Questions in mathematics

Questions in mathematics

📝 Answered - Explain and draw an example of each of the following concepts: a) Line segment b) Parallel lines c) Perpendicular lines

📝 Answered - Simplify the following expression. [tex]$\begin{array}{c} (x-4)^2 \ x^2-8 x+[?] \end{array}$[/tex]

📝 Answered - Determine if the lines $y=2 x+5$ and $4 x-2 y=10$ are parallel, perpendicular, or neither.

📝 Answered - Round to 3 significant figures. [tex]$74.58$[/tex]

📝 Answered - Consider a circle whose equation is $x^2+y^2-2 x-8=0$. Which statements are true? Select three options. A. The radius of the circle is 3 units. B. The center of the circle lies on the $x$-axis. C. The center of the circle lies on the $y$-axis. D. The standard form of the equation is $(x-1)^2+y^2=3$. E. The radius of this circle is the same as the radius of the circle whose equation is $x^2+y^2=9$.

📝 Answered - Which functions are equivalent to [tex]f(x)=\sqrt[4]{162}^x[/tex]? Check all that apply. [tex]f(x)=162^{\frac{x}{4}}[/tex] [tex]f(x)=(3 \sqrt[4]{2})^x[/tex] [tex]f(x)=9 \sqrt[4]{2}^x[/tex] [tex]f(x)=162^{\frac{4}{x}}[/tex] [tex]f(x)=\left[3\left(2^{\frac{1}{4}}\right)\right]^x[/tex]

📝 Answered - Factor $f(x)$ into linear factors given that $k$ is a zero of $f(x)$. $f(x)=2 x^3-5 x^2+1 x+2 ; k=1$ A. $f(x)=(x-1)(x-2)(2 x+1)$ B. $f(x)=(x-1)(x+1)(2 x-2)$ C. $f(x)=(x-1)(x+2)(2 x-1)$ D. $f(x)=(x+1)(x+2)(2 x-1)$

📝 Answered - Explain how Brian placed the decimal point correctly in his product. [tex]$14.73 \times 0.75=11.0475$[/tex]

📝 Answered - Find the middle term in the expansion of $(2 x-y)^4$ and simplify your answer.

📝 Answered - Give answers of angles in radians in terms of [tex]$\pi$[/tex]. QUESTION 1 Find the exact solution for [tex]$x$[/tex], if there is no solution write no solution: 1. [tex]$1.15 e^{3 x}-4=6$[/tex] 2. [tex]$1.2 e^{2 x}-e^x-110=0$[/tex] 3. [tex]$1.3 \ln \left(e^x\right)+e^{(\ln 5)}=25$[/tex] 4. [tex]$1.4 \log _8(7)+\log _8(-4 x)=\log _8(5)$[/tex] 5. [tex]$1.5 \sin ^2 x-\cos ^2 x-\sin x=0$[/tex] on [tex]$[0,2 \pi)$[/tex]. 6. [tex]$x=\sin \left(70^{\circ}\right) \cos \left(25^{\circ}\right)-\cos \left(70^{\circ}\right) \sin \left(25^{\circ}\right)$[/tex] QUESTION 2 Show that the expression [tex]$\frac{\left(1-\cos ^2 x\right)\left(1+\cos ^2 x\right)}{\cos ^2 x}$[/tex] is equivalent to [tex]$\sin ^2 x+\sec ^2$[/tex]