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Questions in mathematics

📝 Answered - Given that [tex]$\int_1^5 f(x) d x=8$[/tex], evaluate [tex]$\int_3^5 f(x) d x+\int_3^1\left[\frac{1}{3 x^2}-f(x)\right] d x$[/tex].

📝 Answered - What is the end behavior of the graph of the polynomial function [tex]f(x)=3 x^0+30 x^3+75 x^4[/tex]? A. As [tex]x \rightarrow-\infty, y \rightarrow-\infty[/tex] and as [tex]x \rightarrow \infty, y \rightarrow-\infty[/tex]. B. As [tex]x \rightarrow-\infty, y \rightarrow-\infty[/tex] and as [tex]x \rightarrow \infty, y \rightarrow \infty[/tex]. C. As [tex]x \rightarrow-\infty, y \rightarrow \infty[/tex] and as [tex]x \rightarrow \infty, y \rightarrow-\infty[/tex]. D. As [tex]x \rightarrow-\infty, y \rightarrow \infty[/tex] and as [tex]x \rightarrow \infty, y \rightarrow \infty[/tex].

📝 Answered - Lunch Accounts Enrique has $50 in his lunch account and spends $5 per day from the account. Maya has $46 in her lunch account and spends $4 per day from the account. Which equations model the situation? A. $50-5x=y$ and $46-4x=y$ B. $5x+50=y$ and $4x+46=y$ C. $5x-50=y$ and $4x-46=y$ D. $5-50x=y$ and $4-46x=y

📝 Answered - Work out $\frac{5}{8} \times \frac{9}{2}$. Answer as a fraction in its simplest form.

📝 Answered - What is the solution to this system of linear equations? $\begin{array}{l} 2 x+3 y=3 \\ 7 x-3 y=24 \end{array}$ A. $(2,7)$ B. $(3,-21)$ C. $(3,-1)$ D. $(9,0)$

📝 Answered - \(\left(2^{2 x+1}\right)\left(3^{2 x+2}\right)+2^x\left(3^{x+2}\right)-2=0\)

📝 Answered - Let $f(x)=x^2-7 x$ and $g(x)=6+x$. Find the following. (a) $(f+g)(x)$ (b) $(f-g)(x)$ (c) $(f \cdot g)(x)$ (d) $\left(\frac{f}{g}\right)(x)$ (e) The domain of $\frac{f}{g}

📝 Answered - Evaluate the function at the given value. [tex] \begin{array}{c} f(x)=(2 x-8)^2\left(x^3+4 x-6\right)^3 \\ f^{\prime}(1)=[?] \end{array} [/tex]

📝 Answered - 36. What factor is common to all the expressions [tex]x^2-x[/tex], [tex]2 x^2+x-1[/tex] and a. [tex]x[/tex] C. [tex]x+1[/tex] b. [tex]x-1[/tex] d. No common factor

📝 Answered - Solve the equation: [tex]7 x=42[/tex]. A) [tex]x=-7[/tex] B) [tex]x=-6[/tex] C) [tex]x=6[/tex] D) [tex]x=7[/tex]