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3 years ago

Are the two lines parallel, perpendicular, or neither? Explain your answer. Show work needed to answer the question.

Mathematics

1 answer:

tatuchka [14]3 years ago

8 0

Answer:

The lines are perpendicular

Step-by-step explanation:

The correct question is

Are the two lines parallel, perpendicular, or neither? Explain your answer

3x + 7y = 15

7x − 3y = 6

we know that

If two lines are parallel, then their slopes are equal

If two lines are perpendicular, then their slopes are opposite reciprocal (the product of the slopes is equal to -1)

Remember that

The equation of the line in slope intercept form is equal to

$y=mx+b$

where m is the slope

b is the y-intercept

we have

$3x + 7y = 15$ ----> equation A

isolate the variable y and convert the equation in slope intercept form

$y=\frac{15-3x}{7}$

$y=\frac{15}{7}-\frac{3}{7}x$

The slope of the line A is $m_A=-\frac{3}{7}$

$7x-3y = 6$ ---> equation B

isolate the variable y and convert the equation in slope intercept form

$y=\frac{7x-6}{3}$

$y=\frac{7}{3}x-2$

The slope of the line B is $m_B=\frac{7}{3}$

Compare the slopes

$m_A\neq m_B$ ---> the lines are not parallel

$m_A* m_B=(-\frac{3}{7})*(\frac{7}{3})=-1$

The slopes are opposite reciprocal

therefore

The lines are perpendicular

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3 years ago

Read 2 more answers

What is the ratio of 1/6:6 = what

frutty [35]

1/6=16.666666...

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3 years ago

Describe and correct the error in finding the tenth term of the arithmetic sequence 4, 12, 20, 28.

ycow [4]

Answer: The tenth term is 76

=======================================================

Explanation:

We use this arithmetic sequence formula to get the nth term

$a_n = a_1 + d(n-1)$

Plug in $a_1 = 4, \ d = 8, \ n = 10$ and you should get the following:

$a_n = a_1 + d(n-1)\\\\a_{10} = 4 + 8(10-1)\\\\a_{10} = 4 + 8(9)\\\\a_{10} = \textbf{76}\\\\$

The tenth term is 76

---------

We can verify this by listing out the terms one by one. Start at 4, add on 8 each time, until you generate the 10th term. A table like the one shown below is a good way to keep track of all the terms.

$\begin{array}{c|c}\boldsymbol{n} & \boldsymbol{a_n}\\1 & 4\\2 & 12\\3 & 20\\4 & 28\\5 & 36\\6 & 44\\7 & 52\\8 & 60\\9 & 68\\10 & \textbf{76}\\\end{array}$

---------

In short, the error is with the "10" in the expression 4+10(8). The student should have used 9 instead. This is because of the n-1 term in $a_n = a_1 + d(n-1)$ which shifts everything one spot to the left.

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2 years ago

PQRS is a rectangle.

Anuta_ua [19.1K]

Answer:

diagram pls

then I can answer this question

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3 years ago

A rectangle has an area of 171 square meters. Its width is ten meters less than the length. Find the measures of the length and

9966 [12]

Step-by-step explanation:

The area of a rectangle is 171 m²

Let l is the length and b is the width of the rectangle

It width is 10 m less than the length. So,

b = l-10 ...(1)

Area of a rectangle is given by :

$A=l\times b\\\\171=l(l-10)\\\\l^2-10l=171\\\\l^2-10l-171=0\\\\l^2-19l+9l-171=0\\\\\text{taking common together}\\\\l(l-19)+9(l-19)=0\\\\(l-9)(l-19)=0$

l = 9 m or l = 19 m

If l = 9 m,

b = 9-10 = -1 m (can't be possible)

If l = 19 m

b = 19-10 = 9 m

So, the length an the breadth of the rectangle is 19 m and 9 m respectively.

8 0

3 years ago