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i, ii, iii, iiii, iiiii, … What is the twentieth term?

iiiiiiiiiiiiiiiiiiii (20 i’s)

Marta is decorating the rectangular top of a jewelry box with antique buttons that are all the same size. She has started by gluing 8 buttons across and 5 buttons down for a total of 13 buttons. Write a sequence of numbers to represent the number of buttons used for each group of buttons across and down that she uses to cover the box. How many total buttons will she need?

48 total buttons 13 11 09 07 05 03 + 48 13 11 9 7 5 3

What was Dylan’s driving speed for the first 2 hours? Explain. Dylan took a one-day driving trip from his home. The graph shows his distance from home after x hours.

speed = 𝒅𝒊𝒔𝒕𝒂𝒏𝒄𝒆 𝒕𝒊𝒎𝒆 Distance: 200 miles Time: 2 hours 𝟏𝟎𝟎 𝒎𝒊𝒍𝒆𝒔 𝟐 𝒉𝒐𝒖𝒓𝒔 = 50 mph

Dylan took a one-day driving trip from his home Dylan took a one-day driving trip from his home. The graph shows his distance from home after x hours. There were two periods of time when Dylan stopped for a rest and food. When did these occur? Explain.

The time were from 2-3 and 5-6. The distance did not change in these time periods.

In terms of the context of this problem, what is the difference between the time periods when the graph is increasing and when it is decreasing? Dylan took a one-day driving trip from his home. The graph shows his distance from home after x hours.

Dylan was going to his destination from hour 0 to hour 6. Then from 6-8 he drove back home.

Dylan took a one-day driving trip from his home Dylan took a one-day driving trip from his home. The graph shows his distance from home after x hours. Is the graph discrete or continuous? Why does this make sense? Is it linear or nonlinear? Why?

This makes sense because driving is a continuous action. Non-Linear. The graph is not a straight line.

The Spanish Club at your school is selling animal piñatas to raise money for a trip to Mexico City. The club earns a profit of $3 on each piñata sold. The sale runs for 5 weeks. The number of piñatas sold each week are 15, 22, 8, 35, and 42. Complete the table of values for the problem situation and write an algebraic equation for the problem.

15 Equation: 𝒚=𝟑𝒙 22 X: Piñatas Y: Profit 8 35 42 3*15 = $45 3*22 = $66 8 3*8 = $24 35 3*35 = $105 42 3*42 = $126

200 programs are printed? Explain your reasoning. The director of a local ballet company needs to print the programs for the next performance. Janet’s Print Shop charges $0.25 per program plus a $35 set-up fee. The Printing Press charges $0.18 per program plus a $50 set-up fee. Which printing company offers the better deal if 200 programs are printed? Explain your reasoning.

Janet’s Print Shop is a better deal Janet’s Print Shop .25 cents / program $ 35 set up fee .25x + 35 x: # of programs .25(200) + 35 = $85 The Printing Press .18 cents / program $50 set up fee .18x + 50 x: # of programs .18(200) + 50 = $86

Eric is a high school junior who earns $8 an hour at his after-school job. Write a sequence with ten terms to represent the total amount he has earned in dollars after 1 hour, 2 hours, 3 hours, and so on. Describe the pattern and interpret the meaning of the last term in the context of the situation.

Describe: The pattern is increasing by $8 every hour. Hours 1 2 3 4 5 6 7 8 9 10 $ 16 24 32 40 48 56 64 72 80 Describe: The pattern is increasing by $8 every hour. Interpret: Eric will earn a total of $80 during his 10th hour of work.

increasing and decreasing, or neither increasing nor decreasing. Classify the graph as discrete or continuous, linear or nonlinear, and increasing, decreasing, both increasing and decreasing, or neither increasing nor decreasing.

increasing and decreasing. Continuous, Nonlinear, both increasing and decreasing.

Write a set of ordered pairs from the picture to represent the mapping Write a set of ordered pairs from the picture to represent the mapping. Does the mapping represent a function? Explain your reasoning.

Ordered Pairs: {(1,2), (2,2), (3,4), (4,4), (5,6), (5,8), (6,6)} This relation is NOT A FUNCTION. The x-value 5 repeats in two ordered pairs. One input has two outputs.

Determine the domain and range of the relation.

Remember: The domain is the x-values

Mexico City? Explain your reasoning and SHOW WORK! Two airlines offer special group rates to your school’s Spanish Club for a trip to Mexico City. Mexican Air airline offers a roundtrip airfare of $250 per person. Fiesta airline offers a roundtrip airfare of $150 per person if the club agrees to pay a one-time group rate processing fee of $1000. Which airline offers the better deal if only nine students from the Spanish Club are able to fly to Mexico City? Explain your reasoning and SHOW WORK!

Mexican Airline has a better deal Mexican Airline $250 / person $ 0 processing fee 250x + 0 x: # of passengers 250(9) + 0 = $2,250 Fiesta Airline $150 / person $ 1000 processing fee 150x + 1000 x: # of passengers 150(9) + 1000 = $2,350

Classify the equation y = 𝑥 2 Classify the equation y = 𝑥 2 . Explain if it represents a function and SHOW WORK!

