Questions in mathematics

Questions in mathematics

[Free] Complete the steps to simplify $\sqrt[5]{4} \cdot \sqrt{2}$. Rewrite using rational exponents. $\checkmark \quad 2^{\frac{2}{6}} \cdot 2^{\frac{1}{2}}$ $4^5 \cdot 2^2$ $4^{\frac{1}{6}} \cdot 2^{\frac{1}{4}}$ COMPLETE What is the least common denominator of the exponents? $\square$

[Free] Solve the system of equations: [tex]$\begin{array}{l} 4 x+3 y=8 \\ 4 x-3 y=-16 \end{array}$[/tex]

[Free] Find: $(4 x^2 y^3+2 x y^2-2 y)-(-7 x^2 y^3+6 x y^2-2 y)$. Place the correct coefficients in the difference.

[Free] The blood types of 900 people are collected at a doctor's office. The table shows the breakdown of patients by blood type. If a person from this group is selected at random, what is the probability that this person has type O blood? Express your answer as a fraction in lowest terms or as a decimal rounded to the nearest millionth (if necessary). | Blood Type | Number of Patients | |---|---| | A | 275 | | B | 265 | | O | 275 | | AB | 85 |

[Free] POLYNOMIAL (P) OR NON-POLYNOMIAL (NP)? 1. 5 2. -2x^2 3. (3/4)x + 21 4. 5x^2 - 4xy + 2y^2 5. a^(-2) + 4 6. sqrt(9h) 7. sqrt(25) 8. (2/k) + 14 9. 1/4 10. 10 - b^(1/2)

[Free] A shopkeeper buys 6 balloons for one rupee. How many balloons should he sell for one rupee so that he makes a profit of 20%? 1. 3 2. 4 3. 5 4. 6

[Free] In \(\triangle PQR\), \(|PO| = 15\) cm, \(|OR| = 16\) cm, \(|RP| = 9\) cm. The bisector of \(\angle P\) meets \(OR\) at \(A\) and \(M\) is the midpoint of \(OR\). Calculate \(|AM|\).

[Free] -x³ + 4x = mx Rearranged as: x³ - 4x + mx = 0 Factored: x(x² - 4 + m) = 0 Using the quadratic formula for x² - 4 + m = 0: x = \frac{0 \pm \sqrt{0 - 4(1)(m - 4)}}{2(1)} = \frac{\pm \sqrt{-4m + 16}}{2} = \pm \frac{\sqrt{4 - m}}{1} = \pm \sqrt{4 - m} Therefore, the solutions are: x = 0, \pm \sqrt{4 - m}

[Free] What is the general equation of a cosine function with an amplitude of 3, a period of [tex]$4 \pi$[/tex], and a horizontal shift of [tex]$-\pi$[/tex]? A. [tex]$y=4 \pi \cos (3(x-\pi))$[/tex] B. [tex]$y=3 \cos (4 \pi(x+\pi))$[/tex] C. [tex]$y=3 \cos (0.5(x+\pi))$[/tex] D. [tex]$y=4 \pi \cos (0.2(x+\pi))$[/tex]

[Free] Solve the linear inequality. Other than empty set ∅, graph the solution set on a number line. 8x - 9 ≤ 3x - 11