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Questions in mathematics

📝 Answered - The standard form of the equation of a parabola is $y=7 x^2+14 x+4$. What is the vertex form of the equation? A. $y=7(x+2)^2+3$ B. $y=7(x+2)^2-3$ C. $y=7(x+1)^2-3$ D. $y=7(x+1)^2+3$

📝 Answered - If [tex]f(x)=3-2 x[/tex] and [tex]g(x)=\frac{1}{x+5}[/tex], what is the value of [tex]\left(\frac{f}{g}\right)(8) ?[/tex]

📝 Answered - Find [tex]$\sin (A)$[/tex] if [tex]$\cos (A)=0.4$[/tex] Round to the nearest ten-thousandth (four decimal places).

📝 Answered - What is the factorization of the trinomial below? [tex]x^3-12 x^2+35 x[/tex] A. [tex](x-7)(x+5)[/tex] B. [tex](x^2-7)(x+5)[/tex] C. [tex]x(x-7)(x+5)[/tex] D. [tex]x(x-7)(x-5)[/tex]

📝 Answered - Which equation is equivalent to [tex]$\log _x 36=2$[/tex]? [tex]$2^x=36$[/tex] [tex]$x^2=36$[/tex] [tex]$36^x=2$[/tex] [tex]$x^2=36^2$[/tex]

📝 Answered - Given the following probability distribution, identify the missing probability that makes [tex]p(x)[/tex] a valid probability distribution. | x | 0 | 1 | 2 | |---|-----|-----|-----| | p(x) | 1 / 4 | ? | 1 / 4 | A. 1 B. [tex]\frac{1}{2}[/tex] C. [tex]\frac{1}{4}[/tex] D. [tex]\frac{2}{3}[/tex]

📝 Answered - z = (9x - 4y)^4. Find the derivative.

📝 Answered - The point-slope form of the equation of the line that passes through $(-5,-1)$ and $(10,-7)$ is $y+7=-\frac{2}{5}(x-10)$. What is the standard form of the equation for this line? A. $2 x-5 y=-15$ B. $2 x-5 y=-17$ C. $2 x+5 y=-15$ D. $2 x+5 y=-17$

📝 Answered - One factor of [tex]f(x)=4 x^3-4 x^2-16 x+16[/tex] is [tex](x-2)[/tex]. What are all the roots of the function? Use the Remainder Theorem. A. [tex]x=1, x=2[/tex], or [tex]x=4[/tex] B. [tex]x=-2, x=1[/tex], or [tex]x=2[/tex] C. [tex]x=2, x=4[/tex], or [tex]x=16[/tex] D. [tex]x=-16, x=2[/tex], or [tex]x=16[/tex]

📝 Answered - According to a recent survey, high school girls average 100 text messages daily (The Boston Globe, 2010). Assume that the survey was based on a random sample of 36 high school girls. The sample standard deviation is computed as 10 text messages daily. (Round answers to 2 decimals.) begin mathsize 24px style bold x with bold bar on top bold equals bold 100 bold italic s bold equals bold 10 bold italic n bold equals bold 36 end style begin mathsize 24px style bold italic C bold italic a bold italic l bold italic c bold italic u bold italic l bold italic a bold italic t bold italic e bold space bold italic t bold italic h bold italic e bold space bold italic m bold italic a bold italic r bold italic g bold italic i bold italic n bold space bold italic o bold italic f bold space bold italic e bold italic r bold italic r bold italic o bold italic r bold space bold italic w bold italic i bold italic t bold italic h bold space bold 99 bold percent sign bold space bold italic c bold italic o bold italic n bold italic f bold italic i bold italic d bold italic e bold italic n bold italic c bold italic e bold. end style