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Question: 12 of 12
12. Ainsley has decided to begin a 5-day sit-up challenge where she plans to increase the number of sit-ups completed each consecutive day by the same amount to
gradually build up her core muscle strength.
After talking with a friend who already began the challenge, she's aware that she needs to complete 20 sit-ups on Day 1 of the challenge and will complete 36 sit-
ups on the last day, Day 5.
What is the common difference of this sequence?
How many sit-ups should Ainsley do on Day 2 of the challenge?
What is the formula of the linear function that models this sequence? y =
If Ainsley continues the challenge for 15 days, how many sit-ups will she complete on Day 15?
24
15
16
20
24
36
68
72
76
80

step-by-step explanation:

we are given a graph for system of inequalities.

in order to write the system of inequalities for the given graph, we need to find the inequality for each of the line separately.

let us find the slope of dotted line first.

taking two coordinates on the graph.

let us say (0,0) and (3,1).

let us find the slope of the line now.

slope of the dotted line would be =.

y-intercept of dotted line is y=0 only.

plugging slope m= and b=0 in slope-intercept form y=mx+b, we get

.

the line is shaded up of that dotted line.

therefore, for shading up we would take greater than inequality symbol > .

and because it's a dotted line we would take only > symbol in place of = sign in above equation of line.

therefore, inequality for dotted line would be

let us take two points (3,1) and (0,4) on the solid line.

slope of the solid line would be =.

for the solid line we have y-intercept b= 4.

plugging slope m= -1 and b=4 in slope-intercept form y=mx+b, we get

y = -1x + 4.

the line is shaded down of that solid line.

therefore, for shading down we would take less than inequality symbol < .

and because it's a solid line we would take ≤ symbol in place of = sign in above equation of line.

therefore, inequality for solid line would be