Use the figure to identify each pair of angles as complementary angles, supplementary angles, vertical angles, or none of these.

The figure shows a vertical line and three points Upper A, Upper P, and Upper E are labeled on it. From the point Upper P, a horizontal ray goes towards right and a point Upper C is labeled on it. A diagonal line also passes through Upper P. Two points, Upper D, and Upper B are shown on this diagonal line such that Upper P is between Upper D, and Upper B. Angle UpperWord APC is a right angle, and is labeled as 2, angle UpperWord CPB is labeled as 1, angle UpperWord BPE is labeled as 5, angle UpperWord EPD is labeled as 4, and angle UpperWord DPA is labeled as 3.

angles 1 and 5
angles 3 and 5
angles 3 and 4

Angle 1 and Angle 5:

complementary angles

Angle 3 and Angle 5:

vertically opposite angles

Angle 3 and Angle 4:

Supplementary angles

comp, vert, then sup

Step-by-step explanation:

Angles 1 and 5 combine to form a 90 degree angle so they are Complementary Angles.

Angles 3 and 5 are on opposite side of the crossed lines and are of equal degree so they are Vertical Angles.

Angles 3 and 4 combine to equal 180 degrees so they are Supplementary Angles.

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

your answer would be b

step-by-step explanation: