What has to be the same in order to add fractions?

Mathematics

1 answer:

RUDIKE [14]3 years ago

8 0

Answer: The denominator

Explanation: you can’t add 3/12 and 2/6. You would have to change it to 3/12 + 4/12.

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29 is what percent of 185? round your answer to the nearest hundredth.

Marina CMI [18]

divide 29 by 185

29/185 = 0.15675 rounded to nearest hundredth would be 0.16

becomes 15.675 percent rounded to nearest hundredth would be 15.68%

check by multiplying 185 x 15.68%

185 x .1568 = 29.008 which is rounded to 29

8 0

3 years ago

Rationalize the denominator of $\displaystyle \frac{1}{\sqrt{2} + \sqrt{3} + \sqrt{7}}$, and write your answer in the form\[

Butoxors [25]

9514 1404 393

Answer:

Step-by-step explanation:

Apparently, you want to simplify ...

$\displaystyle \frac{1}{\sqrt{2} + \sqrt{3} + \sqrt{7}}$

so the denominator is rational. It looks like the form you want is ...

$\dfrac{A\sqrt{2} + B\sqrt{3} + C\sqrt{7} + D\sqrt{E}}{F}$

And you want to know the sum A+B+C+D+E+F.

We can start by multiplying numerator and denominator by a conjugate of the denominator. Then we can multiply numerator and denominator by a conjugate of the resulting denominator.

$\displaystyle =\frac{1}{\sqrt{2} + \sqrt{3} + \sqrt{7}}\cdot\frac{\sqrt{2} + \sqrt{3} - \sqrt{7}}{\sqrt{2} + \sqrt{3} - \sqrt{7}}=\frac{\sqrt{2} + \sqrt{3} - \sqrt{7}}{2\sqrt{6}-2}\\\\=\frac{\sqrt{2} + \sqrt{3} - \sqrt{7}}{2\sqrt{6}-2}\cdot\frac{\sqrt{6}+1}{\sqrt{6}+1}=\frac{(1+\sqrt{6})(\sqrt{2}+\sqrt{3}-\sqrt{7})}{10}\\\\=\frac{\sqrt{2}+\sqrt{3}-\sqrt{7}+2\sqrt{3}+3\sqrt{2}-\sqrt{42}}{10}=\frac{4\sqrt{2}+3\sqrt{3}-\sqrt{7}-\sqrt{42}}{10}$

Comparing this to the desired form we have ...

A = 4, B = 3, C = -1, D = -1, E = 42, F = 10

Then the sum is ...

A +B +C +D +E +F = 4 + 3 -1 -1 +42 +10 = 59 -2 = 57

The sum of interest is 57.

3 0

3 years ago

You find 72 coins consisting only of nickels, dimes, and quarters, with a face value of $10.20. However, the coins all date from

Oliga [24]

Answer:

You have found 24 nickels.

Step-by-step explanation:

Let N be the number of nickles, D be the number of dimes and Q be the number of quarters. The number of coins and their face values are given by the following expressions, respectively:

$N+D+Q=72\\0.05N+0.10D+0.25Q=10.20$

As of now we have three variables and two expressions, the final expression needed to solve the linear system is given by the amount offered by the coin dealer:

$10N+20D+15Q=1,060$

Solving the linear system:

$N+D+Q=72\\5N+10D+25Q=1,020\\10N+20D+15Q=1,060\\\\10N-10N+20D-20D+15Q-50Q=1,060-(2*1,020)\\-35Q=-980\\Q=28\\\\5N-10N+10D-10D+25Q-10Q=1,020-720\\-5N+15Q=300\\-5N=300-(15*28)\\N=24$