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3 years ago

Write an equation of the line that is perpendicular to the line y =

Mathematics

1 answer:

inn [45]3 years ago

6 0

Answer:

Step-by-step explanation:

$\text{Let}\\\\k:y=m_1x+b_1\\\\l:y=m_2x+b_2\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\\\l\ \parallel\ k\iff m_1=m_2\\\\===============================$

$\text{We have the equation}\ y=\dfrac{1}{3}x+6\to m_1=\dfrac{1}{3}.\\\\\text{Therefore}\ m_2=-\dfrac{1}{\frac{1}{3}}=-3.\\\\\text{We have the equation}\ y=-3x+b.\\\\\text{Put the coordinates of the point}\ (2,\ -3):\\\\-3=-3(2)+b\\-3=-6+b\qquad\text{add 6 to both sides}\\3=b\to b=3\\\\\text{Finally:}\\\\y=-3x+3$

You might be interested in

Given the matrices: 1 2 A= 1 -1 2 1 1 B= 3 4 Calculate AB: C11 C12 [2.1] х 1 2 3 4 C21 C22 C11 = C12 = -2 C22 - C215 DONE

eduard

Answer:

$\:c_{11}=-2,\:\:\:c_{12}=-2$

$\:c_{21}=5,\:\:\:c_{22}=8$

Step-by-step explanation:

Given the matrices

$A=\begin{pmatrix}1&-1\\ 2&1\end{pmatrix}$

$B=\begin{pmatrix}1&2\\ \:3&4\end{pmatrix}$

Calculating AB:

$\begin{pmatrix}1&-1\\ \:\:2&1\end{pmatrix}\times \:\begin{pmatrix}1&2\\ \:\:3&4\end{pmatrix}=\begin{pmatrix}c_{11}&c_{12}\\ \:\:\:c_{21}&c_{22}\end{pmatrix}$

Multiply the rows of the first matrix by the columns of the second matrix

$=\begin{pmatrix}1\cdot \:1+\left(-1\right)\cdot \:3&1\cdot \:2+\left(-1\right)\cdot \:4\\ 2\cdot \:1+1\cdot \:3&2\cdot \:2+1\cdot \:4\end{pmatrix}$

$=\begin{pmatrix}-2&-2\\ 5&8\end{pmatrix}$

Hence,

$\begin{pmatrix}c_{11}&c_{12}\\ \:\:\:c_{21}&c_{22}\end{pmatrix}=\begin{pmatrix}-2&-2\\ \:5&8\end{pmatrix}$

Therefore,

$\:c_{11}=-2,\:\:\:c_{12}=-2$

$\:c_{21}=5,\:\:\:c_{22}=8$

5 0

3 years ago

Read 2 more answers

Kurt says factors and multiples are

maxonik [38]

<u>Step-by-step Explanation:</u>

<em>Before heading towards the solution, you need to make sure how multiple and factors are related to each other.</em>

<em>The multiple of a number could be obtained by multiply it with another number. </em>

For example, the first five multiples of 12 are 12, 24, 36, 48 and 60

1 X 12 = 12
2 X 12 = 24
3 X 12 = 36
4 X 12 = 48
5 X 12 = 60

<em>Factors are the numbers that are multiplied to get a given number.</em>

For example,

1 X 12 = 12
2 X 12 = 24
3 X 12 = 36

The factors of 12 are 1, 2, 3, 4, 6 and 12.

As division and multiplication can be used to find factors and multiples.

For example a whole number is a multiple of its factors.

Let w = {2, 4, 6, 8, 10, 12, 14, 16, 18, 20} be the set of even wholes numbers from 2 to 20.

As 2 is a factor of 20 because 20 ÷ 2 = 4

20 is a multiple of 2 because 2 X 10 = 20

So, in the same way, the equation 8 X 5 = 40 can be used to determine how factors and multiples are related.

Let the equation be

8 X 5 = 40

8 is a factor of 40 because 8 X 5 = 40

40 is a multiple of 8 because 40 ÷ 5 = 8

<em>So, this is how factors and multiples are related to each other.</em>

<em />

<em>Keywords: factors, multiples, division, multiplication</em>

<em> Learn more about factors and multiples from brainly.com/question/596356</em>

<em> #learnwithBrainly</em>

4 0

3 years ago

Fred and Sue want to fence in a rectangular area in their yard for a vegetable garden. Suppose that they have 30 feet of fencing

larisa [96]

Answer:

a=35x−x^2

Step-by-step explanation:

Having

70 ft of fencing with a

width of x

feet and knowing the perimeter of a rectangle is

p=2w+2l

we can state the length of the garden as:

70=2x+2l

and solving for l

we know the length with be:

2l=70−2x or l=35−x

And then knowing the formula for the area of a rectangle is

a=w⋅l

we can write the equation as:

a=x⋅(35−x)a=35x−x^2

6 0

3 years ago

Read 2 more answers

Given the quadratic relation y = -x2 + 6x - 6, a) write the equation in vertex form b) graph the quadratic relation (using noteb

Mekhanik [1.2K]

<h3>Answer:</h3>

y = -(x -3)² +3 . . . . (agrees with your answer)
see the attachment for a graph

<h3>Step-by-step explanation:</h3>

Factoring the leading -1 from the first two terms, we have ...

... y = -(x² -6x) -6

Adding 9 inside parentheses to complete the square, then adding the opposite amount outside parentheses, we have ...

... y = -(x² -6x +9) -6 +9

... y = -(x -3)² +3

8 0

4 years ago

If x= -3, and -3 = y, then what can be said about the relationship between x and y? Explain

ella [17]

I'd say that the relationship between y and x is that they're both equivalent to each other, since -3 = -3.

7 0

3 years ago

Read 2 more answers