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Questions in mathematics

📝 Answered - Consider this polynomial, where $a$ is an unknown real number. [tex]p(x)=x^4+5 x^3+a x^2-3 x+11[/tex] The remainder of the quotient of [tex]p(x)[/tex], and [tex](x+1)[/tex] is 17. Braulio uses synthetic division to find the value of $a$, and Zahra uses the remainder theorem to find the value of $a$. Their work is shown. Braulio found the value of a because he Zahra found the value of a because she

📝 Answered - Convert the unit of length. Use $1 m=100 cm$ and $1 m \approx 3.28 ft$. Round the answer to one decimal place if necessary. $1.1 ft \approx \frac{1.1 ft}{\square} \cdot \frac{\square}{\square} \cdot \frac{\square}{\square} \approx 33.5 cm$

📝 Answered - What is the value of [tex]$\lfloor-12\rfloor$[/tex]?

📝 Answered - The ratio of the number of boys to the number of girls at a school is 11:9. There are 124 more boys than girls. Work out the total number of students at the school.

📝 Answered - Factor the quadratic [tex]$5 x^2-9 x-2$[/tex]. List ONLY ONE of the factors with parentheses and no spaces. Example: [tex]$(x+1)$[/tex]

📝 Answered - If $y=x-6$ were changed to $y=x+8$, how would the graph of the new function compare with the first one? A. It would be shifted right. B. It would be shifted down. C. It would be shifted up. D. It would be steeper.

📝 Answered - A phrase is shown. "three times the quantity five less than $x$, divided by the product of six and $x$" Which expression is equivalent to this phrase? A. $\frac{3 x-5}{6 x}$ B. $\frac{3 x-5}{x+6}$ C. $\frac{3(x-5)}{6 x}$ D. $\frac{3(x-5)}{6} \cdot x$

📝 Answered - Solve the inequality algebraically. [tex]2\left(x^2+4\right)\ \textgreater \ 3(x-1)^2-x^2[/tex] The solution set is $\square$ (Type your answer in interval notation. Simplify your answer. Use integers or fractions for any numbers in the expression.)

📝 Answered - Perform the indicated operation. 1) [tex] \begin{array}{l} h(x)-9 x \\ g(x)=4 x+2 \\ \text { Find }(h \cdot g)(4) \end{array} [/tex] 2) [tex] \begin{array}{l} h(x)-2 z \\ g(x)-8 x^3+6 x^2 \\ \text { Find }\left(\frac{f}{h}\right)(x) \end{array} [/tex] 3) [tex] \begin{array}{l} h(x)=10 x \\ g(x)=30 x^3+40 x^3 \\ \text { Find }\left(\frac{q}{h}\right)(1) \end{array} [/tex] 4) [tex] \begin{array}{l} h(x)=-4 x \\ g(x)=2 x-3 \\ \text { Find }(h \cdot g)(x) \end{array} [/tex] 5) [tex] \begin{array}{l} h(x)=7 z \\ g(z)-8 x+3 \\ \text { Find }(h \cdot g)(1) \end{array} [/tex] 6) [tex] \begin{array}{l} h(x)=3 x \\ g(x)-6 x+4 \\ \text { Find }(h \cdot g)(3) \end{array} [/tex] 7) [tex] \begin{array}{l} h(x)=-2 z \\ g(z)=4 x-3 \\ \text { Find }(h, g)(z) \end{array} [/tex] 8) [tex] \begin{array}{l} h(x)=5 z \\ g(z)--10 x^3+10 z^2 \\ \text { Find }\left(\frac{z}{h}\right)(z) \end{array} [/tex] 9) [tex] \begin{array}{l} h(x)=10 x \\ g(x)=8 x+3 \\ \text { Find }(h . g)(x) \end{array} [/tex] 10) [tex] \begin{array}{l} h(x)=9 z \\ g(x)=-27 x^3+36 z^3 \\ \text { Find }\left(\frac{g}{h}\right)(z) \end{array} [/tex] 11) [tex]h(x)=2 z[/tex] [tex] \begin{array}{l} g(x)=-4 x^3+8 x^2 \\ \text { Find }\left(\frac{9}{h}\right)(3) \end{array} [/tex] 12) [tex] \begin{array}{l} h(x)=-5 z \\ g(z)=6 z-2 \\ \text { Find }(h \cdot g)(z) \end{array} [/tex] 13) [tex] \begin{array}{l} h(x)=4 x \\ g(x)=16 x^3+16 x^3 \\ \text { Find }\left(\frac{g}{h}\right)(3) \end{array} [/tex] 14) [tex] \begin{array}{l} h(x)=6 z \\ g(x)=-18 x^3+12 z^3 \\ \text { Find }\left(\frac{7}{h}\right)(4) \end{array} [/tex] 15) [tex]h(x)=10 x[/tex] [tex](2) =20 x^3+20 x^2[/tex] [tex]=z^{\prime}=\text { ind }\left(\frac{g}{b}\right)(z)[/tex] 16) [tex] \begin{array}{l} h(x)=8 z \\ g(x)=-24 x^3+32 z^2 \\ \text { Find }\left(\frac{z}{h}\right)(2) \end{array} [/tex]

📝 Answered - Which expression represents how much money you will have in one year if $6 \%$ is compounded quarterly on a $\$800$ for one year? A. $(800 \times 0.06 \times 3)+800$ B. $800 \times 0.06 \times 1 / 4$ C. $(800 \times 0.06 \times 1 / 4)+800$ D. $800 \times 0.06 \times 3