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nikklg [1K]
3 years ago
10

i need help with this one, like i chose 3/5,5 but i cant exactly explain my reasoning and im still second guessing myself lol so

can someone please help me with this?

Mathematics
1 answer:
solmaris [256]3 years ago
4 0

oh because in each one they are flipped

even in the one with 4, 1/4 because 4 = 4/1

and 5 would be 5/1 which would not be the flip of 3/5

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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
What is the equation of the line, in slope-intercept form, that passes through the point (0,7) and is perpendicular to the line
Alex Ar [27]
A line perpendicular to another occurs at the negative reciprocal of the slope of the original line. Why this is, I can further explain in the comments if you're interested. What is a reciprocal though? a reciprocal, if you're unfamiliar, is just the flipped form of it.

As an example, the negative reciprocal of 1/4 is -4/1. I multiplied 1/4 by a negative, and flipped the fraction.

So, what would the negative reciprocal of 3 be? well, you can imagine 3 to be 3/1 to help. so we multiply it by a negative, which gives us -3/1, and then we flip it, giving us -1/3. This is the slope of our unknown line. Because of this, we can mark out...well all of them haha. You need to double check your question and answers provided. With the info you've given me, none of your answers are correct. Let me know what happened if you can! if not, I would question your teacher, cause they messed up somewhere haha.
5 0
3 years ago
A bike repair shop charges $15.40 for parts plus $8.50 for labor to fix Jessica's bike. a) How much would Jessica pay for 2.5 ho
Alika [10]
15.40 + 8.50l (l is variable for labor)
8.50 x 2.5 = 21.25
15.40 + 21.25 = 36.65.
That is the answer for A.

504.20 - 15.40 = 488.80
488.80 / 8.50 = <span>57.50
About 57.50 hours for B.</span>
7 0
3 years ago
What is the length of each side of a square that has the same areas as the rectangle below? Round to the nearest tenth. Height:
NikAS [45]
I feel like the answer is c

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3 years ago
A trapezoid is a quadrilateral with exactly one pair of parallel sides <br> A) true <br> B)False
Alenkinab [10]
The answer is true to your question
7 0
3 years ago
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