Your cousin has $90 to spend on video games and movies. The equation 30x+15y=90 represents this situation, where x is the number of video games purchased and y is the number of movies purchased. Graph the equation.

9514 1404 393

  see attached

Step-by-step explanation:

The intercepts can be found by setting one variable to zero and solving for the other.

y-intercept: 30·0 +15y = 90  ⇒  y = 90/15 = 6, point (0, 6)

x-intercept: 30x +15·0 = 90  ⇒  x = 90/30 = 3, point (3, 0)

The graph is easily made by plotting the intercepts and drawing a line through them.

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I like to let a graphing calculator do the graphing.

since your problem is x^4 = 81, what you have to undeo is the "to the fourth power" part.

the inverse (opposite operation) of "to the fourth power" is "to the fourth root".

  (x^4) ^ ¼   = 81 ^ ¼  

  81 = 3^4     so (3 ^ 4) ^ ¼   =   3 ^ 1   = 3

by hand: (3 ^ 4) ^ ¼   =   3 ^ (4 x ¼) = 3 ^ 1   = 3   (when you take a power to a power, multiply the exponents.)

or, do it by calculator. one way of finding the fourth root is to use ^ (1/4)

step-by-step explanation:

walter needs to make at least 5 more cookies but no more than 40. 5 ≤ x ≤ 40

step-by-step explanation:

20 ≤ x + 15 ≤ 55

subtract 15 from all parts

20-15 ≤ x + 15-15 ≤ 55-15

5 ≤ x ≤ 40

this means how many more cookies he has to make

walter needs to make at least 5 more cookies, but no more than 40 cookies; 5 ≤ x ≤ 40