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Questions and Answers
What is the result of the expression $-|-2| + (-3-2)² - (-5+2)⁰$?
What is the result of the expression $-|-2| + (-3-2)² - (-5+2)⁰$?
22
What is the x-intercept of the equation $y=-3x+6$?
What is the x-intercept of the equation $y=-3x+6$?
(2,0)
What is the result of the expression $-|-3-2³| + 2 × 6² - 6$?
What is the result of the expression $-|-3-2³| + 2 × 6² - 6$?
55
If $f(x)= 4-x²$, what is $f(-2)$?
If $f(x)= 4-x²$, what is $f(-2)$?
What is the result of the expression $(14a⁴b⁻⁷) ÷ (42b⁷a⁵)$?
What is the result of the expression $(14a⁴b⁻⁷) ÷ (42b⁷a⁵)$?
Evaluate $2x²-3y-3z$ if $x=-2$, $y=3$ and $z=-5$.
Evaluate $2x²-3y-3z$ if $x=-2$, $y=3$ and $z=-5$.
Translate the following sentence into an algebraic expression: The product of a number and six is three times the same number less than ten.
Translate the following sentence into an algebraic expression: The product of a number and six is three times the same number less than ten.
Solve the inequality $3(5x-1) < 4(x-6)$.
Solve the inequality $3(5x-1) < 4(x-6)$.
Find the solutions for $x$ in the equation $(3x+2)(x-4) = 0$.
Find the solutions for $x$ in the equation $(3x+2)(x-4) = 0$.
Multiply the binomials $(3x-5)(2x+5)$.
Multiply the binomials $(3x-5)(2x+5)$.
Solve for $x$: $3(x-5) - 4x = 6(x-10) - (x+5)$.
Solve for $x$: $3(x-5) - 4x = 6(x-10) - (x+5)$.
Simplify the expression $-[-5-(2+x)] - 2(-5+2x)$.
Simplify the expression $-[-5-(2+x)] - 2(-5+2x)$.
Solve the system of equations: $2x-5y=-4$, $x+6y=15$.
Solve the system of equations: $2x-5y=-4$, $x+6y=15$.
Write the equation that passes through the points (-3,-16) and (0,-10).
Write the equation that passes through the points (-3,-16) and (0,-10).
Simplify the expression $-3(x-5x²) + 3x² - 6x$.
Simplify the expression $-3(x-5x²) + 3x² - 6x$.
Simplify the expression $-10(x+4) - 5(-x+6x)$.
Simplify the expression $-10(x+4) - 5(-x+6x)$.
Simplify the expression $√(a³b⁷z³)$.
Simplify the expression $√(a³b⁷z³)$.
Find the perpendicular slope of the line $3x-9y=15$.
Find the perpendicular slope of the line $3x-9y=15$.
Factor the quadratic $5x²-17x+14$.
Factor the quadratic $5x²-17x+14$.
Simplify the expression $3 + 2 × 3 ÷ (-2+3)²$.
Simplify the expression $3 + 2 × 3 ÷ (-2+3)²$.
Solve $2|5x-4| - 6 = 10$.
Solve $2|5x-4| - 6 = 10$.
What is $(3/x)-(2/y)$?
What is $(3/x)-(2/y)$?
Factor the quadratic $7z²+60z-27$.
Factor the quadratic $7z²+60z-27$.
Factor the quadratic $2x²+25x+50$.
Factor the quadratic $2x²+25x+50$.
What is $(2ⁿ)ⁿ + n²$ if $n=2$?
What is $(2ⁿ)ⁿ + n²$ if $n=2$?
If $f(x) = 2x²+5x-6$, what is $f(x+3)$?
If $f(x) = 2x²+5x-6$, what is $f(x+3)$?
Solve for $x$: $ax+by=cd$.
Solve for $x$: $ax+by=cd$.
What is $√225 + √900$?
What is $√225 + √900$?
If the original price of an item was $30 and Joan only paid $24, what was the percentage of the discount Joan received?
If the original price of an item was $30 and Joan only paid $24, what was the percentage of the discount Joan received?
What is $(30/7) ÷ (-19/5)$?
What is $(30/7) ÷ (-19/5)$?
Solve: $(4/x) = (12/7.5)$.
Solve: $(4/x) = (12/7.5)$.
What is 0.0000968 in scientific notation?
What is 0.0000968 in scientific notation?
What is 968000 in scientific notation?
What is 968000 in scientific notation?
Solve: $4x²-16x+16=0$.
Solve: $4x²-16x+16=0$.
$₃√(27x³y⁶)+√(4x²y⁴)$ results in what expression?
$₃√(27x³y⁶)+√(4x²y⁴)$ results in what expression?
Multiply the expressions $(3x+2y)(x-3y)$.
Multiply the expressions $(3x+2y)(x-3y)$.
If $g(x) = 3x²+4x-7$, what is $g(-1)$?
If $g(x) = 3x²+4x-7$, what is $g(-1)$?
Solve the equation: $½(3x+5) - ½x = ¾(x+1)$.
Solve the equation: $½(3x+5) - ½x = ¾(x+1)$.
Solve the inequality $2(x+3) - 4x > 6(2x-1)$.
Solve the inequality $2(x+3) - 4x > 6(2x-1)$.
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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