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Shkiper50 [21]
3 years ago
8

What is the unit rate of 6 eggs in 7 days

Mathematics
1 answer:
alexgriva [62]3 years ago
7 0
6 eggs= 7 days

1 egg = x days


7 days _
----------- = 1. 6 days per 1 egg
6 eggs
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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:

  57

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
2 years ago
HARD QUADRATICS!!!! A quadratic of the form $-2x^2 + bx + c$ has roots of $x = 3 + \sqrt{5}$ and $x = 3 - \sqrt{5}.$ The graph o
iren2701 [21]

Answer:

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Step-by-step explanation:

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3 years ago
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5a + 3b - 6a - b.
5a - 6a + 3b - b.  Then simplify.
-a + 2b.

That's it.
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