Questions and Answers
What is the result of the expression $\frac{-5 \times 9 - 4(7 + 3 \times 7) + 1}{6 - 4}$?
79
What is the result of the expression $\frac{7(2 - 4) + 1}{(8 \times 3 + 6) / 15}$?
-6
What is the result of the expression $5 \times 4 - 3 + 2(4 - 6 \times 2)$?
1
What is the result of the expression $(\frac{56}{8}) + 3 - 2(8 - 3)$?
Signup and view all the answers
What is the result of the expression $7 + 3(6 - \frac{2}{1}) + (5 - 1) / 2$?
Signup and view all the answers
Which system of equations can be used to model the wrapping paper sales problem?
Signup and view all the answers
Which system of equations can be used to model the shipping packages problem?
Signup and view all the answers
How many people ordered each dinner at the restaurant if there are 5 steak dinners and 1 chicken dinner?
Signup and view all the answers
How many right-handed and left-handed gloves were sold, if 12 gloves were sold for a total revenue of $561?
Signup and view all the answers
How many orchestra and balcony tickets were sold if 350 orchestra and 250 balcony tickets were sold?
Signup and view all the answers
How many bottles of apple juice and orange juice were bought if there were 4 orange and 8 apple bottles?
Signup and view all the answers
How many packages of diet and regular pop were bought if there were 6 of each?
Signup and view all the answers
If you need 5 hot dogs and 3 hamburgers for the cookout, how many packages of each can you buy?
Signup and view all the answers
What is the solution of the system given by $y = 2x - 3$ and $y = -3x + 2$?
Signup and view all the answers
What is the solution of the system given by $y = 4x + 1$ and $y = x - 2$?
Signup and view all the answers
What is the solution for the system $y = -2x - 4$ and $y = 4x + 2$?
Signup and view all the answers
What is the solution of the system represented by $x + 3y = 6$ and $2x + y = -3$?
Signup and view all the answers
What is the solution of the system represented by $y = -x + 3$ and $y = 5$?
Signup and view all the answers
What is the solution you find?
Signup and view all the answers
What is the solution you can find?
Signup and view all the answers
What is the solution you encounter?
Signup and view all the answers
What solution can you derive?
Signup and view all the answers
What solution can you determine?
Signup and view all the answers
What solution can you publish?
Signup and view all the answers
What solution can you unveil?
Signup and view all the answers
What is the slope between the points (6, 2) and (10, 5)?
Signup and view all the answers
What is the slope between the points (-2, 3) and (-4, -1)?
Signup and view all the answers
What is the slope between the points (6, 1) and (6, -3)?
Signup and view all the answers
What is the slope between the points (-7, 2) and (-4, 1)?
Signup and view all the answers
What is the slope between the points (5, 1) and (7, -2)?
Signup and view all the answers
What is the slope between the points (3, 5) and (-7, 5)?
Signup and view all the answers
What is the slope?
Signup and view all the answers
What is the slope?
Signup and view all the answers
What is the slope?
Signup and view all the answers
What is the slope?
Signup and view all the answers
What is the rate of change when it is said to be 5 miles per hour?
Signup and view all the answers
What is the rate of change when it is specified as 7.5 miles per hour?
Signup and view all the answers
Study Notes
Algebra Expressions and Evaluations
- Expression: (-5x9-4(7+3x7)+1)/(6-4) evaluates to 79.
- Expression: (7(2-4)+1)/((8x3+6)/15) evaluates to -6.
- Expression: 5x4-3+2(4-6x2) evaluates to 1.
- Expression: (56/8)+3-2(8-3) evaluates to 0.
- Expression: 7+3(6-2/1)+(5-1)/2 evaluates to 21.
Systems of Equations
- Fund-raiser wrapping paper sale:
- Model: x + y = 14, 6x + 8y = 92 (where x and y represent $6 and $8 rolls sold).
- Shipping packages scenario:
- Model: x + y = 31, 3.5x + 5y = 8 (x: $3.50 packages, y: $5 packages).
Word Problems
- Dinner orders at a restaurant: 5 steak dinners and 1 chicken dinner for a total bill of $99.
- Baseball glove sales: 9 right-handed and 3 left-handed gloves sold for $561 with right-handed at $45 each and left-handed at $52.
- Theater ticket sales: 350 orchestra and 250 balcony tickets resulting in total receipts of $4750.
- Juice purchases: 4 bottles of orange juice at $1.75 and 8 apple juice bottles at $1.00, totaling $15.00.
- Soft drink purchase for a school event: 6 diet and 6 regular bottles for $15.00.
- Cookout meat purchase: 5 hot dogs and 3 hamburgers with a total cost of $23.00.
Graphing Systems of Equations
- For y = 2x - 3 and y = -3x + 2, the solution by graphing is (1, -1).
- For y = 4x + 1 and y = x - 2, the solution is (-1, -3).
- For y = -2x - 4 and y = 4x + 2, the solution is (-1, -2).
- For x + 3y = 6 and 2x + y = -3, the solution is (-3, 3).
- For y = -x + 3 and y = 5, the solution is (-2, 5).
Solutions to Coordinate Points
- Given points: (4, 2), (2, 3), (3, 2), (0, 0), (2, 4), (2, 6), and (-2, -2).
Slope Calculations
- Slope between (6, 2) and (10, 5) is 3/4.
- Slope between (-2, 3) and (-4, -1) is 2.
- Slope for points (6, 1) and (6, -3) is undefined (vertical line).
- Slope between (-7, 2) and (-4, 1) is -1/3.
- Slope between (5, 1) and (7, -2) is -3/2.
- Slope between (3, 5) and (-7, 5) is 0 (horizontal line).
Rates of Change
- Rate of change for specific scenarios is given as 5 miles per hour, 7.5 miles per hour, and 10 miles per hour for various problems.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Description
This quiz covers various algebraic expressions, their evaluations, and systems of equations related to real-world scenarios. Test your understanding of how to manipulate and solve these algebraic concepts through word problems and expressions. Perfect for reinforcing your algebra skills!
