Define the following words:
- Algebraic expression
- Algebraic inequality
- Independent variable
Evaluate the following expressions.
3y(7−(z−y)); use y=−7 and z=2
m+3n−p4; use m=9, n=7, and p=2
|p|−(n2)3; use n=2 and p=3
Choose an appropriate variable to describe the situation.
- The number of candies you can eat in a day
- The number of tomatoes a plant can grow
- The number of cats at a humane society
- The amount of snow on the ground
- The number of water skiers on a lake
- The number of geese migrating south
- The number of people at a trade show
Insert parentheses to make a true equation.
Translate the following into an algebraic equation or inequality.
- Thirty-seven more than a number is 612.
- The product of u and –7 equals 343.
- The quotient of k and 18
- Eleven less than a number is 43.
- A number divided by –9 is –78.
- The difference between 8 and h is 25.
- The product of 8, –2, and r
- Four plus m is less than or equal to 19.
- Six is less than c.
- Forty-two less than y is greater than 57.
Write the pattern shown in the table with words and with an algebraic equation.
Movies watchedTotal time0011.52334.54657.5
- A case of donuts is sold by the half-dozen. Suppose 168 people purchase cases of donuts. How many individual donuts have been sold?
- Write an inequality to represent the situation: Peter’s Lawn Mowing Service charges $10 per mowing job and $35 per landscaping job. Peter earns at least $8,600 each summer.
Check that the given number is a solution to the given equation or inequality.
- Logan has a cell phone service that charges $18 dollars per month and $0.05 per text message. Represent Logan’s monthly cost as a function of the number of texts he sends per month.
- An online video club charges $14.99 per month. Represent the total cost of the video club as a function of the number of months that someone has been a member.
- What is the domain and range for the following graph?
- Henry invested $5,100 in a vending machine service. Each machine pays him $128. How many machines does Henry need to install to break even?
- Is the following relation a function?
Solve the following questions using the 4-step problem-solving plan.
- Together, the Raccoons and the Pelicans won 38 games. If the Raccoons won 13 games, how many games did the Pelicans win?
- Elmville has 250 fewer people than Maplewood. Elmville has 900 people. How many people live in Maplewood?
- The cell phone Bonus Plan gives you 4 times as many minutes as the Basic Plan. The Bonus Plan gives you a total of 1200 minutes. How many minutes does the Basic Plan give?
- Margarite exercised for 24 minutes each day for a week. How many total minutes did Margarite exercise?
- The downtown theater costs $1.50 less than the mall theater. Each ticket at the downtown theater costs $8. How much do tickets at the mall theater cost?
- Mega Tape has 75 more feet of tape than everyday tape. A roll of Mega Tape has 225 feet of tape. How many feet does everyday tape have?
- In bowling DeWayne got 3.5 times as many strikes as Junior. If DeWayne got 28 strikes, how many strikes did Junior get?