PERT Math Flashcards

Questions and Answers

What is the result of the expression $-|-2| + (-3-2)² - (-5+2)⁰$?

What is the x-intercept of the equation $y=-3x+6$?

(2,0)

What is the result of the expression $-|-3-2³| + 2 × 6² - 6$?

If $f(x)= 4-x²$, what is $f(-2)$?

0 Signup and view all the answers

What is the result of the expression $(14a⁴b⁻⁷) ÷ (42b⁷a⁵)$?

1/3ab¹⁴ Signup and view all the answers

Evaluate $2x²-3y-3z$ if $x=-2$, $y=3$ and $z=-5$.

14 Signup and view all the answers

Translate the following sentence into an algebraic expression: The product of a number and six is three times the same number less than ten.

6x = 10 - 3x Signup and view all the answers

Solve the inequality $3(5x-1) < 4(x-6)$.

x < -21/11 Signup and view all the answers

Find the solutions for $x$ in the equation $(3x+2)(x-4) = 0$.

x = -2/3 and 4 Signup and view all the answers

Multiply the binomials $(3x-5)(2x+5)$.

6x² + 5x - 25 Signup and view all the answers

Solve for $x$: $3(x-5) - 4x = 6(x-10) - (x+5)$.

x = 25/3 Signup and view all the answers

Simplify the expression $-[-5-(2+x)] - 2(-5+2x)$.

17-3x Signup and view all the answers

Solve the system of equations: $2x-5y=-4$, $x+6y=15$.

(3,2) Signup and view all the answers

Write the equation that passes through the points (-3,-16) and (0,-10).

y=2x-10 Signup and view all the answers

Simplify the expression $-3(x-5x²) + 3x² - 6x$.

18x² - 9x Signup and view all the answers

Simplify the expression $-10(x+4) - 5(-x+6x)$.

-35x - 40 Signup and view all the answers

Simplify the expression $√(a³b⁷z³)$.

ab³z√abz Signup and view all the answers

Find the perpendicular slope of the line $3x-9y=15$.

-3 Signup and view all the answers

Factor the quadratic $5x²-17x+14$.

(5x-7)(x-2) Signup and view all the answers

Simplify the expression $3 + 2 × 3 ÷ (-2+3)²$.

9 Signup and view all the answers

Solve $2|5x-4| - 6 = 10$.

x = 12/5 and -4/5 Signup and view all the answers

What is $(3/x)-(2/y)$?

(3x-2y)/xy Signup and view all the answers

Factor the quadratic $7z²+60z-27$.

(7z-3)(z+9) Signup and view all the answers

Factor the quadratic $2x²+25x+50$.

(2x+5)(x+10) Signup and view all the answers

What is $(2ⁿ)ⁿ + n²$ if $n=2$?

20 Signup and view all the answers

If $f(x) = 2x²+5x-6$, what is $f(x+3)$?

2x²+17x+27 Signup and view all the answers

Solve for $x$: $ax+by=cd$.

x=(cd-by)/a Signup and view all the answers

What is $√225 + √900$?

45 Signup and view all the answers

If the original price of an item was $30 and Joan only paid $24, what was the percentage of the discount Joan received?

20 Signup and view all the answers

What is $(30/7) ÷ (-19/5)$?

(-150/133) Signup and view all the answers

Solve: $(4/x) = (12/7.5)$.

2.5 Signup and view all the answers

What is 0.0000968 in scientific notation?

9.68 × 10⁻⁵ Signup and view all the answers

What is 968000 in scientific notation?

9.68 × 10⁵ Signup and view all the answers

Solve: $4x²-16x+16=0$.

2 Signup and view all the answers

$₃√(27x³y⁶)+√(4x²y⁴)$ results in what expression?

5xy² Signup and view all the answers

Multiply the expressions $(3x+2y)(x-3y)$.

3x²-7xy-6y² Signup and view all the answers

If $g(x) = 3x²+4x-7$, what is $g(-1)$?

-8 Signup and view all the answers

Solve the equation: $½(3x+5) - ½x = ¾(x+1)$.

-7 Signup and view all the answers

Solve the inequality $2(x+3) - 4x > 6(2x-1)$.

6/7 Signup and view all the answers

Study Notes

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.

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Test your knowledge of basic math concepts with these PERT Math flashcards. Each card covers different mathematical expressions and equations, helping you enhance your problem-solving skills. Perfect for students preparing for the PERT exam!