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eduard
3 years ago
14

Evaluate 7/8xc for c=8

Mathematics
1 answer:
Morgarella [4.7K]3 years ago
8 0
If it's 8 times c, your answer should be 7/64.
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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
2 years ago
Can somebody help me please
Andrej [43]

Answer:

A. 34/40

Step-by-step explanation:

8 0
3 years ago
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The table shows the results of rolling a number cube with sides labeled 1 through 6 several times.
faust18 [17]

Total times die rolled =10+6+4+8+6+6=40

Times 3 and 6 appears

  • 4+6=10

Experimental probability

P(3 or 6)

  • 10/40
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8 0
2 years ago
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Rectangle measures 15/2 inches by 4/3 inches. What is it’s area?
erica [24]

Answer:

10 inches squared

Step-by-step explanation:

Area is length times width

A= lw

A= 15/2 x 4/3

A = 60/6

A= 10 in^2

5 0
3 years ago
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In the game of roulette in the United States a wheel has 38 slots: 18 slots are black, 18 slots are red, and 2 slots are green.
topjm [15]

Answer:

green. You watched a friend play roulette for two hours. In that time you noted that the wheel was spun 50 times and that out of those 50 spins black came up 22 times. Based on this data, the This is an exgreen. You watched a friend play roulette for two hours. In that time you noted that the wheel was spun 50 times and that out of those 50 spins black came up 22 times. Based on this data, the This is an ex

Step-by-step explanation:

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8 0
2 years ago
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