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2 years ago

Find an equation of the line perpendicular to the graph of 15x-5y=7 that passes through the point at (0,-4)

Mathematics

2 answers:

vichka [17]2 years ago

7 0

Answer:

b. y=-1/3x-4

Step-by-step explanation:

shusha [124]2 years ago

4 0

Perpendicular lines have slopes that multiply to -1
get into y=mx+b form
minus 15x both sides and divide by -5
y=3x-7/5
slope is 3

3 times what=-1?
what=-1/3

so the slope is -1/3

so
y=-1/3x+b
we use the point (0,-4)
x=0 and y=-4
-4=-1/3(0)+b
-4=b

y=(-1/3)x-4 is da equation

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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.

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2 years ago

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ikadub [295]

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Step-by-step explanation:

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2 years ago

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zepelin [54]

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3 years ago

Kate begins solving the equation StartFraction 2 Over 3 EndFraction left-parenthesis 6 x minus 3 right-parenthesis equals StartF

mixas84 [53]

Answer:

<h3>The best interpretation of this equation 4x=3x is that the equation has no solution</h3>

Step-by-step explanation:

Given that Kate begins solving the equation

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<h3>To find the best interpretation of the given equation :</h3><h3>Katie's steps are</h3>

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When she adds 2 to both sides, the equation becomes

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<h3>Therefore the given equation has no solution </h3><h3>The best interpretation of this equation 4x=3x is that the equation has no solution.</h3><h3>Therefore the option no solution is correct</h3>

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Step-by-step explanation:

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