answer  }

\huge \red{\boxed{\green{\boxed{\boldsymbol{\purple{Pisces04}}}}}}

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<h3>Answer: Choice D) 22.5</h3>

========================================

Explanation:

x = length of BC

AC = AB+BC

AC = 6 + x

CE = CD+DE

CE = 22+8

CE = 30

Triangles ACE and BCD are similar triangles (can be proven by the AA similarity theorem due to the fact that AE || BD)

Therefore the corresponding sides are proportional letting us set up the proportion below

AC/BC = CE/CD

(6+x)/x = 30/22 .... substitution

22(6+x) = 30x ... cross multiply

132+22x = 30x

132 = 30x-22x ..... subtract 22x from both sides

132 = 8x

8x = 132

x = 132/8 .... divide both sides by 8

x = 16.5

Now use this to find the length of AC

AC = 6+x

AC = 6+16.5

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kompoz [17]

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