A comedy troupe is going on tour. The amount of money in the troupe’s account C(d) is a function of the number of days d since they started the tour. The graph below shows their day-to-day account balance. Although the axes are not labeled with tick marks, you can answer the questions by using the given information and your knowledge of graphs of functions.1.The troupe went on a 3 week tour, and the graph shows the entire 3 weeks. During that time, their greatest balance was $500.(a)Give the domain and range of the function. Domain: 0 < D < 21Range: 0 < C(D) < 500(b)Give an estimate to the nearest hundreds for C(0). Explain how you determined this value and what it means in the context of this problem. C0 = 250 The Y intercept is halfway between the minimum and the maximum of the range.(c)The troupe’s account first reached $0 on Day 11. How would you show that information in function notation? C(11) = 0(d)The balance remained at $0 from Day 11 through Day 16. As you count segments from the left, which segment on the graph1, 2, 3, 4, 5, or 6 represents that information? Explain. Counting from the left, the 4th segment is the one that represents the information. 2.The troupe’s account balance first reached $500 on Day 4. The last day the account balance was $500 was Day 8.(a)Determine C(5), C(6), and C(7). Explain how you determined these amounts.(b)Estimate C(1), C(2), and C(3). Explain how you determined these amounts.(c)The stage manager said that the amount of money taken out of the account each day between Day 8 and Day 11 was the same amount of money put into the account each day between Day 0 and Day 4. Recall that Day 11 is when the balance first reached $0. Without doing any calculations, how could you show the stage manager was incorrect?3.On Day 17, the troupe deposited $100 into the account. On each day after Day 17, segment 5, the troupe made daily, equal deposites.(a)Explain how you can determine, just by looking at the graph, whether the amounts deposited after Day 17 were each less than $100, $100, or more than $100.(b)Use the graph to estimate C(21) in hundreds. Explain how you determined this estimate. How can you estimate the deposits after Day 17?

all teachers

step-by-step explanation:

3x^3-x^2+6x-9

d

step-by-step explanation:

hello and welcome!

so, when we see the words "proportional" along with a table, we need to know that we're looking numbers that divide by the same thing.

looking at this table, we simply have to do a trial and error, and divide to see which numbers have the same quotient. if you look at choice a & c, they both have equal quotients for three of the numbers, with one exception, so those can't be the answer. looking at b, there is no similarity, so that can't be it. then, we see d; if you divide all the numbers in the table, you'll see that they all divide by two, which is a proportional relationship, and our answer!

also, always remember that the x will always be the number that goes into y, and somewhere behind this table, is a formula. for this specific table, the formula would be:

since our x-value is being divided by two to get the y-value. and if they were to ask for more numbers in the series, this is the formula you would use to find them.

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