The price for digital downloads of music is represented by the linear functions f(x) shown on the graph. The price for digital downloads of movies is represented by g(x) = 3x, where x is the number of movies downloaded and g(x) is the total cost in dollars.

You don't have enough money for 2 downloads

Step-by-step explanation:

The complete question is

The price for digital downloads of music is represented by the linear function f(x) shown on the graph. The price for digital downloads of movies is represented by g(x) = 3x, where x is the number of movies downloaded and g(x) is the total cost in dollars. Graph of a line with equation f of x equals one half times x plus 2. The x-axis is labeled Number of Songs, and the y-axis is labeled Price in Dollars. You want to make 2 downloads, and you have $2.50. Determine the least expensive option.

You download 2 songs.

You download 2 movies.

You download 1 song and 1 movie.

You don't have enough money for 2 downloads.

we have

---> price for digital downloads of music

---> price for digital downloads of movies

Verify all the options

case 1) You download 2 songs

Calculate f(2)

For x=2

This option is not possible because

$3>$2.50 (don't have enough money)

case 2) You download 2 movies.

Calculate g(2)

For x=2

This option is not possible because

$6>$2.50 (don't have enough money)

case 3) You download 1 song and 1 movie.

Calculate f(1) and g(1)

For x=1

so

This option is not possible because

$5.5>$2.50 (don't have enough money)

case 4) You don't have enough money for 2 downloads

The statement is true

You have only enough money for download 1 song

5x + 3y = - 4

step-by-step explanation:

the equation of a line in standard form is

ax + by = c ( a is a positive integer and b, c are integers )

express the line first of all in slope- intercept form

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

to calculate m use the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (7, - 3) and (x₂, y₂ ) = (4, - 8)

m = = -

y = - x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (4, - 8 ), then

- 8 = - + c ⇒ c = -

y = - x - ← in slope-intercept form

multiply all terms by 3 to eliminate the fractions

3y = - 5x - 4 ( add 5x to both sides )

5x + 3y = - 4 ← in standard form

answer: -10

step-by-step explanation:

s(t) = 1 - 10t

s(x) = 1 - 10x

s(x + h) = 1 - 10(x + h)

            = 1 - 10x - 10h

s(x + h) - s(x) = 1 - 10x - 10h - (1 - 10x)

                      = 1 - 10x - 10h - 1 + 10x

                      = -10h

= -10