PERT Math Flashcards

Mathematical Expressions and Solutions

• Evaluating expressions such as -|-2| + (-3-2)² - (-5+2)⁰ results in a total of 22.
• The x-intercept for the linear equation y = -3x + 6 can be found at (2,0).
• Another expression, -|-3-2³| + 2 × 6² - 6, simplifies to 55.
• For the function f(x) = 4 - x², computing f(-2) yields 0.

Algebraic Manipulations

• Dividing the expression (14a⁴b⁻⁷) by (42b⁷a⁵) gives a simplified result of 1/3ab¹⁴.
• Evaluating the expression 2x² - 3y - 3z at x = -2, y = 3, z = -5 results in 14.
• Translating a sentence into an algebraic expression: "The product of a number and six is three times the same number less than ten" gives 6x = 10 - 3x.
• An inequality, 3(5x - 1) < 4(x - 6), simplifies to x < -21/11.

Solutions to Equations and Systems

• The solutions for x in the equation (3x + 2)(x - 4) = 0 are x = -2/3 and x = 4.
• Multiplying out (3x - 5)(2x + 5) results in 6x² + 5x - 25.
• Solving 3(x - 5) - 4x = 6(x - 10) - (x + 5) leads to x = 25/3.
• Simplifying expressions like -[-5 - (2 + x)] - 2(-5 + 2x) yields 17 - 3x.

Systems of Equations and Linear Functions

• The solution to the system of equations 2x - 5y = -4 and x + 6y = 15 is (3, 2).
• The equation passing through points (-3, -16) and (0, -10) can be written as y = 2x - 10.

Further Simplifications and Factoring

• The expression -3(x - 5x²) + 3x² - 6x simplifies to 18x² - 9x.
• Simplifying -10(x + 4) - 5(-x + 6x) results in -35x - 40.
• The expression √(a³b⁷z³) simplifies to ab³z√(abz).

Slope and Factoring

• The perpendicular slope for the line represented by 3x - 9y = 15 is -3.
• Factoring the expression 5x² - 17x + 14 gives (5x - 7)(x - 2).
• Further factoring 7z² + 60z - 27 leads to (7z - 3)(z + 9).
• The expression 2x² + 25x + 50 can be factored as (2x + 5)(x + 10).

Special Values and Properties

• For n = 2 in the expression (2ⁿ)ⁿ + n², the result is 20.
• Evaluating f(x) = 2x² + 5x - 6 at x + 3 results in 2x² + 17x + 27.
• Extracting a square root √225 + √900 gives a result of 45.
• If the original price of an item was $30 and the paid price was $24, the discount percentage is 20%.

Operations and Simplified Outcomes

• The division (30/7) ÷ (-19/5) simplifies to (-150/133).
• To solve (4/x) = (12/7.5), the result is 2.5.
• Converting .0000968 to scientific notation yields 9.68 × 10⁻⁵ and 968000 converts to 9.68 × 10⁵.
• The quadratic equation 4x² - 16x + 16 = 0 has a solution of x = 2.
• The expression ₃√(27x³y⁶) + √(4x²y⁴) simplifies to 5xy².
• The product (3x + 2y)(x - 3y) expands to 3x² - 7xy - 6y².
• Evaluating g(x) = 3x² + 4x - 7 at x = -1 gives -8.
• Solving the equation ½(3x + 5) - ½x = ¾(x + 1) results in -7.
• The inequality 2(x + 3) - 4x > 6(2x - 1) leads to x > 6/7.