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tatiyna
4 years ago
7

Paul needs to buy 5/8th pounds of peanuts. The scale measures parts of a pound in 16th's. What measurement is equivalent to 5/8p

ounds?
Mathematics
1 answer:
Marysya12 [62]4 years ago
6 0
Equivalent fractions can be formed by multiplying (or dividing) numerator and denominator by the same number.
\frac{5}{8} = \frac{5 \times 2}{8 \times 2} = \frac{10}{16}

A measurement of 10/16 pounds is equivalent to 5/8 pounds.
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Form a polynomial whose zeros and degree are given.<br> Zeros:-4,4,5; degree:3
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f(x) = x³ − 5x² − 16x + 80

Step-by-step explanation:

The degree is 3, so there are exactly 3 zeros.

The zeros are -4, 4, and 5.

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f(x) = (x² − 16) (x − 5)

f(x) = x³ − 5x² − 16x + 80

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As far as I can tell is just a Permutation.

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Express (8 - 3sqrt(2))/(4 + 3sqrt(2)) in the form of a + b * sqrt(2) where a and b are integers.​
Naya [18.7K]

Answer:   \boldsymbol{-25+18\sqrt{2}}

The expression is in the form a+b\sqrt{2} where a = -25 and b = 18

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

Work Shown:

Let x = 3\sqrt{2} and then square both sides

x = 3\sqrt{2}\\\\x^2 = \left(3\sqrt{2}\right)^2\\\\x^2 = \left(3\right)^2*\left(\sqrt{2}\right)^2\\\\x^2 = 9*2\\\\x^2 = 18\\\\

We'll use both x and x^2 later on.

---------------------

The denominator is in the form 4+x. We'll multiply top and bottom by 4-x to then use the difference of squares rule. This will allow us to eliminate the square root in the denominator.

\frac{8-3\sqrt{2}}{4+3\sqrt{2}}\\\\\frac{8-x}{4+x}\\\\\frac{(8-x)(4-x)}{(4+x)(4-x)}\\\\\frac{32-8x-4x+x^2}{16-x^2} \ \text{ difference of squares rule}\\\\\frac{32-12x+x^2}{16-x^2}\\\\

\frac{32-12*3\sqrt{2}+18}{16-18} \ \text{ plug in } x = 3\sqrt{2} \text{ and } x^2 = 18\\\\\frac{50-36\sqrt{2}}{-2}\\\\\frac{-2(-25+18\sqrt{2})}{-2}\\\\\boldsymbol{-25+18\sqrt{2}}

Therefore,

\frac{8-3\sqrt{2}}{4+3\sqrt{2}}=\boldsymbol{-25+18\sqrt{2}}

-------------------------------------

Checking the answer:

Use a calculator to find that,

\frac{8-3\sqrt{2}}{4+3\sqrt{2}} \approx 0.45584412271571 \\\\-25+18\sqrt{2} \approx 0.45584412271571

We get the same decimal approximation, which helps confirm the correct answer.

Or you could use the idea that if M = N, then M-N = 0 to subtract the original expression M and the final result N. You should get 0 or very close to it.

3 0
3 years ago
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