ADS by LearnersUpdate March 27, 2024 Can you SOLVE:\(\frac{4!}{3!-2!}\) ? A. \(6\) B. \(8\) C. \(7\) D. \(None\) Simplify the following expression: \(\sqrt{50} + \sqrt{27}\) A. \(9\sqrt{2}\) B. \(5\sqrt{2} + 3\sqrt{3}\) C. \(8\sqrt{2} + 2\sqrt{3}\) D. \(7\sqrt{2} + 3\sqrt{3}\) Can you simplify: \(\frac{3^{x}\times3^{2x}}{9^x}\) ? A. \(3^x\) B. \(9^x\) C. \(3\) D. \(none\) Evaluate the integral:\(\int (x^2 + 3x) \, dx\) A. \(\frac{1}{3}x^3 + \frac{3}{2}x^2 + C\) B. \(x^3 + 3x^2 + C\) C. \(\frac{1}{2}x^3 + 2x^2 + C\) D. \(\frac{1}{3}x^3 + 3x^2 + C\) Evaluate: \(6^{-1}\) A. 6 B. 0 C. -6 D. \(\frac{1}{6}\) Simplify: \(\frac{5^6}{5^4}\) A. \(5^{-2}\) B. \(5^{10}\) C. 25 D. 30 Evaluate: \(3^0\) A. 3 B. 0 C. 1 D. Undefined Simplify: \(2^3 \times 2^4\) A. \(2^6\) B. \(2^{12}\) C. \(4^7\) D. \(2^7\) Simplify: \(8^2 \times 8^3\) A. \(8^5\) B. \(8^6\) C. \(64^5\) D. \(8^{10}\) Rewrite in simplified form: \(d^{5} \times d^{-5}\) A. 1 B. \(d^{10}\) C. 0 D. \(d^{1}\) \(Simplify: \sqrt{250}\) A. 50 B. 25 C. \(5\sqrt{10}\) D. 10 Solve for \(a\) and \(b\):\( a - b = 5 \) and \( 2a + b = 4 \) A. \(a = 5, b = 0\) B. \(a = 4, b = -1\) C. \(a = 3, b = -2\) D. \(a = 6, b = 1\) Solve for \(x\) and \(y\):\( 2x + 3y = 9 \) and \( x - 2y = 1 \) A. \(x = 4, y = 0\) B. \(x = 2, y = 2\) C. \(x = 1, y = 3\) D. \(x = 3, y = 1\) Solve for \(x\) and \(y\):\( 5x - 2y = 11\) and \( x + y = 5 \) A. \(x = 3, y = 2\) B. \(x = 4, y = 1\) C. \(x = 2, y = 3\) D. \(x = 1, y = 4\) Solve for \(x\) and \(y\):\( 2x + y = 9 \) and \( -3x - y = -11\) A. \(x = 2, y = 5\) B. \(x = 4, y = 2\) C. \(x = 3, y = 3\) D. \(x = 5, y = 1\) If \(y = x + 7\) and \(k = 2y\), what is \(k\) when \(x = 5\)? A. \(k = 24\) B. \(k = 14\) C. \(k = 17\) D. \(k = 19\) Given \(a = b + c\) and \(b = 2c - 4\), express \(a\) in terms of \(c\). A. \(a = 3c - 4\) B. \(a = 2c - 4\) C. \(a = c - 4\) D. \(a = c\) Substitute \(x = 3\) into \(f(x) = 2x^2 + 4x - 5\). A. \(f(3) = 32\) B. \(f(3) = 20\) C. \(f(3) = 25\) D. \(f(3) = 30\) If \(z = 4x + 2\) and \(x = 3y + 7\), what is \(z\) in terms of \(y\)? A. \(z = 12y + 30\) B. \(z = 7y + 9\) C. \(z = 4y + 14\) D. \(z = y + 9\) Find:\( \int (6x^4 - 4x^3 + 5x^2 - x + 2) \, dx\) A. \(\frac{6}{5}x^5 - x^4 + \frac{5}{3}x^3 - \frac{1}{2}x^2 + 2x + C\) B. \(\frac{1}{5}x^5 - x^4 + \frac{5}{3}x^3 - \frac{1}{2}x^2 + 2x + C\) C. \(\frac{6}{5}x^5 - \frac{4}{4}x^4 + \frac{5}{2}x^3 - x^2 + 2x + C\) D. \(\frac{6}{6}x^5 - x^4 + \frac{1}{3}x^3 - \frac{1}{2}x^2 + x + C\) \(\text{Find } \int (3x^3 - 5x^2 + 4x - 8) \, dx\) A. \(\frac{3}{4}x^4 - \frac{5}{3}x^3 + 2x^2 - 8x + C\) B. \(\frac{3}{4}x^4 - \frac{5}{2}x^3 + x^2 - 8x + C\) C. \(\frac{1}{4}x^4 - \frac{5}{3}x^3 + 2x^2 - 9x + C\) D. \(\frac{3}{5}x^4 - \frac{5}{4}x^3 + 2x^2 - 7x + C\) Find:\( \int (x^5 - 4x^4 + 3x^3 - 2x^2 + x) \, dx\) A. \(\frac{1}{6}x^6 - \frac{4}{5}x^5 + \frac{3}{4}x^4 - \frac{2}{3}x^3 + \frac{1}{2}x^2 + C\) B. \(\frac{1}{6}x^6 - x^5 + \frac{3}{4}x^4 - \frac{1}{3}x^3 + \frac{1}{2}x^2 + C\) C. \(\frac{1}{5}x^6 - \frac{4}{5}x^5 + \frac{1}{4}x^4 - \frac{2}{3}x^3 + x^2 + C\) D. \(\frac{1}{6}x^6 - \frac{4}{4}x^5 + \frac{3}{3}x^4 - \frac{1}{2}x^3 + \frac{1}{2}x^2 + C\) \(\text{Find } \int (-3x^3 + 2x^2 + x - 5) \, dx\) A. \(-\frac{3}{4}x^4 + \frac{2}{3}x^3 + \frac{1}{2}x^2 - 5x + C\) B. \(-\frac{1}{4}x^4 + x^3 + \frac{1}{2}x^2 - 5x + C\) C. \(-\frac{3}{4}x^4 + \frac{2}{3}x^3 + \frac{1}{3}x^2 - 4x + C\) D. \(-\frac{3}{5}x^4 + \frac{2}{3}x^3 + \frac{1}{2}x^2 - 5x + C\) \(\text{Find } \int (2x^2 + 7x - 4) \, dx\) A. \(\frac{2}{3}x^3 + \frac{7}{2}x^2 - 4x + C\) B. \(\frac{1}{3}x^3 + \frac{7}{2}x^2 - 4x + C\) C. \(\frac{2}{4}x^3 + 3x^2 - 4x + C\) D. \(\frac{2}{3}x^3 + \frac{7}{3}x^2 - 5x + C\) \(\text{Find } \int (4x^4 - 3x^3 + x^2 + 1) \, dx\) A. \(\frac{4}{5}x^5 - \frac{3}{4}x^4 + \frac{1}{3}x^3 + x + C\) B. \(\frac{1}{5}x^5 - \frac{3}{4}x^4 + \frac{1}{2}x^3 + x + C\) C. \(\frac{4}{5}x^5 - \frac{1}{4}x^4 + \frac{1}{3}x^3 + x + C\) D. \(\frac{4}{6}x^5 - \frac{3}{3}x^4 + \frac{1}{3}x^3 + x + C\) \(\text{Find } \int (5x^2 - 4x + 9) \, dx\) A. \(\frac{5}{3}x^3 - 2x^2 + 9x + C\) B. \(\frac{5}{4}x^3 - \frac{4}{2}x^2 + x + C\) C. \(\frac{5}{2}x^3 - 2x^2 + 9x + C\) D. \(\frac{5}{4}x^3 - \frac{4}{2}x^2 + 9x + C\) Find \( \int (-2x^5 + 6x^4 - x^3 + 5) \, dx\) A. \(-\frac{2}{6}x^6 + \frac{6}{5}x^5 - \frac{1}{4}x^4 + x + C\) B. \(-\frac{1}{3}x^6 + \frac{6}{5}x^5 - \frac{1}{4}x^4 + 5x + C\) C. \(-\frac{2}{7}x^6 + \frac{1}{5}x^5 - \frac{1}{4}x^4 + 5x + C\) D. \(-\frac{1}{3}x^6 + \frac{1}{5}x^5 - \frac{1}{3}x^4 + 5x + C\) \(\text{Find } \int (x^4 + 3x^3 - 2x^2 + 7) \, dx\) A. \(\frac{1}{5}x^5 + \frac{3}{4}x^4 - \frac{2}{3}x^3 + 7x + C\) B. \(\frac{1}{5}x^5 + \frac{1}{4}x^4 - \frac{2}{3}x^3 + 7x + C\) C. \(\frac{1}{4}x^5 + \frac{3}{4}x^4 - \frac{2}{3}x^3 + 7x + C\) D. \(\frac{1}{5}x^5 + \frac{3}{4}x^4 - \frac{1}{2}x^3 + 7x + C\) Find \(\frac{dy}{dx}\) given that:\(y = 6x^4 - 4x^3 + 5x^2 - x + 2\) A. \(24x^3 - 12x^2 + 10x - 1\) B. \(12x^3 - 8x^2 + 10x - 1\) C. \(24x^4 - 4x^3 + 10x^2 - x\) D. \(18x^3 - 6x^2 + 5x - 1\) Find \( f'(x) \)if \(f(x) = 3x^3 - 5x^2 + 4x - 8\) A. \(9x^2 - 10x + 4\) B. \(6x^2 - 10x + 4\) C. \(9x^3 - 5x^2 + 4\) D. \(6x^3 - 10x + 3\) Find \( f'(x)\) if\(f(x) = x^5 - 4x^4 + 3x^3 - 2x^2 + x\) A. \(5x^4 - 16x^3 + 9x^2 - 4x + 1\) B. \(4x^4 - 12x^3 + 6x^2 - 2x\) C. \(5x^5 - 16x^4 + 9x^3 - 4x^2\) D. \(5x^4 - 12x^3 + 6x^2 - 2x\) Find \( \frac{dy}{dx}\)if \( y = -3x^3 + 2x^2 + x - 5\) A. \(-9x^2 + 4x + 1\) B. \(-6x^2 + 4x + 1\) C. \(-9x^3 + 2x^2 + 1\) D. \(-9x^2 + 4x\) \(\text{Find } f'(x) \text{ if } f(x) = 2x^2 + 7x - 4\) A. \(4x + 7\) B. \(4x\) C. \(2x + 7\) D. \(4x - 7\) Find \( f'(x)\) if\( f(x) = 4x^4 - 3x^3 + x^2 + 1\) A. \(16x^3 - 9x^2 + 2x\) B. \(8x^3 - 9x^2 + 2x\) C. \(16x^4 - 3x^3 + 2x\) D. \(12x^3 - 6x^2 + 2x\) \(\text{Find } f'(x) \text{ if } f(x) = x^3 - 7x + 10\) A. \(3x^2 - 7\) B. \(3x^3 - 7x\) C. \(x^2 - 7\) D. \(2x^3 - 7\) \(\text{Find } f'(x) \text{ if } f(x) = 5x^2 - 4x + 9\) A. \(10x - 4\) B. \(10x + 4\) C. \(5x^2 - 4\) D. \(10x\) Find \( f'(x)\) if\(f(x) = -2x^5 + 6x^4 - x^3 + 5\) A. \(-10x^4 + 24x^3 - 3x^2\) B. \(-10x^5 + 6x^4 - 3x^3\) C. \(-10x^4 + 18x^3 - 2x^2\) D. \(-10x^4 + 24x^3 - 2x^2\) Find \( f'(x)\) if\( f(x) = x^4 + 3x^3 - 2x^2 + 7\) A. \(4x^3 + 9x^2 - 4x\) B. \(4x^4 + 3x^3 - 2x\) C. \(4x^3 + 6x^2 - 4\) D. \(3x^4 + 6x^3 - 2x^2\) \({\text{Evaluate: } \frac{7\sqrt{2}}{4-\sqrt{3}}}\) A. \(\frac{28\sqrt{2}}{13} + \frac{21\sqrt{6}}{13}\) B. \(\frac{27\sqrt{2}}{13} + \frac{21\sqrt{6}}{13}\) C. \(\frac{28\sqrt{2}}{13} - \frac{21\sqrt{6}}{13}\) D. \(\frac{26\sqrt{2}}{13} + \frac{20\sqrt{6}}{13}\) \(\text{Evaluate: } \frac{6\sqrt{5}}{5-\sqrt{3}}\) A. \(\frac{15\sqrt{5}}{11} + \frac{3\sqrt{15}}{11}\) B. \(\frac{15\sqrt{5}}{11} - \frac{9\sqrt{15}}{11}\) C. \(\frac{13\sqrt{5}}{11} + \frac{9\sqrt{15}}{11}\) D. \(\frac{17\sqrt{5}}{11} + \frac{7\sqrt{15}}{11}\) \(\text{Evaluate: } \frac{3+\sqrt{6}}{\sqrt{4}-\sqrt{2}}\) A. \(\frac{1}{2}\left(3\sqrt{2}+2\sqrt{3}+2\sqrt{6}\right)\) B. \(4 + \sqrt{12} - \sqrt{6}\) C. \(5 - \sqrt{12} + \sqrt{6}\) D. \(6 + \sqrt{12} + \sqrt{6}\) \(\text{Evaluate: } \left(6+\sqrt{13}\right)\left(6-\sqrt{13}\right)\) A. \(23\) B. \(12\) C. \(6\sqrt{13}\) D. \(6+\sqrt{13}\) \(\text{Evaluate: } \left(3+\sqrt{11}\right)\left(3-\sqrt{11}\right)\) A. \(- 2\) B. \(6\) C. \(3\sqrt{11}\) D. \(9\sqrt{11}\) \(\text{Evaluate: } \left(5+\sqrt{2}\right)\left(5-\sqrt{2}\right)\) A. \(23\) B. \(10\) C. \(5\sqrt{2}\) D. \(27\) \(\text{Evaluate: } \left(4+\sqrt{7}\right)\left(4-\sqrt{7}\right)\) A. \(16 - \sqrt{7}\) B. 9 C. 8 D. \(4\sqrt{7}\) \(\text{Evaluate: } \left(2+\sqrt{3}\right)\left(2-\sqrt{3}\right)\) A. 1 B. \(2\sqrt{3}\) C. \(5- 2\sqrt{3}\) D. \(2-\sqrt{3}\) Expand and simplify: \(\left(3+\sqrt{5}\right)\left(3-\sqrt{5}\right)\) A. 4 B. \(6\sqrt{5}\) C. \(5\sqrt{3}\) D. 14 \(\text{Simplify: } \sqrt[3]{64}\) A. \(4\) B. \(16\) C. \(8\) D. \(6\) \(\text{Simplify the surd: } \sqrt{45}\) A. \(3\sqrt{5}\) B. \(9\sqrt{5}\) C. \(5\sqrt{9}\) D. \(7\sqrt{5}\) \(\text{Simplify: } 7\sqrt{28} + 4\sqrt{7}\) A. \(15\sqrt{7}\) B. \(18\sqrt{7}\) C. \(7\sqrt{4}\) D. \(11\sqrt{7}\) \(\text{Rationalize the denominator: } \frac{5}{\sqrt{3}}\) A. \(\frac{5\sqrt{3}}{3}\) B. \(\frac{5\sqrt{3}}{9}\) C. \(\frac{15}{\sqrt{3}}\) D. \(\frac{10}{3}\) \(\text{Simplify: } 3\sqrt{12} - 2\sqrt{3}\) A. \(5\sqrt{3}\) B. \(6\sqrt{3}\) C. \(4\sqrt{3}\) D. \(1\sqrt{3}\) \(\text{Rationalize the denominator: } \frac{4}{\sqrt{7}}\) A. \(\frac{4\sqrt{7}}{7}\) B. \(\frac{4\sqrt{7}}{49}\) C. \(\frac{28}{\sqrt{7}}\) D. \(\frac{8}{7}\) Perform the operation:\( 5\sqrt{5} + 7\sqrt{5}\) A. \(12\sqrt{5}\) B. \(35\sqrt{5}\) C. \(5\sqrt{7}\) D. \(2\sqrt{10}\) \(\text{Simplify the surd: } \sqrt{32}\) A. \(4\sqrt{2}\) B. \(16\sqrt{2}\) C. \(2\sqrt{8}\) D. \(5\sqrt{2}\) \(\text{Simplify the surd: } \sqrt{27}\) A. \(3\sqrt{3}\) B. \(9\sqrt{3}\) C. \(3\sqrt{9}\) D. \(6\sqrt{3}\) \(\text{Simplify: } 5\sqrt{8} - 3\sqrt{2}\) A. \(7\sqrt{2}\) B. \(10\sqrt{2}\) C. \(2\sqrt{6}\) D. \(8\sqrt{2}\) \(\text{Rationalize the denominator: } \frac{3}{\sqrt{5}}\) A. \(\frac{3\sqrt{5}}{5}\) B. \(\frac{3\sqrt{5}}{10}\) C. \(\frac{15}{\sqrt{5}}\) D. \(\frac{6}{5}\) \(\text{Simplify the surd: } \sqrt{18}\) A. \(9\sqrt{2}\) B. \(3\sqrt{2}\) C. \(2\sqrt{9}\) D. \(6\sqrt{3}\) \(\text{Simplify the surd: } \sqrt{50}\) A. \(5\sqrt{2}\) B. \(25\sqrt{2}\) C. \(2\sqrt{5}\) D. \(7\sqrt{2}\) Your score isShare your score with friends! 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