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Questions and Answers
If A represents the number of apples purchased at 15 cents each, and B represents the number of bananas purchased at 10 cents each, which of the following represents the total value of the purchases in cents?
If A represents the number of apples purchased at 15 cents each, and B represents the number of bananas purchased at 10 cents each, which of the following represents the total value of the purchases in cents?
- 15A + 10B (correct)
- 10A + 15B
- 25(A + B)
- A + B
What is the result of √2 × √15?
What is the result of √2 × √15?
- 30
- 17
- √30 (correct)
- √17
What is the value of the expression 2x² + 3xy - 4y² when x = 2 and y = -4?
What is the value of the expression 2x² + 3xy - 4y² when x = 2 and y = -4?
- 80
- -32
- 32
- -80 (correct)
If the radius of the larger circle is R and the smaller circle's radius is 3 units less than R, which of the following represents the area of the shaded region?
If the radius of the larger circle is R and the smaller circle's radius is 3 units less than R, which of the following represents the area of the shaded region?
What is the expansion of (3x - 2y)²?
What is the expansion of (3x - 2y)²?
If x > 2, then what is x² - x - 6 / x² - 4?
If x > 2, then what is x² - x - 6 / x² - 4?
What is the value of 4 - (-6) / -5?
What is the value of 4 - (-6) / -5?
If 2x - 3(x + 4) = -5, then what is the value of x?
If 2x - 3(x + 4) = -5, then what is the value of x?
What is the result of -3(5 - 6) - 4(2 - 3)?
What is the result of -3(5 - 6) - 4(2 - 3)?
Which inequalities are equivalent to 20 - ⅘x ≥ 16?
Which inequalities are equivalent to 20 - ⅘x ≥ 16?
Which of the following lists of numbers is ordered from least to greatest?
Which of the following lists of numbers is ordered from least to greatest?
If 5t + 2 = 6, then what is the value of t?
If 5t + 2 = 6, then what is the value of t?
For which of the following equations are x = 5 and x = -5 both solutions?
For which of the following equations are x = 5 and x = -5 both solutions?
If x ≠0, then what is u/x + 5u/x - u/5x?
If x ≠0, then what is u/x + 5u/x - u/5x?
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Study Notes
Algebra Basics
- Total value of apples (A at 15 cents) and bananas (B at 10 cents) is represented as 15A + 10B.
- Simplifying the product of roots: √2 × √15 = √30.
Polynomial Evaluation
- Evaluate the expression 2x² + 3xy - 4y² for x = 2 and y = -4 results in -80.
Geometry and Area
- The area of the shaded region between two concentric circles with radii R and R-3 is represented as πR² - π(R - 3)².
Expanding Binomials
- The square of the binomial (3x - 2y)² expands to 9x² - 12xy + 4y².
Rational Expressions
- For the expression (x² - x - 6)/(x² - 4) with x > 2, the simplified form is (x-3)/(x-2).
Simple Arithmetic
- The calculation 4 - (-6)/-5 results in -2.
Solving Linear Equations
- Solving the equation 2x - 3(x + 4) = -5 gives x = -7.
Simplifying Expressions
- For the expression -3(5 - 6) - 4(2 - 3), the result is 7.
Solving Inequalities
- The inequality 20 - (4/5)x ≥ 16 is equivalent to x ≤ 5.
Ordering Numbers
- The correct ordering of the numbers from least to greatest is -3/5, -1/3, 2/3, 3/5.
Solving for Variables
- For the equation 5t + 2 = 6, the solution for t is 4/5.
Quadratic Equations
- The equation that has solutions x = 5 and x = -5 is x² - 25 = 0.
Combining Rational Expressions
- For the expression u/x + 5u/x - u/5x, the simplified result is 29u/5x.
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