The equation 𝒚= 𝒙 𝟐 is a QUADRATIC FUNCTION It IS a function because it passes the “Vertical Line Test”

Is the following a function? Why or why not?

This mapping is NOT a function. The x-value 3 and x-value 4 repeat. {(3,3), (3,5)} {(4,4), (4,6)} This relation has one input assigned to two different outputs.

Is the following a function? Why or why not?

Yes. The relation is a function. None of the x-values repeat. Each input has one and only one output.

Determine the domain and range for each relation defined by the set of ordered pairs or mapping. {(24, 27), (23, 13), (22, 3), (21, 23), (0, 25), (1, 23), (2, 3), (3, 13), (4, 27)}

Domain: {24, 23, 22, 21, 0, 1, 2, 3, 4} x-values Range: {27, 13, 3, 23, 25} y-values

For what weight of flour is the cost equal for both companies? Why? Tate is ordering flour for her bakery. Baker’s Supplies charges $0.30 per pound, plus a $10 delivery fee. Best Flour charges $0.80 per pound, but delivery is free. The graph of the equations that represent this situation is shown. For what weight of flour is the cost equal for both companies?

The price is equal at 20 pounds Bakers Supplies .30 cents / pound $ 10 delivery fee .30x + 10 x: # of pounds Best Flour .80 cents / pound $ 0 delivery fee .80x + 0 x: # of pounds .30x + 10 = .80x 10 = .50x x = 20 pounds

Tate is ordering flour for her bakery. Baker’s Supplies charges $0 Tate is ordering flour for her bakery. Baker’s Supplies charges $0.30 per pound, plus a $10 delivery fee. Best Flour charges $0.80 per pound, but delivery is free. The graph of the equations that represent this situation is shown. For what weight of flour is the cost equal for both companies? Which company would be better for 25 pounds of flour? WHY? For 6 pounds?

25lb: Bakers Supplies / 6lb: Best Flour .30 cents / pound $ 10 delivery fee .30x + 10 x: # of pounds Best Flour .80 cents / pound $ 0 delivery fee .80x + 0 x: # of pounds 25 Pounds BS: .30(25) + 10 = $17.50 BF: .80(25) + 0 = $20.00 6 Pounds BS: .30(6) + 10 = $11.80 BF: .80(6) + 0 = $4.80

Consider the equation 3(x + 1) + x + 2 = 2(2x + 1) + 3. Solve the equation.

Infinite # of solutions 3(x + 1) + x + 2 = 2(2x + 1) + 3 3x + 3 + x + 2 = 4x + 2 + 3 4x + 5 = 4x + 5 (x = x) (0 = 0) Infinite # of solutions

Consider the equation 3(x + 1) + x + 2 = 2(2x + 1) + 3. How many solutions does the equation have? Is the resulting equation always true, sometimes true, or never true?

Infinite # of solutions Always True and Sometimes True 3(x + 1) + x + 2 = 2(2x + 1) + 3 3x + 3 + x + 2 = 4x + 2 + 3 4x + 5 = 4x + 5 (x = x) (0 = 0) Infinite # of solutions Always True and Sometimes True

Consider the equation 3(x + 1) + x + 2 = 2(2x + 1) + 3. If you were to graph the left side of the equation as one line and the right side of the equation as another, how would they appear on a graph?

Infinite # of solutions One line on top of the other. 3(x + 1) + x + 2 = 2(2x + 1) + 3 3x + 3 + x + 2 = 4x + 2 + 3 4x + 5 = 4x + 5 (x = x) (0 = 0) Infinite # of solutions They are the same line. One line on top of the other.

Define a variable for the number of quarters collected. A charity organization is collecting change to raise money. They have collected twice as many dimes as quarters, 22 more nickels than dimes, and 3 times as many pennies as nickels. Define a variable for the number of quarters collected.   Use your defined variable to write algebraic expressions to represent the number of quarters, dimes, nickels, and pennies collected.

q: quarters d: 2q n: 2q + 22 p: 3(2q + 22)

A charity organization is collecting change to raise money A charity organization is collecting change to raise money. They have collected twice as many dimes as quarters, 22 more nickels than dimes, and 3 times as many pennies as nickels. If they have collected a total of 2134 coins, how many of each coin have they collected?

q: quarters d: 2q n: 2q + 22 p: 3(2q + 22) = 6q + 66 q 2q 2q + 22 6q + 66 11q + 88 = 2,134 11q = 2,046 q = 186 + Quarters: 186 Dimes: 2(186) = 372 Nickels: 2(186) + 22 = 394 Pennies: 6(186) + 66 = 1,182

In how many minutes will the balloon be 1885 feet above sea level? A weather balloon is 625 feet above sea level. It is ascending at a rate of 315 feet per minute. In how many minutes will the balloon be 1885 feet above sea level? SHOW ALL WORK!

Staring height: 625 feet Increases: 315 ft / minute x: # of minutes 315x + 625 = 1,885 315x = 1,260 x = minutes