Algebra Unit 5HW Day 1 SOLVING GRAPHICALLY
Graph the following systems:
1)2)
3)4) Solve for this system using your graphing
calculator. [You will still need to put each
equation into y = mx + b form before
inputting them to your calculator].
Use your calculator to check the solutions for the following systems of equations:
5)6)
Review:
7.Given the function , find x when h(x) = 25
8. At Joe’s Clown Car rental agency, renting a car costs $35 plus $0.75 for every
mile driven. What is the equation that can be used to find the number of miles,
m, a vehicle was driven, if the total charge was $222.50?
(1) (3)
(2) (4)
Algebra Unit 5HW Day 2 SOLVING ALGEBRAICALLY
Solve the following systems algebraically:
1)2)
3)4)
Review:
5.Mr. Mahoney is describing a function to his students. He says that the output is equal to five less than three times the input. Which of the following equations models this relationship?
(1) f(x) = 5 – 3x (2) f(x) = 3(x – 5) (3) f(x) = 3(5 – x) (4) f(x) = 3x – 5
6.Which of the graphs below shows the solution set of ?
7. Solve for x:?
Algebra Unit 5HW DAY 3 MORE SOLVING ALGEBRAICALLY
Solve the following systems algebraically:
1)2)
3)4)
Review:
- What interval notation represents the data graphed below?
(1) (1, 4](2) [4, 1)(3) (4, 1)(4) (1, 4)
- Solve for x:
7.Write an equation of a line that is perpendicular to .
EXTRA CREDIT: Solve the following system algebraically:
Algebra Unit 5HW Day 4 APPLICATION WP
1)A baseball manager bought 4 bats and 9 balls for $76.50. On another day, she bought 3 bats and 1 dozen balls at the same prices and paid $81.00. How much did she pay for each bat and each ball?
2)For 30 minutes you do a combination of walking and jogging. At the end of your workout, your pedometer displays a total of 2.5 miles. You know that you walk 0.05 mile per minute and jog 0.1 mile per minute. How much time were you walking? How much time were you jogging?
3)One admission to a roller skating rink costs x dollars and renting a pair of skates costs y dollars. A group pays $243 for admission for 36 people and 21 skate rentals. Another group pays $78 for admission for 11 people and 7 skate rentals. How much does it cost for admission?
4)The measure of the smaller of two supplementary angles is more than the measure of the larger angle. Find the degree of the measure of each angle.
5)Max and his father Kirk are comparing their ages. They know that the sum of their ages is 52 and that Kirk is seven years older than four times Max’s age.
a) If Max’s age is represented by m and Kirk’s age by k, write a system of
equations that describes the two relationships from the problem.
b) Solve the system using substitution to find both of their ages.
REVIEW:
6)Write the equation of a line that has undefined slope and passes through the point (7, -6).
7)Write the equation of a line that has zero slope and passes through the point
(-3, 4).
Algebra Unit 5HW DAY 5 SOLVING APPICATONS WP GRAPHICALLY
1)
a) The U-Drive-IT car rental agency rents cars for $50 a day with unlimited free
mileage. Write an equation to show the cost of renting a car from U-Drive-IT
for one day, y, if the car is driven for x miles.
b) The Safe Travel car rental agency rents cars for $30 a day plus $0.20 a mile.
Write an equation to show the cost of renting a car from Safe Travel for one
day, y, if the car is driven for x miles.
c) Draw, on the same set of axes, the graphs of the equations written in parts a
and b. Watch your scales on the axes!!!
d) If Greg drives the car he rents
for 200 miles, which agency
offers the less expensive car?
e) If Sarah drives the car she rents
for 50 miles, which agency
offers the less expensive car?
f) If Phillip finds the price that
both agencies will be the
same, how far is he planning
on driving the car?
2.
3.Write an example of the Associative Property: ______
4.a) If n – 7 represents an odd integer, what would be the next greater odd
integer?
b) If n – 7 represents an even integer, what would be the next greater even
integer?
