Questions in mathematics

Questions in mathematics

[Free] Solve on the interval $[0,2 \pi)$. Hint: Factor! $2 \cos ^2 x+\cos x-1=0$ A. There are no solutions in the given interval. B. $\left\{0, \frac{2 \pi}{3}, \frac{4 \pi}{3}\right\}$ C. $\left\{\frac{\pi}{2}, \frac{5 \pi}{6}, \frac{7 \pi}{6}\right\}$ D. $\left\{\frac{\pi}{3}, \pi, \frac{5 \pi}{3}\right\}$ E. $\{0\}$ F. $\left\{\frac{\pi}{6}, \frac{3 \pi}{2}, \frac{11 \pi}{6}\right\}$

[Free] Solve the exponential equation for $x$. $216=6^{(4 x+11)}$ A. $x=2$ B. $x=-2$ C. $x=3$ D. $x=-3

[Free] Factor completely. $5 x^2-45$ A. $5(x+3)(x-3)$ B. $5\left(x^2-45\right)$ C. $(5 x+9)(x-5)$ D. $5(x-9)(x+9)$

[Free] Multiply: [tex]4 x \sqrt[3]{4 x^2}\left(2 \sqrt[3]{32 x^2}-x \sqrt[3]{2 x}\right)[/tex]

[Free] Let f(x) = (x^x)^x and g(x) = x^{(x^x)}. Determine the relationship between f(x) and g(x).

[Free] What does the regression line represent in a simple linear regression analysis? A) The line that perfectly fits all sample data points. B) The average of all data points. C) The maximum distance between the data points and the line. D) The line of best fit that models the relationship between the independent and dependent variables.

[Free] If x = \sqrt[3]{28} and y = \sqrt[3]{27}, find the value of x + y - \frac{1}{x^2 + xy + y^2}

[Free] 1) Convert 2.5 × 10^5 seconds to hours. 2) Convert 0.06 tons to grams. 3) Convert 4.46 gallons to quarts.

[Free] Find the slope of the line defined by the parametric equations [tex]$x=-6$[/tex] and [tex]$y=5+8t$[/tex] without eliminating the parameter. If the slope is undefined, enter [tex]$\varnothing$[/tex].

[Free] What is the equation of the line that is parallel to the line $y-1=4(x+3)$ and passes through the point $(4,32)$? A. $y=-\frac{1}{4} x+33$ B. $y=-\frac{1}{4} x+36$ C. $y=4 x-16$ D. $y=4 x+16$