What can be concluded about a cylinder and a cone with the same height and radius measures? Check all that apply.
The cone has the greater volume.
The cone and cylinder have the same base area.
The volume of the cone is One-third the volume of the cylinder.
The cylinder can fit inside the cone.
The cone and cylinder have the same diameter.

I) The cone and cylinder have the same base area.

ii) The volume of the cone is One-third the volume of the cylinder.

iii) The cone and cylinder have the same diameter

Step-by-step explanation:

i) The cone and cylinder have the same base area.

Since they both have the same radius measures. And formula for

base area of cone = πr²

base area of cylinder = πr²

Therefore, the cone and cylinder have the same base area

ii) The volume of the cone is One-third the volume of the cylinder

The Formula's for volume a cylinder is πr²h and the volume of a Cone is 1/3πr²h.

And since they both have the same radius and height measurement, So the volume of a cone is one-third the volume of a cylinder.

iii) The cone and cylinder have the same diameter.

Since they both have same radius measures and diameter = 2*radius.

Therefore, the cone and cylinder have the same diameter.

B) The cone and cylinder have the same base area.

C) The volume of the cone is One-third the volume of the cylinder.

E) The

Step-by-step explanation:

i) The cone and cylinder have the same base area. Since they both have the same radius measures. And formula for base area of cone = πr² base area of cylinder = πr²

Therefore, the cone and cylinder have the same base area

ii) The volume of the cone is One-third the volume of the cylinder

The Formula's for volume a cylinder is πr²h and the volume of a Cone is 1/3πr²h.

And since they both have the same radius and height measurement, So the volume of a cone is one-third the volume of a cylinder.

iii) The cone and cylinder have the same diameter.

Since they both have same radius measures and diameter = 2*radius.

Therefore, the cone and cylinder have the same diameter.

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

or

step-by-step explanation:

we need to solve for 'x' the following equation:  

we have that:

⇒

⇒ ⇒

factorizing, we get that:

  ⇒

then, the solutions are: or

nothing extraneous has been found!