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OleMash [197]
3 years ago
5

6 4/5 + 3 2/3add and simplify ​

Mathematics
1 answer:
hram777 [196]3 years ago
5 0

Answer:

10 3/5

Step-by-step explanation:

6 4/5 + 3 4/5

First convert to improper fraction,

34/5 + 19/5

Then add the improper fractions,

=>53/5

Then convert improper fraction to mixed fraction,

=> 53/5 = 10 3/5

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Write an equation for the line parallel to the given line that contains <br> C(4,8);y=-3x+4
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Parallel line means they have the same slope 
y = mx + b 
where m = slope 
y = -3 + 4
here the slope is negative 3
y = -3x + b
plug in (4, 8)
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The answer is y = -3x + 20
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What is an exaple of linear
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Step-by-step explanation:

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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
Solve for x and complete the table
Naya [18.7K]

Answer:

x = 2

Table:

0,0

3,9

-2,-6

4,12

Step-by-step explanation:

distribute

3(2x+1)=15

6x+3 = 15

subtract 3 from both sides

6x + 3 = 15

6x + 3 - 3 = 15 - 3

simplify

6x= 12

divide both sides by 6

answer= x=2

8 0
3 years ago
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