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3 years ago

Write the equation for a line that is perpendicular to the line 8x-4y=12 and passes through the orgin

Mathematics

1 answer:

Delicious77 [7]3 years ago

5 0

Answer:

y = - $\frac{1}{2}$ x

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Rearrange 8x - 4y = 12 into this form

Subtract 4x from both sides

- 4y = - 8x + 12 ( divide all terms by - 4 )

y = 2x - 3 ← in slope- intercept form

with slope m = 2

Given a line with slope m then the slope of a line perpendicular to it is

$m_{perpendicular}$ = - $\frac{1}{m}$ = - $\frac{1}{2}$

Since the line passes through the origin then c = 0

y = - $\frac{1}{2}$ x ← equation of perpendicular line

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What is the slope between the points (3, 5) and (-2, -4)

Tamiku [17]

The slope is 9/5! hope this helps!!

6 0

3 years ago

Which of the following matrices is the solution matrix for the given system of equations? x + 5y = 11 x - y = 5

givi [52]

<h2>The required solution is x = 6 and y = 11 </h2>

Step-by-step explanation:

Given system of equations are

x+5y = 11 and x-y =5

$A= \left[\begin{array}{cc}1&5\\1&-1\end{array}\right]$ $X=\left[\begin{array}{c}x\\y\end{array}\right]$

and $B= \left[\begin{array}{c}11\\5\end{array}\right]$

∴AX=B

$adj A = \left[\begin{array}{cc}{-1}&{-5}\\{-1}&1\end{array}\right]$

$A= \left|\begin{array}{cc}1&5\\1&-1\end{array}\right|=-6$

∴ $A^{-1} =\frac{adj A}{|A|}$

So, $A^{-1} =\frac{ \left[\begin{array}{cc}{-1}&{-5}\\{-1}&1\end{array}\right]}{-6}$

$A^{-1} ={ \left[\begin{array}{c \c} {{\frac{1}{6} }}&{\frac{5}{6}}\ \\ {{\frac{1}{6} }}&{\frac{-1}{6}} \end{array}\right]}$

$X =A^{-1}\times B$

⇒ $\left[\begin{array}{c}x\\y\end{array}\right] ={ \left[\begin{array}{c \c} {{\frac{1}{6} }}&{\frac{5}{6}}\ \\ {{\frac{1}{6} }}&{\frac{-1}{6}} \end{array}\right]} \times \left[\begin{array}{c}11\\5\end{array}\right]$

⇒ $\left[\begin{array}{c}x\\y\end{array}\right] ={ \left[\begin{array}{c} {6}\\ {11} \end{array}\right]}$

∴ x= 6 and y = 11

The required solution is x = 6 and y = 11

7 0

3 years ago

Please help me with this question. Thank you so much everyone.

LiRa [457]

Answer:

1159

Step-by-step explanation:

She wants to read 1000 pages per week for five weeks.

So in total she wants to read 1000 * 5 = 5000 pages.

The first three weeks she read 894 pages per week.

So during the first three weeks she read a total of 894 * 3 = 2682 pages.

We want to find how many pages she must read per week for the last two weeks to reach her goal.

Goal: 5000 pages

Pages read so far: 2682

Weeks remaining: 2

To find how many pages she must read for the last two weeks we simply subtract the number of pages she read during the first 3 weeks (2682 ) by her goal ( 5000 )

5000 - 2682 = 2318

So she must read 2318 pages during the last 2 weeks.

If we want to find the amount of pages she must read per week during the last 2 weeks to reach her goal, we simply divide the amount of pages she must read during the last few weeks to reach her goal ( 2318 ) by the number of remaining weeks ( 2 )

2318 / 2 = 1159

So for the last two weeks she must average 1159 pages per week.

8 0

3 years ago

Read 2 more answers

Pls dont give just the answer, (you dont need to explain how to do it)

Alik [6]

Answer: 72

Step-by-step explanation: volume of a pyramid = v= lwh/3

v= 6*6*6/3

v = 216/3

v = 72