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3 years ago

Write an equation of the line satisfying the given conditions. Through (2, -5), parallel to 5x 6y + 7

Mathematics

1 answer:

mojhsa [17]3 years ago

8 0

We have to determine the equation of the line passing through the point (2,-5) and parallel to the line $5x = 6y+7$

When two lines are parallel, then the slopes of the two lines are equal.

Equation of line with point $(x_1, y_1)$ and slope 'm' is given by:

$(y-y_1) = m(x-x_1)$

Since, we have to determine the equation of a line with point (2,-5).

So, the equation of the line is : $(y-(-5)) = m(x-2)$

$y+5 = m(x-2)$

Since, the line is parallel to the line $5x = 6y+ 7$

So, $6y +7 = 5x$

$6y = 5x - 7$

$y = \frac{5}{6}x - \frac{7}{6}$

So, slope of the line 'm' is $\frac{5}{6}$ .

Therefore, the equation of the line is:

$(y+5) = \frac{5}{6}(x-2)$

$6y + 30 = 5x - 10$

$6y - 5x = -10-30$

$6y - 5x = -40$

Therefore, $6y - 5x = -40$ is the required equation of the line.

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Answer:

0.45

Step-by-step explanation:

4/10 is 0.4

and

5/100 is 0.05

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3 years ago

Complete these activities. Consider the following information from Tiger Oil Company: By multiplying matrices, calculate the mat

kherson [118]

Given the matrix

$\left[\begin{array}{cc}20&30\\15&5\\5&2\end{array}\right]$

representing the number of thousands of gallons of regular and premium oil sold by the three stations of Tiger oil company and the matrix

$\left[\begin{array}{c}500\\600\end{array}\right]$

representing dolloars per thousands of gallons of regular and premium oil sold by Tiger oil company.

The matrix for total dollar volume of sales using matrix multiplication is given by:

$\left[\begin{array}{cc}20&30\\15&5\\5&2\end{array}\right] \left[\begin{array}{c}500\\600\end{array}\right]= \left[\begin{array}{c}20(500)+30(600)\\15(500)+5(600)\\5(500)+2(600)\end{array}\right] \\ \\ = \left[\begin{array}{c}10000+18000\\7500+3000\\2500+1200\end{array}\right] =\left[\begin{array}{c}28000\\10500\\3700\end{array}\right]$

Therefore, the total dolar volume of sales is per thousand of gallons of oil is given by:

$\left[\begin{array}{c}28000\\10500\\3700\end{array}\right]$

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4 years ago

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In a market economy, if the price of a good increases, the quantity demanded by consumers and the quantity supplied by producers

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The correct answer is A hope this helps

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4 years ago

Original price: $23.37 with tax : $24.91 what is the sales tax percentage

Marina86 [1]

Answer:

6.6% = tax rate

Step-by-step explanation:

The first step is to find out how much was paid in tax

24.91 - 23.37 =1.54

The tax is 1.54

The tax is the original price * tax rate

1.54 = 23.37 * tax rate

Divide each side by 23.37

1.54/23.37 = tax rate

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Changing to percent form

6.6% = tax rate

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4 years ago

If cos Θ = square root 2 over 2 and 3 pi over 2 < Θ < 2π, what are the values of sin Θ and tan Θ? sin Θ = square root 2 ov

densk [106]

Answer:

$\huge\boxed{\sin\theta=-\dfrac{\sqrt2}{2};\ \tan\theta=-1}$

Step-by-step explanation:

We have:

$\\cos\theta=\dfrac{\sqrt2}{2},\ \dfrac{3\pi}{2}$

For sine use:

$\sin^2x+\cos^2x=1\to\sin^2x=1-\cos^2x$

Substitute:

$\sin^2\theta=1-\left(\dfrac{\sqrt2}{2}\right)^2\\\\\sin^2\theta=1-\dfrac{(\sqrt2)^2}{2^2}\\\\\sin^2\theta=1-\dfrac{2}{4}\\\\\sin^2\theta=\dfrac{4}{4}-\dfrac{2}{4}\\\\\sin^2\theta=\dfrac{4-2}{4}\\\\\sin^2\theta=\dfrac{2}{4}\to\sin\theta=\pm\sqrt{\dfrac{2}{4}}\\\\\sin\theta=\pm\dfrac{\sqrt2}{\sqrt4}\\\\\sin\theta=\pm\dfrac{\sqrt2}{2}$

θ in IV quadrant, therefore sine is negative.

$\sin\theta=-\dfrac{\sqrt2}{2}$

For tangent use:

$\tan x=\dfrac{\sin x}{\cos x}$

Substitute:

$\tan\theta=\dfrac{-\frac{\sqrt2}{2}}{\frac{\sqrt2}{2}}=-\dfrac{\sqrt2}{2}\cdot\dfrac{2}{\sqrt2}=-1$

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3 years ago