Linear Programming (Graphing Only)

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Linear Programming (Graphing Only)

Representing Arithmetic Sequences Graphically

Review for Unit 2 Part 1 Test

Unit 2 Part 1 Test

Unit 2 – Part 1: Modeling Linear Equations

Math 3 Unit 2 Homework Packet

Homework 2-1

1. A car enters an interstate highway 15 miles north of the city. The car travels due north at an average speed of 30 miles per hour. Write an equation to model the car’s distance d from the city after traveling for h hours. Graph the equation

1. A tree 5 feet tall grows an average of 8 inches each year. Write and graph an equation to model the tree’s height h after x years.

Find a linear model and use it to make a prediction

1. There are 2 leaves along 3 inches of an ivy vine. There are 14 leaves along 15 inches of the same vine. How many leaves are there along 6 inches of the vine?

1. The table below shows the average energy requirements for male children and adolescents.
2. Graph the data. Use linear regression to model the data with a linear equation
3. Estimate the daily energy requirements for a male 16 year old.

1. Do you think the model also applies to adult males? Explain.

1. The time needed to roast a chicken depends on its weight. Allow at least 20 min/lb for a chicken weighing as much as 6 lb. Allow at least 15 min/lb for a chicken weighing more than 6 lb.
2. Write two inequalities to represent the time needed to roast a chicken.
3. Graph the inequalities.
4. What do the shaded areas represent?

1. Graph 5x – 2y > - 10 on the coordinate plane.

Homework 2-2

Solve each system by graphing. Check your results.

1. y = x – 22. -5x + y = -9

y = -2x + 7 x + 3y = 21

Solve each system by substitution. Check your results.

1. 3x – 2y = 84. 2x + 8y = 6

4y = 6x – 5 x = -4y + 3

Solve Each system of equations by elimination. Check your results.

1. -6y + 18 = 12x6. x + 4y = 12

3y + 6x = 9 -x -2y = -6

1. 6x + 4y = 128. 2x – 7y = 21

-12x – 8y = -24 -2x + 7y = 12

1. You want to bake at least 6 and at most 11 loaves of bread for a bake sale. You want at least twice as many loaves of banana bread as nut bread. Write and graph a system of inequalities to model the situation.

1. A psychologist needs at least 40 subjects for her experiment. She cannot use more than 30 children. Write an graph a system of inequalities.

Homework 2-3

1. 5.

1. 7.

1. 9.

Homework 2-4

1. A biologist is developing two new strains of bacteria. Each sample of Type I bacteria produces four new viable bacteria, and each sample of Type II produces three new viable bacteria. Altogether, at least 240 new viable bacteria must be produced. At least 30, but not more than 60, of the original samples must be Type I. Not more than 70 can be Type II. A sample of Type I costs $5 and a sample of Type II costs $7. How many samples of Type II bacteria should be used to minimize cost?

Homework 2-5

1. If the first term of an arithmetic sequence is 5 and the common difference is -2, find the next four terms.

1. If I know that the first term of the arithmetic sequence is -2 and the fifth term is 6, find the second, third, and fourth terms in the sequence.

1. If the first term of an arithmetic sequence is -25 and the third term is 14, find the second term.

1. If the first term of an arithmetic sequence is 15 and the third term is 65, find the second term.

Is the given sequence arithmetic? If so state the common difference

1. 12, 15, 18

1. 100, 110, 130

1. -2, -1, 0

1. 123, 221, 319

Homework 2-6

Given the recursive equation for each arithmetic sequence, write the explicit equation.

1. f(n) = f(n – 1) – 2; f(1) = 8

1. 5. f(n) = 5 + f(n – 1); f(1) = 0

6. Find the 125th term of the sequence 5, 11, 17, 23, …

1. Abbie decides to start doing crunches as part of her daily workout. She decides to do 15 crunches the first day and then increase the number by 4 each day after that. Write an explicit formula for the number of crunches Abbie will do on day n. How many crunches would she do on day 25?

Homework 2-7

1. Fill in the rest of the table.
2. Graph the sequence.

c. How is the common difference related to the graph?

d. Use the graph to find the y-intercept

e. How can you calculate the y-intercept of the sequence without having to graph it first?

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