Questions in mathematics

Questions in mathematics

[Free] Keisha and David each found the same value for [tex]\cos \theta[/tex], as shown below, given [tex]\sin \theta=-\frac{8}{17}[/tex] | Kersha's Solution | David's Solution | |---|---| | [tex]\begin{array}{c} \frac{\left(-\frac{8}{17}\right)^2}{\cos ^2 \theta}+1=\frac{1}{\cos ^2 \theta} \ \left(-\frac{8}{17}\right)^2+\cos ^2 \theta=1 \ \cos \theta= \pm \sqrt{1-\frac{64}{289}}\end{array}[/tex] | [tex]\begin{array}{l} \sin ^2 \theta+\cos ^2 \theta=1 \ \cos ^2 \theta=1-\left(-\frac{8}{17}\right)^2 \ \cos \theta= \pm \sqrt{\frac{225}{281}} \ \cos \theta= \pm \frac{15}{17}\end{array}[/tex] |

[Free] A population of bacteria is treated with an antibiotic. It is estimated that 5,000 live bacteria existed in the sample before treatment. After each day of treatment, $40 \%$ of the sample remains alive. Which best describes the graph of the function that represents the number of live bacteria after $x$ days of treatment? A. [tex]f(x)=5000(0.4)^x[/tex], with a horizontal asymptote of [tex]y=0[/tex] B. [tex]f(x)=5000(0.6)^x[/tex], with a vertical asymptote of [tex]x =0[/tex] C. [tex]f(x)=5000(1.4)^x[/tex], with a horizontal asymptote of [tex]y=0[/tex] D. [tex]f(x)=5000(1.6)^x[/tex], with a vertical asymptote of [tex]x=0[/tex]

[Free] Solve the nonlinear inequality. Express the solution using interval notation. [tex]x^2\ \textgreater \ 2(x+4)[/tex]

[Free] Jeff invested $[tex]$3000$[/tex] in an account that earns [tex]$6.5 %$[/tex] interest, compounded annually. The formula for compound interest is [tex]$A(t)=P(1+i)^t$[/tex]. How much did Jeff have in the account after 3 years? A. $[tex]$9585.00$[/tex] B. $[tex]$3390.00$[/tex] C. $[tex]$13,476.38$[/tex] D. $[tex]$3623,85$[/tex]

[Free] The domain of $f(x)$ is the set of all real values except 7, and the domain of $g(x)$ is the set of all real values except -3. Which of the following describes the domain of $(g \circ f)(x)$? A. all real values except $x \neq -3$ and the $x$ for which $f(x) \neq 7$ B. all real values except $x \neq -3$ and the $x$ for which $f(x) \neq -3$ C. all real values except $x \neq 7$ and the $x$ for which $f(x) \neq 7$ D. all real values except $x \neq 7$ and the $x$ for which $f(x) \neq -3

[Free] A teacher wrote the equation [tex]$3 y+12=6 x$[/tex] on the board. For what value of b would the additional equation [tex]$2 y=4 x$[/tex] [tex]$b$[/tex] form a system of linear equations with infinitely many solutions? A. [tex]$b=-8$[/tex] B. [tex]$b=-4$[/tex] C. [tex]$b=2$[/tex] D. [tex]$b=6$[/tex]

[Free] A) i) If today is Tuesday, what day will it be after 200 days? ii) If [tex]$\log (5 x-4)=\log (x+1)+\log 4$[/tex], find the value of [tex]$x$[/tex] B) Express [tex]$\frac{1}{\sqrt{5}}+\sqrt{20}$[/tex] in the form [tex]$a \sqrt{b}$[/tex] C) If [tex]$2^x+2^{(x-1)}=48$[/tex], find the value of [tex]$x$[/tex]

[Free] Find the area of the shape below: 20cm 2cm 18cm 20cm 2cm

[Free] Select the correct answer. Last year, the school library had a total of $x$ books. Over the summer, the library acquired another 46 books and now has a total of 1,191 books. Which equation could be used to find $x$, the number of books the library had last year? A. $x-46=1,191$ B. $46 x=1,191$ C. $1,191+x=46$ D. $x+46=1,191

[Free] Given the function [tex]f(x)=x^3-6[/tex], complete parts a through c. (a) Find an equation for [tex]f^{-1}(x)[/tex]. (b) Graph f and f[tex]{ }^{-1}[/tex] in the same rectangular coordinate system. (c) Use interval notation to give the domain and the range of f and [tex]f^{-1}[/tex] (a) Find [tex]f ^{-1}( x )[/tex] [tex]f^{-1}(x)=\sqrt[3]{x+6}[/tex] (Type an exact answer, using radicals as needed.) (b) Graph f and f [tex]{ }^{-1}[/tex] in the same coordinate system. Choose the correct graph below. A. B. C. D.