Which of the points are solutions to the inequality? check all that apply. (–3, 3) (–2, –2) (–1, 1) (0, 1) (2, 5)

The points (–2, –2), (–1, 1), (0, 1), and (2, 5) satisfy the inequality. While, the point (–3, 3) doesn't satisfy the inequality.

The given inequality is .

Refer to the image, to understand the graph of the given inequality.

Now, it is required to check whether the points satisfy the inequality or not.

Consider the point (–3, 3). Now, check if the point satisfies the inequality or not as,

The above conclusion is wrong as 3 is greater than -3. So, the point doesn't satisfy the inequality.

Consider the point (–2, –2). Now, check if the point satisfies the inequality or not as,

The above conclusion is right as -2 is less than -1. So, the point satisfies the inequality.

Consider the point (–1, 1). Now, check if the point satisfies the inequality or not as,

The above conclusion is right as -1 is less than 5. So, the point satisfies the inequality.

Consider the point (0, 1). Now, check if the point satisfies the inequality or not as,

The above conclusion is right as 0 is less than 5. So, the point satisfies the inequality.

Consider the point (2, 5). Now, check if the point satisfies the inequality or not as,

The above conclusion is right as 2 is less than 13. So, the point satisfies the inequality.

Therefore, the points (–2, –2), (–1, 1), (0, 1), and (2, 5) satisfy the inequality.

For more details, refer to the link:

link

replace x with the first number inside the parenthesis, do the equation and see if the answer is greater than the 2nd number inside the parenthesis.

 when doing that (-2,-2), (0,1) and (2,5) are all solutions

a) $ 9.50

b) 17

c) y-intercept (0, 12). this is the initial amount of money that joe had prior to playing any game.

d) x-intercept ( 24, 0). this is the number of games that joe will play before he depletes the initial amount of money that he had.

e) slope is -0.5. joe's balance will reduce by 0.5 for every game that he plays.

f)

domain; [0,24]

range; [0,12]

g) x + 2y = 24

step-by-step explanation:

a)

if joe plays 5 games, this will imply that x = 5. substitute x = 5 in the equation and solve for y;

y = -.50x + 12

y = -0.50(5) + 12

y = 9.50

b)

if joe leaves the arcade with $3.50, this will mean that y = 3.50. plug in y = 3.50 in the given equation and solve for x;

y = -.50x + 12

3.50 = -0.50x + 12

0.50x = 12 - 3.50

0.5x = 8.5

x = 17

c)

the function given is   y = -.50x + 12.

the y-intercept is the point where the graph of this function will intersect the y-axis. at this point, the value of x is usually 0. plug in x = 0 in the given equation and determine y;

y = -0.50(0) + 12

y = 12

the y-intercept is thus (0, 12). this is the initial amount of money that joe had prior to playing any game.

d)

the x-intercept refers to the point where the graph of a function intersects with the x-axis. at this point, the value of y is 0. substitute y = 0 in the given equation and solve for x;

0 =   -.50x + 12

0.5x = 12

x = 24

x-intercept ( 24, 0). this is the number of games that joe will play before he depletes the initial amount of money that he had.

e)

the slope of the given equation is -0.5. the equation has been given in slope-intercept form. thus the slope is simply the coefficient of x.

joe's balance will reduce by 0.5 for every game that he plays. this is the interpretation of the slope.

f)

domain is the set of x values for which the function is real and defined. the domain will thus be; [0,24]. this will restrict the balance to only assume positive values.

on the other hand, the range is the set of y values for which a function is real and defined. the range in our case will be [0,12]. joe can have between $0 and $12 balance.

g)

the standard form of the equation of a straight line is;

ax + by = c

where a, b, and c are integers.

our equation is given as;

y = -.50x + 12

re-writing the equation we have;

0.5x + y = 12

divide all through by 0.5;

x + 2y = 24