Questions in mathematics

Questions in mathematics

📝 Answered - If point $P$ is $\frac{4}{7}$ of the distance from $M$ to $N$, what ratio does the point $P$ partition the directed line segment from $M$ to N into? A. $4: 1$ B. $4: 3$ C. $4: 7$ D. $4: 10

📝 Answered - Which is equivalent to $\sqrt[3]{8}^x$ ? $\sqrt[x]{8}^3$ $8^{\frac{3}{x}}$ $8^{\frac{x}{3}}$ $8^{3 x}$

📝 Answered - Find all real solutions of the equation. (Enter your answers as a comma-separated list. If there is no solution, enter NO SOLUTION.) [tex]$x-\sqrt{8 x-16}=0$[/tex]

📝 Answered - The proof that point $(1, \sqrt{3})$ lies on the circle that is centered at the origin and contains the point $(0,2)$ is found in the table below. What is the justification for the 5th statement? | Statement | Justification | | --------- | ------------- | | A circle is centered at $(0,0)$ and contains the point $(0,2)$. | Given | | The radius of the circle is the distance from $(0,0)$ to $(0,2)$. | Definition of radius | | The distance from $(0,0)$ to $(0,2)$ is $\sqrt{(0-0)^2+(2-0)^2}=\sqrt{2^2}=2$ | Distance formula | | If $(1, \sqrt{3})$ lies on the circle it must be the same distance from the center as $(0,2)$. | Definition of a circle | | The distance from $(1, \sqrt{3})$ is $\sqrt{(0-1)^2+(0-\sqrt{3})^2}=\sqrt{1+3}=2$ | | Since $(1, \sqrt{3})$ is 2 units from $(0,0)$, it lies on a circle that is centered at the origin and contains the point $(0,2)$.

📝 Answered - Simplify $\frac{9^{2 x+3} \div 27^{4 x-7}}{81^x \times 3^{x+1}}$

📝 Answered - What is the solution of $\log _x 728=3$?

📝 Answered - Which exponent is missing from this equation? [tex]$5.6 \times 10^{\square}=56,000$[/tex] A. 5 B. 4 C. 3 D. 2

📝 Answered - Perform the indicated operations. $\left[\left(9 m^2+3 m-6\right)-\left(7 m^2-5 m+7\right)\right]-\left(m^2+m+5\right)$

📝 Answered - Write the rational expression in lowest terms. [tex]$\frac{x^2-11 x+28}{x^2+4 x-32}$[/tex]

📝 Answered - Multiply: $\sqrt[6]{x} \cdot \sqrt[4]{y^3}$