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Questions in mathematics

[Done] Solve for $y$. $ \begin{array}{l} y+2=5(x-3) \\ y=[?] x+\square \end{array} $

[Done] To obtain the graph of [tex]y=(x-8)^2[/tex], shift the graph of [tex]y=x^2[/tex].

[Done] $\frac{1}{4}+(\frac{1}{4} \div \frac{1}{3})-(\frac{2}{3} \times \frac{3}{4})=$ A. $\frac{1}{4}$ B. 1 C. $\frac{1}{2}$ D. $\frac{5}{8}$ E. None of these

[Done] According to a city's power authority, all streetlamps in the city can draw a percentage of power from a company's new solar panels. [tex]$E(n)$[/tex] is a function that represents the relationship between the number of solar panels installed and the amount of energy generated per day in megawatt hours (MWh), where E(n) [tex]$=0.3 n$[/tex]. [tex]$D ( e )$[/tex] is a function that represents the relationship between the number of days and the energy in (MWh) consumed by the street lamps in a city, where [tex]$D(e)=5 e$[/tex]. Which of the following functions could be used to determine the number of days the streetlamps stay on, based on the number of solar panels installed? A. [tex]$E(D(e))=(0.3 n)(5 e)$[/tex] B. [tex]$E(D(e))=0.3(5 e)$[/tex] C. [tex]$D(E(n))=5(0.3 n)$[/tex] D. [tex]$D(E(n))=5.3 n$[/tex]

[Done] Consider the equation [tex]9 \cdot e^{2 z}=54[/tex]. Solve the equation for [tex]z[/tex]. Express the solution as a logarithm in base-e. [tex]z=[/tex] Approximate the value of [tex]z[/tex]. Round your answer to the nearest thousandth. [tex]z \approx[/tex]

[Done] The temperature at 9 a.m. is 2 degrees. The temperature rises 3 more degrees by noon. Which expression describes the temperature at noon? [tex]$2+3$[/tex] [tex]$2+(-3)$[/tex] [tex]$-2+(-3)$[/tex] [tex]$-2+3$[/tex]

[Done] Use the information given about the angle, [tex]$0 \leq \theta\ \textless \ 2 \pi$[/tex], to find the exact value of each trigonometric function. [tex]$\tan \theta=-12, \sin \theta\ \textless \ 0$[/tex] (a) [tex]$\sin (2 \theta)$[/tex] (b) [tex]$\cos (2 \theta)$[/tex] (c) [tex]$\sin \frac{\theta}{2}$[/tex] (d) [tex]$\cos \frac{\theta}{2}$[/tex] (e) [tex]$\tan 2 \theta$[/tex] (f) [tex]$\operatorname { tan } \frac{\theta}{2}$[/tex] (a) [tex]$\operatorname { s i n } (2 \theta)=$[/tex] $\square$ (Type an exact answer, using radicals as needed.)

[Done] Multiply $(x^2+3 x+4)(3 x^2-2 x+1)$. A. $3 x^4+11 x^3+19 x^2+11 x+4$ B. $4 x^2+x+5$ C. $3 x^4+7 x^3+7 x^2-5 x+4$ D. $3 x^4-6 x^2+4$

[Done] a) Write $2 \frac{3}{4}$ as an improper fraction in its simplest form. b) Work out $2 \frac{3}{4} \times 5$ Give your answer as a fraction in its simplest form.

[Done] Kellie randomly chooses a number from 1 to 10. What is the probability she chooses a number less than 3? A. $\frac{4}{5}$ B. $\frac{1}{5}$ C. $\frac{2}{9}$ D. $\frac{3}{10}$