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3 years ago

Find the equation of the lines perpendicular and parallel to 2x-3y=8 line through the point (-2,-4)

Mathematics

1 answer:

marysya [2.9K]3 years ago

8 0

Answer:

y= -1.5x-7 is the equation of the perpendicular line

Here's why:

when we convert 2x-3y=8 to standard form, we get y= 2/3x-8/3. This means the perpendicular line will have a slope of the negative reciprocal of the original one, so the perpendicular slope is -1.5. When we substitute the points (-2,-4) into the equation y=-1.5x+b, we get a b value of -7. So the perpendicular line equation is y= -1.5x-7. You can't the parallel line equation with the points (-2,-4) as it is part of the line 2x-3y=8.

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Adrian is a songwriter who collects royalties on his songs whenever they are played in a commercial or movie. Adrian will earn $

gayaneshka [121]

Answer:

Adrian's songs played on 9 commercials and 5 movies.

Step-by-step explanation:

Let x denotes number of commercials and y denotes number of movies.

Total number of commercials and movies = 14

So,

$x+y=14\\x=14-y\,\,\,\,...(i)$

Adrian will earn $40 every time one of his songs is played in a commercial and he will earn $130 every time one of his songs is played in a movie

Total amount earned = $1010

$40x+130y=1010\,\,\,...(ii)$

Put $x=14-y$ in (ii)

$40(14-y)+130y=1010\\560-40y+130y=1010\\90y=1010-560\\90y=450\\y=\frac{450}{90}=5$

Put $y=5$ in $x=14-y$

$x=14-5=9$

Therefore, Adrian's songs played on 9 commercials and 5 movies.

7 0

3 years ago

A rectangular soccer field is twice as long as it is wide. If the perimeter of a soccer field is 300 yards, what are the fields'

Masteriza [31]

<span>A rectangular soccer field is twice as long as it is wide. If the perimeter of the soccer field is 300 yards , what are its dimensions?
I know the basic formula is 2W+2L=300 but i am not sure where to go from there...
-----
Equations:
2W + 2L = 300
L = 2W
----
Substitute for "L" and solve for "W":
</span><span>2W + 2(2W) = 300
6W = 300
W = 50 yds (width)
----
Solve for "L":
L = 2W
L = 100 yds (length)
========================
Cheers.
</span>

8 0

3 years ago

Prove that <img src="https://tex.z-dn.net/?f=cos%209x-cos%205x%2Fsin17x-sin3x%3D-sin2x%2Fcos10x" id="TexFormula1" title="cos 9x-

maria [59]

Cos9x - cos5x = -2sin2x.sin7x
sin17x - sin3x = 2sin7x.cos10x
so f(x) = $\frac{-2sin2x.sin7x}{2sin7x.cos10x}$ = $\frac{-sin2x}{cos10x}$

8 0

3 years ago

Please help in all :)

storchak [24]

1.object pronoun
2subject pronoun
3reflexive pronoun 4.object pronoun

7 0

3 years ago

Which graph represents the function f(x) = 2 x – 1 + 2?

tatuchka [14]

Answer:

The graph is positive and would have a y intercept of 1 and a slope of 2 which means choose a point on the graph and add 2 to the y and 1 to the x and you should be at the next point on the line.

Step-by-step explanation:

y=mx+b

f(x)=y

m = slope

b = y intercept

First you need to make it look like y=mx+b

y = 2x - 1 + 2

y = 2x + 1

Now we can say,

m = 2

b = 1

or,

Slope = $\frac{2}{1}$

y intercept = 1

Slope (m) = $\frac{rise}{run}$

So the numerator is the value your are going to go up or down along the graph and the denominator is the value of how far you are going to go left or right along the graph. If the slope is positive then the graph is inclining. If the slope is negative, the graph is declining.

5 0

3 years ago