Questions in mathematics

Questions in mathematics

📝 Answered - Use logarithms to solve the exponential equation. [tex]e^{5 x}=6[/tex] The solution is [tex]x =[/tex] $\square$ . (Type an integer or decimal rounded to three decimal places as needed.)

📝 Answered - D = \{x \in \mathbb{R} \mid (x^2 - 10x + 21)(x^3 - x) = 0\}

📝 Answered - OAB is a triangle. [tex]\overrightarrow{OA} = 3a + 5b[/tex] [tex]\overrightarrow{OB} = 4a - b[/tex] Write [tex]\overrightarrow{AB}[/tex] in terms of [tex]a[/tex] and [tex]b[/tex]. Fully simplify your answer.

📝 Answered - Solve: [tex]$\cos (x+\pi)=\frac{1}{2}$[/tex] over the interval [tex]$\left[\frac{\pi}{2}, \pi\right]$[/tex]

📝 Answered - Janet wants to solve the equation [tex]y+\frac{y^2-5}{y^2-1}=\frac{y^2+y+2}{y+1}[/tex]. What should she multiply both sides of the equation by? A. [tex]y[/tex] B. [tex]y^2-1[/tex] C. [tex]y+1[/tex] D. [tex]y^2+y+2[/tex]

📝 Answered - Solve the equation. $-9 x+1=-x+17$

📝 Answered - Barry is trying to calculate the distance between point E(3, 1) and point F(4, 7). Which of the following expressions will he use? A. √(7-1)²+(4-3)² B. √(7-3)²+(4-1)² C. (7-4)²+(3-1)² D. √(4-7)²+(1-3)²

📝 Answered - Select the correct answer. The height of a right rectangular pyramid is equal to [tex]$x$[/tex] units. The length and width of the base are [tex]$(x+5)$[/tex] units and [tex]$\left(x-\frac{1}{2}\right)$[/tex] units. What is an algebraic expression for the volume of the pyramid? A. [tex]$\frac{1}{3} x^3-\frac{11}{6} x^2-\frac{5}{6} x$[/tex] B. [tex]$\frac{1}{3} x^3+\frac{3}{2} x^2-\frac{5}{6} x$[/tex] C. [tex]$x^3-\frac{9}{2} x^2-\frac{5}{2} x$[/tex] D. [tex]$\frac{1}{3} x^3+\frac{3}{2} x^2-\frac{5}{6} x$[/tex]

📝 Answered - Which rule describes a composition of transformations that maps pre-image PQRS to image P"Q"R"S"? A. [tex]R_{0,2700} \circ T_{-2,0}(x, y)[/tex] B. [tex]T_{-2,0^{\circ}} R_{0,270^{\circ}}(x, y)[/tex] C. [tex]R_{0,2700}{ }^{\circ} r_{y-2 x i s}(x, y)[/tex] D. [tex]r_{y \text {-axis }}{ }^{\circ} R_{0,2700}(x, y)[/tex]

📝 Answered - Find the simplified product $\sqrt[3]{9 x^4} \cdot \sqrt[3]{3 x^8}$