Me you are deciding on two different designs for envelopes. picture below a. which design has the greater area? the area of the first design is square inches and the area of the second design is square inches. so, the has the greater area. b. you make 500 envelopes using the design with the greater area. using the same amount of paper, how many more envelopes can you make with the other design? you could make about more envelopes

I can help with A. The area of a triangle is base times height divided by 2. The area of a rectangle is length times width.

The area of the first one's rectangle is 4.5 times 5.5, which is 24.75.

The area of each triangle is 6.75 for the two side ones and 6.875 for the top and bottom ones.

Added together, the area of the first envelope is 52 in squared.

The area of the second one's middle rectangle is 24.75. The area of the top one is 11. The area of the bottom one is 19.25.

The shapes on either side of the middle rectangle are trapezoids. To find the area of a trapezoid, you add the lengths of both bases and multiply that by its height. Then, you divide that by 2.

The lengths of both bases in this case are 4 and 4.5, which makes 8.5. Then, you multiply this by 0.75 and get 6.375. This divided by 2 is 3.8175.

All of the areas added together equal 62.365.

The first one has a bigger area. Hope this helps!

Heather :)

Sorry if this is wrong

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

b. 153 students do not participate in sports and seventy-five 12th graders were surveyed