All categories

4 years ago

Find the equation of the line through ( - 10, - 8) that is perpendicular to the line through (10,6), (5,5).

Mathematics

1 answer:

Furkat [3]4 years ago

4 0

Answer:

y=-5x-58

Step-by-step explanation:

The equation of a line in slope-intercept form is y=mx+b where m is the slope and b is the y-intercept.

Perpendicular lines have opposite reciprocal slopes.

Anyways we need to find the slope of the line going through (10,6) and (5,5).

To find the slope, we are going to line up the points vertically and subtract vertically, then put 2nd difference over 1st difference. Like so:

( 10 , 6)

- ( 5 , 5)

------------------

5 1

So the slope of the line through (10,6) and (5,5) is 1/5.

The slope of a line that is perpendicular will be the opposite reciprocal of 1/5.

The opposite reciprocal of 1/5 is -5.

The line we are looking for is y=-5x+b where we need to find the y-intercept b.

y=-5x+b goes through (-10,-8)

So we can use (x,y)=(-10,-8) to find b in y=-5x+b.

y=-5x+b with (x,y)=(-10,-8)

-8=-5(-10)+b

-8=50+b

Subtract 50 on both sides:

-8-50=b

-58=b

So the equation is y=-5x-58

You might be interested in

Help with matrices please? Any wrong/not applicable answers will be reported and BLOCKED

marin [14]

m x H = $\left[\begin{array}{ccc}-25&37.5&-12.5\\\9\end{array}\right]$

Step-by-step explanation:

Step 1; Multiply 5 with this matrix $\left[\begin{array}{ccc}-1&2\\4&8\\\end{array}\right]$ and we get a matrix $\left[\begin{array}{ccc}-5&10\\20&40\\\end{array}\right]$

Multiply the fraction $\frac{2}{5}$ with the matrix $\left[\begin{array}{ccc}-1&2\\4&8\\\end{array}\right]$ and we get $\left[\begin{array}{ccc}-\frac{2m}{5} &\frac{4m}{5} \\\frac{8m}{5} &\frac{16m}{5} \\\end{array}\right]$

Step2; Now equate corresponding values of the matrices with each other.

-5 = $\frac{-2m}{5}$ and so on. By equating we get the value of m as $\frac{25}{2}$

Step 3; Add the matrices to get the value of matrix m.

Adding the three matrices on the RHS we get $\left[\begin{array}{ccc}2&9&-9\\\end{array}\right]$ .

Step 4; Adding the matrices on the LHS we get the resulting matrix as H +

$\left[\begin{array}{ccc}4&6&-8\\\9\end{array}\right]$ . Equating the matrices from step 3 and 4 we get the value of H as $\left[\begin{array}{ccc}-2&3&-1\\\9\end{array}\right]$

Step 5; Now to find the value of m x H we need to multiply the value of $\frac{25}{2}$ with the matrix $\left[\begin{array}{ccc}-2&3&-1\\\9\end{array}\right]$

Step 6; Multiplying we get the matrix m x H = [ -25 $\frac{75}{2}$ $\frac{-25}{2}$ ]

8 0

3 years ago

Write the recurring decimal 0.05 as a fraction in its simplest form

lidiya [134]

Answer:

1/20

Step-by-step explanation:

Step 1: Write the given number as the numerator and place 1 in the denominator right below the decimal point followed by the number of zeros required accordingly.

In this case, 0.05 has two numbers after the decimal, so, we place 100 in the denominator and remove the decimal point. This will make it 5/100

Step 2: Then, this fraction can be simplified. 5/100 = 1/20

Thus, 0.05 as a fraction is written as 1/20

6 0

2 years ago

Read 2 more answers

Y 5x=2<br><br> What are the coordinates

Brums [2.3K]

Answer:move -5x to the right becomes 5x

Y=5X+2

When x =1 5(1)+2= 7 for Y

When X=2 5(2)+2= 12 for Y

When X =-1 5[-1)+2/ -3

Coordinates (1,7).(2,12)(-1,-3)

Step-by-step explanation:

3 0

3 years ago

pychu [463]

B and D when you multiply them there 11.16 but we want 1.116

5 0

3 years ago

Select the correct answer.

Elena L [17]

Answer:

b because first u need to remove the parentheses then u disturbe

8 0

3 years ago