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Home Question Bank Math Algebra Archive 2024 November 09

Algebra Questions from Nov 09,2024

Browse the Algebra Q&A Archive for Nov 09,2024, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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Mary's hourly wage is \( 1 \frac{1}{2} \) times greater than John's. John's and Dennis' hourly wages added together total \( \$ 32.07 \) an hour. If Dennis earns one-half of John's rate, what is Mary's hourly wage? b. \( \left\{\begin{array}{l}-x+3 y=-1 \\ 4 x-12 y=4\end{array}\right. \) Find all the zeros of the polynomial function. Use the Rational Zero Theorem, Descartes's Rule of Signs obtaining the first zero. \( f(x)=x^{3}-4 x^{2}-7 x+10 \) The zeros of the function are \( \square \). (Use a comma to separate your answers as needed.) The following function is given. \( f(x)=x^{3}-3 x^{2}-25 x+75 \) a. List all rational zeros that are possible according to the Rational Zero Theorem. \( \pm 1, \pm 3, \pm 5, \pm 15, \pm 25, \pm 75 \) (Use a comma to separate answers as needed.) b. Use synthetic division to test several possible rational zeros in order to identify one actual zero One rational zero of the given function is 3 . (Simplify your answer.) c. Use the zero from part (b) to find all the zeros of the polynomial function. The zeros of the function \( f(x)=x^{3}-3 x^{2}-25 x+75 \) are (Simplify your answer. Type an integer or a fraction. Use a comma to separate answers as needer The following function is given. \( f(x)=x^{3}-3 x^{2}-25 x+75 \) a. List all rational zeros that are possible according to the Rational Zero Theorem. \( \pm 1, \pm 3, \pm 5, \pm 15, \pm 25, \pm 75 \) (Use a comma to separate answers as needed.) b. Use synthetic division to test several possible rational zeros in order to identify one actual zero. One rational zero of the given function is (Simplify your answer.) Simplify the radical expression \( \sqrt[3]{8 c^{9} g^{12} a^{24}} \) Assume all variables represent positive values. The following function is given. \( f(x)=x^{3}-3 x^{2}-25 x+75 \) a. List all rational zeros that are possible according to the Rational Zero Theorem. \( \square \) Use the Rational Zero Theorem to list all possible rational zoros for the given function, \( f(x)=4 x^{4}-x^{3}+4 x^{2}-2 x-10 \) Which of the following is the complete list of possible zeros of the given function? A. \( \pm 1, \pm 2, \pm 5, \pm 10, \pm \frac{1}{2}, \pm \frac{5}{2}, \pm \frac{1}{4}, \pm \frac{5}{4} \) B. \( \pm 1, \pm 2, \pm \frac{5}{2}, \pm \frac{1}{4}, \pm \frac{5}{4} \) C. \( \pm 1, \pm 2, \pm 5, \pm \frac{1}{2}, \pm \frac{5}{2} \) D. The function has no rational zeros. Use the Rational Zero Theorem to list all possible rational zeros for the given function. \( f(x)=-5 x^{4}+7 x^{3}+11 x^{2}+17 x+10 \) Choose the answer below that lists all possible rational zeros. A. \( -1,1,-2,2,-5,5,-10,10,-\frac{1}{2}, \frac{1}{2},-\frac{1}{10}, \frac{1}{10},-\frac{1}{5}, \frac{1}{5},-\frac{2}{5}, \frac{2}{5},-\frac{5}{2}, \frac{5}{2} \) B. \( -1,1,-5,5,-\frac{1}{2}, \frac{1}{2},-\frac{1}{10}, \frac{1}{10},-\frac{1}{5}, \frac{1}{5},-\frac{5}{2}, \frac{5}{2} \) C. \( -1,1,-2,2,-5,5,-10,10,-\frac{1}{5}, \frac{1}{5},-\frac{2}{5}, \frac{2}{5} \) D. \( -1,1,-2,2,-5,5,-10,10,-\frac{1}{2}, \frac{1}{2},-\frac{1}{5}, \frac{1}{5},-\frac{1}{10}, \frac{1}{10} \) Use the Rational Zero Theorem to list all possible rational zeros for the given function. \( f(x)=x^{3}-11 x^{2}+16 x-6 \) Choose the answer below that lists all possible rational zeros. A. \( -1,1,-\frac{1}{2}, \frac{1}{2},-\frac{1}{3}, \frac{1}{3},-\frac{1}{6}, \frac{1}{6} \) B. \( -1,1,-2,2,-3,3,-6,6,-\frac{1}{2}, \frac{1}{2},-\frac{1}{3}, \frac{1}{3},-\frac{1}{6}, \frac{1}{6} \) C. \( -1,1,-2,2,-3,3,-6,6 \) D. \( -1,1,-6,6 \)
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