Questions and Answers
What is the result of $√12 × √8$?
What is $√18/144$ simplified?
√2 / 4
What is the value of $2/3 (9) - 5(2)³ + 6 ÷ 2$?
-31
What is the result of $√36 + 8×5 - 3²$?
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What is the result of $(3+6)² - 27 ÷ 9$?
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What is the value of $(36/(8-2)² - 1)²$?
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What is the solution to the equation $2b - 10 = -3b + 5$?
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What is the solution for $7/6 x - 2 = 1/3$?
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What is the value of $3(q-5) = 2(q+5)$?
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Solve for $a$ in $7 + 2(a - 3) = -9$.
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What is the solution for the inequality $-2x + 7 ≤ 45$?
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What is the solution for $5n - 3 > -18$?
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What is $(4x³)³$ evaluated?
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What is the simplified form of $(2x² × y/z)³$?
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What is the product of $(3m²)² × (2n)³$?
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What is the result of $(m^{-5} × n^3)(n^4 × m^{0})^{-2}$?
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What is the result of $(x²/y)² × (x/y³)³$?
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What is $9r³s^{-5} / 18rs³$ simplified?
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What are the solutions for $x² - 81 = 0$?
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What is the simplified form of $f² - 12f + 27 + 0$?
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What are the solutions for $n² - 13 + 42 = 0$?
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What are the solutions for $49 - x² = 0$?
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What are the solutions for $a³ - 7a² - 30a = 0$?
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What are the solutions for $2z³ + 8z² + 6z = 0$?
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What are the solutions for the system of equations $y = 5x + 4$ and $15x - y = 26$?
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What are the solutions for the system of equations $y - x = 4$ and $2y + 3x = 18$?
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What points lie on the line represented by $y = 3x + 4$?
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What points lie on the line represented by $4x - 2y = 10$?
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What points lie on the line represented by $y = -x$?
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Find the slope, m, between the two points (5, -6) and (-3, 6). What is m?
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Find the slope, m, between the two points (-6, 4) and (-4, 8). What is m?
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Solve for b in the equation $a/b = c/d$.
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Solve for x in the equation $y=-v(u-x)$.
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Solve for h in the equation $V= rac{1}{3} πr²h$.
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Study Notes
Radical Expressions
- √12 × √8 simplifies to 4√6.
- √18/144 can be reduced to √2/4.
Evaluating Expressions
- Expression 2/3 (9) - 5(2)³ + 6 ÷ 2 evaluates to -31.
- √36 + 8×5 - 3² totals 43.
- (3 + 6)² - 27 ÷ 9 simplifies to 78.
- (36/(8 - 2)² - 1)² results in 0.
Solving Linear Equations
- The equation 2b - 10 = -3b + 5 solves to b = 3.
- 7/6 x - 2 = 1/3 gives x = 2.
- The equation 3(q - 5) = 2(q + 5) simplifies to q = 25.
- 7 + 2(a - 3) results in a = -5.
Inequalities
- The inequality -2x + 7 ≤ 45 gives x ≥ -19.
- Solving 5n - 3 > -18 leads to n > -3.
Exponent Rules
- (4x³)³ equals 64x^9.
- The expression (2x² × y/z)³ expands to 8x^6 × y³/z³.
- (3m²)² × (2n)³ simplifies to 72m^4 × n^3.
- The expression (m^-5 × n³)(n^4 × m^0)^-2 reduces to 1/m^5 × n^5.
Rational Expressions
- (x² / y)² × (x / y³)³ simplifies to x^7 / y^11.
- The expression 9r³s^-5 / 18rs³ reduces to r² / 2s^8.
Solving Quadratic Equations
- The equation x² - 81 = 0 has solutions x = 9 and x = -9.
- f² - 12f + 27 remains as f² - 12f + 27.
- The equation n² - 13 + 42 = 0 results in n = 7 and n = 6.
- 49 - x² = 0 gives x = 7 and x = -7.
- The cubic equation a³ - 7a² - 30a = 0 has roots a = 0, a = 10, and a = -3.
- The equation 2z³ + 8z² + 6z = 0 leads to z = 0, z = -1, and z = -3.
Systems of Equations
- For the system y = 5x + 4 and 15x - y = 26, the solution is x = 3 and y = 19.
- The system y - x = 4 and 2y + 3x = 18 results in x = 2 and y = 6.
Graphing Linear Equations
- The equation y = 3x + 4 passes through points (0, 4) and (1, 7).
- The line 4x - 2y = 10 includes points (0, -5) and (1, -3).
- The equation y = -x contains points (0, 0) and (1, -1).
Finding the Slope
- The slope m between points (5, -6) and (-3, 6) is m = -3/2.
- For points (-6, 4) and (-4, 8), the slope m = 2.
Solving for Variables in Formulas
- Rearranging a/b = c/d gives b = ad/c.
- For y = -v(u - x), solving for x leads to x = y/v + u.
- From V = 1/3 πr²h, solving for h gives h = 3V/πr².
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