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Questions and Answers
What is the result of $7^2$?
What is the result of $7^2$?
If $x = 3$, what is the value of $2x + 5$?
If $x = 3$, what is the value of $2x + 5$?
Which expression is equivalent to $3(x + 2)$?
Which expression is equivalent to $3(x + 2)$?
What is the perimeter of a rectangle with length $4$ and width $7$?
What is the perimeter of a rectangle with length $4$ and width $7$?
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Which of these numbers is a prime number?
Which of these numbers is a prime number?
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Study Notes
Equation Solving
- Equation: 4 + 1/2x - 8 = 12. Solution is x = 32.
Graphing Linear Relationships
- Example: Emily sells greeting cards. A graph shows a linear relationship between the number of cards sold and her profit.
- Relationship: As boxes sold increase, profit increases linearly.
- Profit Data (Example): Profit increases $7.50 per box.
Cookies Eaten at Events
- Data: A catering company recorded the total number of cookies eaten at events, with different numbers of guests.
- Scatterplot: Scatterplot shows results, with potential correlation between guests and cookies eaten.
- Summary: Data shows some correlation between the number of guests and the total cookies eaten, though not perfectly linear.
Mapping Representations of Functions
- Concept: Determining when a mapping represents a function of x (mapping x to y values).
- Examples: Some examples of mappings are given, with the correct choice of x being mapped to y, forming a function.
Equations in Slope-Intercept Form
- Concept: Finding the equation in slope-intercept form to present a linear relationship.
- Data: A table shows several pairs of x and y values for a linear relationship.
- Task: Creating an equation in slope-intercept form that describes this relationship based on the data trend (values).
Geometric Figures - Perimeter
- Triangle and Square: The side lengths of a triangle and a square are given in variables.
- Perimeter Relationship: The perimeter of the triangle is equal to the perimeter of the square.
- Calculations: To solve for the unknown variable 'x', use the perimeter formula (side lengths x 3 in the triangle, and side lengths x 4 in the square).
Equation Truth Values
- Concept: Determining if an equation is true or false given a value of a variable.
- Examples: Testing given equations, by inserting the provided value of the variable to the equation and see if the expression is equal.
Linear Relationships (Slope and Y-intercept)
- Concept: Identifying the linear relationship between x and y variables using a supplied table.
- Results: Calculating the slope and y-intercept of the linear relationship.
- Table Input: The data from a table (like x and y values) provides the relationship.
Graphing Proportional Relationships
- Concept: Identifying a graph which shows a proportional relationship between x and Y values. There should be a constant ratio between x to y values (or x being zero when 'y' is zero)
- Example: Graphing relationship between, for example time vs painted cabinets).
Tank/Pool Relationship (Varying quantities)
- Concept: Determining the inequality that represents a scenario with a tank being filled/emptied with varying amounts of water over time.
- Water Quantity Data: Water fills in a pool at rate 480 gallons per hour. A tank starts with 1060 gallons and water leaks at a rate of 35 gallons per hour.
- Comparison: The point where the quantity of water in the tank (starting from an initial amount minus leaking), is less than the quantity of water in the pool (starting from zero and increasing at the stated rate).
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Description
This quiz covers key concepts in solving equations, graphing linear relationships, and interpreting data through scatterplots. It also includes understanding mappings and functions. Test your knowledge in these crucial areas of mathematics.