Please answer this correctly

The quarter circle's area is 38.47 yard²

Step-by-step explanation:

The area of a full circle is pi * r ²

The area of a quarter circle is 1/4 * pi * r ²

Given:

Use 3.14 for pi

Round to the nearest hundredths.

Perimeter of quarter circle is 24.99 yards

For r you must leave it as 'r' because we do not know it for now...

1. Circumference of a full circle = 2* pi * r

2. 1/4 * ( 2 * pi * r )

1/4 * ( 2 * 3.14 * r )

1/2 * 3.14 * r

1.57 * r

3 Since r = 'r'

We have to 2 sides running from the centre of the 'pie' to the left and right of the quarter circle which both have a length of exactly 'r'. So you just add 2 * r.

4. The outcome of step 2 + step 3 is the perimeter of quarter circle, which was given as 24.99 inch

1.57 * r + 2 * r = 24.99

( 1.57 + 2 ) * r = 24.99

3.57 * r = 24.99

Divide left and right of the = sign by 3.57

3.57 / 3.57 * r = 24.99 / 3.57

1 * r = 24.99 / 3.57

r = 7

The area of a quarter circle is 1/4 * pi * r ²

1/4 * pi * 7²

1/4 * 49 * pi

49/4 * pi

49/4 * 3.14

38.465

Round to the nearest hundredths gives 38.47 yard²

The quarter circle's area is 38.47 yard²

true

explanation:

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