Alexa is a songwriter who collects royalties on her songs whenever they are played in a commercial or a movie. alexa will earn $20 every time one of her songs is played in a commercial and she will earn $110 every time one of her songs is played in a movie. alexa earned a total of $340 in royalties on 8 commercials and movies. write a system of equations that could be used to determine the number of commercials and the number of movies on which alexa's songs were played. define the variables that you use to write the system.

the equations are

x + y = 8

20x + 110y = 340

Step-by-step explanation:

Let x represent the number of commercials on which Alexa's songs were played.

Let y represent the number of movies on which Alexa's songs were played.

The total number of movies and commercials on which Alexa earned is 8. It means that

x + y = 8 - - - - - - - - - - - -1

Alexa will earn $20 every time one of her songs is played in a commercial and $110 every time one of her songs is played in a movie. Alexa earned a total of $340 in royalties. This means that

20x + 110y = 340 - - - - - - - - - - - -2

x =±sqrt(1/3)

step-by-step explanation:

x+4/6x=1/x

multiply each side by 6x to get rid of the fractions

6x*(x+4/6x)=1/x*6x

distribute

6x^2 +4 = 6

subtract 4 from each side

6x^2 +4-4 = 6-4

6x^2 =2

divide by 6

6x^2/6 = 2/6

x^2 = 1/3

take the square root of each side

sqrt(x^2) = ±sqrt(1/3)

x =±sqrt(1/3)

c. y = 1/4 x + 5

step-by-step explanation:

first, put the equation of the line on the graph into slope-intercept form

(y = mx + b):   y = -4x + 8

second, a perpendicular line has to have "an opposite/reciprocal slope" to the original slope. so, find the "m" value in your original equation (it's -4, right? )

original slope: m = -4   perpendicular slope: change the sign to its opposite and find the reciprocal ("flip" the number)

new slope is now positive (b/c the original slope was negative 4), and it's 1/4 (not the original slope of 4 or 4/1)