5.Graph the following inequality on the grid:
Algebra Unit 5HW DAY 6 MONEY/PERCENT WP
1.Mr. Daniels invested a sum of money in saving bonds yielding 6% a year and in a certificate of deposit (CD) yielding 4% a year. In all, he invested $4000. If his total annual income from his investments was $188, find the amount he invested in each rate.
2. At McDonald’s, four hamburgers and two orders of French fries cost $27.10. Three hamburgers and four orders of fries cost $25.20. If all hamburgers cost the same price and all orders of fries cost the same price, find the price of each.
3.Lisa and George went shopping at Price Buster. George bought 2 rolls of aluminum foil and 3 packages of batteries for a total cost of $21. Lisa bought 5 identical rolls of aluminum foil and 2 identical packages of batteries for a total cost of $25. Find the cost of each item.
4.Two cell phone plans offer differing text packages. The two plans are outlined below:
Plan A: $5.00 per month charge along with a charge of $0.03 per text.
Plan B: No per month charge, but a charge of $0.10 per text.
Is there a certain number of texts, when the two plans cost the same amount? Determine your answer by setting up a system of equations that model the two plans.
5.A catering company is setting up tables for a big event that will host 764 people. When they set up the tables they need 2 forks for each child and 5 forks for each adult. The company ordered a total of 2992 forks. Set up a system of equations involving the number of adults, a, and the number of children, c, and solve to find out how many of each attended the event.
Review:MATCHING: Match the property to its illustration.
______(ab)c = a(bc)A.Multiplicative Identity
______x + y = y + xB.Multiplicative Inverse
______x + 0 = xC.Additive Identity
______x 1 = xD.Additive Inverse
______7 + (-7) = 0E.Commutative Property of Addition
______F.Associative Property of Multiplication
______2(x + y) = 2x + 2yG.Distributive Property
ALGEBRA UNIT 5HW DAY 7 SYSTEMS OF INEQUALITIES
1)2)
3)4)
5. Which equation represents the line that passes through thepoints (-3, 7) and (3, 3)
(1) (3)
(2) (4)
6. Which of the following does not represent a rational number?
(1) (3)
(2) (4)
7. Which equation below illustrates the associative property?
(1) (3)
(2) (4)
8. Which inequality is represented in the accompanying graph?
(1) (3)
(2) (4)
9.If find
Algebra Unit 5HW DAY 8 APPLICATION WP
1)You are planning a cookout. You figure that you will need at least 4 packages of hot dogs and hamburgers. A package of hot dogs costs $12 and a package of hamburgers costs $20. You can spend a maximum of $60 on the hotdogs and hamburgers.
a) Let x represent the number of packages of hot dogs and let y represent the number of packages of hamburgers. Write a system of linear inequalities for the number of packages of each that can be bought.
b) Graph the system of inequalities.
c)Identify two possible combinations of packages of hot dogs and hamburgers they can buy.
2)Danielle needs at least 4 hours to do her chores, which include cleaning out the garage and weeding the flower beds around her house. It is 1:30 p.m. on Sunday and her friend wants to go to the movies at 7:00 p.m.
a) How much time does Danielle have between now and 7:00 p.m. to do her chores?
b) Let x represent the number of hours spent cleaning out the garage and let y represent the number of hours spent on weeding the flower beds. Write and graph a system of linear equalities that shows the number of hours Danielle can work on each chore if she is to go to the movies.
c) Identify two possible combinations
of time she can spend on each chore.
3)John mows yards for his father’s landscaping business for $10 per hour and also works at a bakery for $15 per hour. He can work at most 52 hours per week during the summer. He needs to make at least $600 per week to cover his living expenses.
a)If John works 14 hours mowing and 30 hours at the bakery, does this satisfy all of the problem’s constraints?
b)If x represents the hours John spends mowing and y represents the hours he spends at the bakery, write a system of inequalities that describes this scenario. DO NOT SOLVE.