Questions in mathematics

Questions in mathematics

📝 Answered - If n and k are numbers greater than 1 and [tex]\( \sqrt[3]{n^4} \)[/tex] is equivalent to [tex]\( \sqrt[3]{k^3} \)[/tex], for what value of [tex]\( a \)[/tex] is [tex]\( n^{4a+1} = k \)[/tex]?

📝 Answered - Which of the following is equivalent to [tex]$\frac{1}{\log _b(4)}$[/tex] ? Choose 1 answer: A. [tex]$\log _b(4)$[/tex] B. [tex]$\log _4(b)$[/tex] C. [tex]$-\log _b(4)$[/tex] D. [tex]$-\log _4(b)$[/tex]

📝 Answered - Below is a two-way table for student activities: Follow the steps to find the probability a student is in sports, given that they are a senior. First, find the probability that a student is a senior. [tex]P(\text { senior }) = [?][/tex] Enter your answer in decimal form. Do not round.

📝 Answered - Which statement about the following equation is true? [tex]3 x^2-8 x+5=5 x^2[/tex] A. The discriminant is less than 0, so there are two real roots. B. The discriminant is greater than 0 so there are four real roots. C. The discriminant is less than 0, so there are two complex roots. D. The discriminant is greater than 0, so there are two complex roots.

📝 Answered - Which statement proves that parallelogram KLMN is a rhombus? The midpoint of both diagonals is $(4,4)$. The length of $\overline{ KM }$ is $\sqrt{72}$ and the length of $\overline{ NL }$ is $\sqrt{8}$. The slopes of $\overline{ LM }$ and $\overline{ KN }$ are both $\frac{1}{2}$ and $NK = ML$ =$\sqrt{20}$. The slope of $\overline{ KM }$ is 1 and the slope of $\overline{ NL }$ is -1.

📝 Answered - Study the products shown. Is there a pattern? [tex]\begin{array}{l} (x+3)^2=x^2+6 x+9 \\ (x+4)^2=x^2+8 x+16 \\ (x+5)^2=x^2+10 x+25 \\ (x+6)^2=x^2+12 x+36 \end{array}[/tex] Each product is in the form [tex]$a x^2+b x+c$[/tex]. Which of the following describes the relationship between [tex]$b$[/tex] and [tex]$c$[/tex]? A. [tex]$c$[/tex] is the square of half of [tex]$b$[/tex]. B. [tex]$c$[/tex] is the square of [tex]$b$[/tex] C. [tex]$c$[/tex] is 1.5 times that of [tex]$b$[/tex].

📝 Answered - Find the surface area for the solid of revolution obtained by rotating $y=e^{2 x}$ around the $x$-axis over the interval $[-1,2]$. Round your answer to the nearest thousandth.

📝 Answered - Use the arithmetic series [tex]$14+6+(-2)+(-10)+(-18)+(-26)+(-34)$[/tex] to answer each question. What is the common difference [tex]$d$[/tex] of the arithmetic sequence on which the series is based? [tex]$d=\square$[/tex]

📝 Answered - What is the value of the arithmetic series below? [tex]S_{19}=\sum_{k=1}^{19}(4-3 k)[/tex]

📝 Answered - Two cards are drawn from a deck of cards. What is the probability of drawing two hearts?