Questions in mathematics

Questions in mathematics

[Free] Perform the indicated operations on the following polynomials. Arrange answer in descending powers. $\left(6 x^3+27 x-19 x^2-15\right) \div(3 x-5)=$ A. $4 x^2-3 x+2+\frac{3}{5 x-5}$ B. $3 x^2-2 x+5+\frac{4}{3 x-5}$ C. $2 x^3-4 x+3+\frac{4}{3 x-5}$ D. $2 x^2-3 x+4+\frac{5}{3 x-5}$

[Free] Simplify the expression: $(2 x)^2 \cdot 3 x^3$

[Free] The polynomial equation $x^3+x^2=-9 x-9$ has complex roots $\pm 3 i$. What is the other root?

[Free] What is the equation of the line that is perpendicular to the line [tex]y=\frac{3}{5} x+10[/tex] and passes through the point (15,-5)? A. [tex]y=\frac{3}{5} x-20[/tex] B. [tex]y=-\frac{3}{5} x+20[/tex] C. [tex]y=\frac{5}{3} x-20[/tex] D. [tex]y=-\frac{5}{3} x+20[/tex]

[Free] What is $2\left(\log _3 8+\log _3 z\right)-\log _3\left(3^4-7^2\right)$ written as a single logarithm? A. $\log _3 2 z$ B. $\log _3 2 z^2$ C. $\log _3 \frac{z^2}{4}$ D. $\log _3 \frac{64 z^2}{\frac{81}{49}}$

[Free] Which of the following is a logarithmic function? [tex]y=\log _3 x[/tex] [tex]y=3^x[/tex] [tex]y=x+3[/tex] [tex]y=x^3[/tex]

[Free] Which functions represent exponential growth? y = f(x) y = h(x) y = g(x) y = k(x)

[Free] Explain why someone would choose to use a graphing calculator to solve a system of linear equations instead of graphing by hand.

[Free] A rocket is launched from atop a 36-foot cliff with an initial velocity of 107 feet per second. The height of the rocket, [tex]$t$[/tex] seconds after launch is given by the equation [tex]$h=-16 t^2+107 t+36$[/tex]. Use the quadratic formula to find out how long after the rocket is launched it will hit the ground ([tex]$h=0$[/tex]). Round your answer to the nearest tenth of a second. A. 1.5 sec B. 0.3 sec C. 7.0 sec D. 6.3 sec

[Free] You have shown the series can be expanded as shown: [tex]\sum_{n=37}^{75} 3 n^2 \rightarrow 3\left[\sum_{n=1}^{75} n^2-\sum_{n=1}^{36} n^2\right][/tex] Evaluate the expanded form.