Mathematics: Algebraic Concepts Flashcards

A company charges a $75 delivery fee and $50 per hour to rent a large tent. Which expression represents the total cost, C, to rent the tent for *h* hours?

Answer: C = 50h + 75

The total cost is the sum of the one-time delivery fee ($75) and the variable hourly cost. The hourly cost is $50 multiplied by the number of hours, *h*, which is represented as 50*h*. Therefore, the correct expression is C = 50h + 75.

What is the value of *x* in the equation 3x + 8 = 29?

Answer: x = 7

To solve for *x*, first isolate the term with the variable. Subtract 8 from both sides of the equation: 3x + 8 - 8 = 29 - 8, which simplifies to 3x = 21. Then, divide both sides by 3: 3x / 3 = 21 / 3, which gives x = 7.

An elevator has a maximum weight capacity of 2,000 pounds. Let *w* represent the total weight of the people and cargo in the elevator. Which inequality correctly represents the weight that can be safely transported by the elevator?

Answer: w ≤ 2,000

The weight capacity is the maximum amount allowed. This means the total weight, *w*, must be less than or equal to 2,000 pounds. The symbol '≤' represents 'less than or equal to'.

A lemonade stand sells lemonade at a constant price per cup. The table below shows the relationship between the number of cups sold and the total earnings. | Cups Sold (c) | Earnings (E) | |---|---| | 3 | $4.50 | | 5 | $7.50 | | 8 | $12.00 | Which equation represents the proportional relationship between the earnings (E) and the number of cups sold (c)?

Answer: E = 1.50c

To find the constant of proportionality (the price per cup), divide the earnings by the number of cups for any row. For example, $4.50 / 3 cups = $1.50 per cup. Also, $7.50 / 5 cups = $1.50 per cup. The relationship is E = 1.50 * c.

What is the value of the expression 5(y² - 2) + 3 when y = 4?

Answer: 73

First, substitute y = 4 into the expression: 5(4² - 2) + 3. Following the order of operations (PEMDAS/BODMAS), calculate the exponent first: 4² = 16. The expression becomes 5(16 - 2) + 3. Next, perform the operation inside the parentheses: 16 - 2 = 14. The expression is now 5(14) + 3. Then, perform the multiplication: 5 * 14 = 70. Finally, perform the addition: 70 + 3 = 73.

Which of the following algebraic expressions correctly represents the phrase "seven less than the product of a number, *n*, and four"?

Answer: 4n - 7

The phrase 'the product of a number, *n*, and four' translates to 4 * n or 4n. The phrase 'seven less than' means you subtract 7 from the previous part. Therefore, the complete expression is 4n - 7.