What steps would you use to plot (−3, −4, 0) in a 3-dimensional coordinate system?

a. from the origin, move back 3 units and down 4 units.
b. from the origin, move back 3 units and left 4 units.
c. from the origin, move down 3 units and left 4 units.
d. from the origin, move back 3 units and up 4 units.

a. From the origin, move back 3 units and down 4 units

Step-by-step explanation:

Given:

The coordinates of a point in a 3-dimensional space is given as:

(-3, -4, 0)

The value of 'x' = -3

The value of 'y' = -4

The value of 'z' = 0

At the origin, the values of 'x', 'y', and 'z' are each equal to 0.

So, the coordinates of origin is (0, 0, 0). In order to reach the point (-3, -4, 0) from the point (0, 0, 0), we don't move along the z-axis as the 'z' value remains the same. We need to move along the 'x' and 'y' directions only.

Now, 'x' is equal to -3. Negative values of 'x' occur backwards from origin. So, we move back by 3 units. to reach the point (-3, 0).

Now, the value of 'y' is -4. Negative values of 'y' occur below the origin. So, we move down by 4 units to reach the point (-3, -4).

Therefore, the correct option is option (a)

A graph in 2 dimensional is shown in support of the answer.

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

whose power in the senate is equal to the power of the speaker of the house?

step-by-step explanation: