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Home Question Bank Math Archive 2025 January 15

Math Questions from Jan 15,2025

Browse the Math Q&A Archive for Jan 15,2025, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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1) \( \frac{4^{x-1}+4^{x+1}}{17 \cdot 12^{x}} \) Simplify 2) \( \frac{\frac{3^{x+1}-3^{x-1}}{2 \cdot 3^{x}}}{\text { 3) } \frac{5^{a-2} \cdot 2^{a+2}}{10^{a}-10^{a-1} \cdot 2}} \begin{array}{l}\text { 4) } \frac{3^{m+4}-6 \cdot 3^{m+1}}{7 \cdot 3^{m+2}}\end{array} \) 25. What is the measure of angle 3 ? \( \begin{array}{llll}\text { a. } 45^{\circ} & \text { b. } 90^{\circ} & \text { c. } 110^{\circ} & \text { d. } 180^{\circ}\end{array} \) Perform the indicated operation and simplify. \( -(7 x-8)^{2} \) \( -(7 x-8)^{2}=\square \) (Simplify your answer.) 11. En un triángulo acutángulo \( A B C, m \hat{B}-m \hat{A}=20^{\circ} \). En el lado \( A C \) se toma el punto P de tal manera que \( B C=C P \). Calcular la medida de \( \angle P B A \). \( \begin{array}{llll}\text { a) } 20^{\circ} & \text { b) } 25^{\circ} & \text { c) } 19^{\circ} & \text { d) } 15^{\circ} \\ \text { e) } 10^{\circ}\end{array} \) What are the coordinates of the terminal point determined by \( t=\frac{20 \pi}{3} \) ? \[ \text { A. }\left(-\frac{1}{2}, \frac{\sqrt{3}}{2}\right) \] B. \( \left(\frac{1}{2},-\frac{\sqrt{3}}{2}\right) \) C. \( \left(-\frac{1}{2},-\frac{\sqrt{3}}{2}\right) \) D. \( \left(\frac{1}{2}, \frac{\sqrt{3}}{2}\right) \) \( 1 \leftarrow \begin{array}{l}\text { Perform the indicated operation and simplify. } \\ \qquad \begin{array}{l}(3 x-8 y)(x+3 y)\end{array} \\ (3 x-8 y)(x+3 y)=\square\end{array} \) \( 1 \leftarrow \begin{array}{l}\text { Perform the indicated operations and simplify. } \\ 2(y-7)-(3 y+6)-8(9 y-4)\end{array} \) \( 2(y-7)-(3 y+6)-8(9 y-4)=\square \) possible) the rational zeros of the function. (Enter your answers as a comma-separa \( g(t)=t^{3}-3 t^{2}+3 \) 4) Name a decimal greater than 2.15 and less than 2.25 . Which fractions are equivalent to \( 1 . \overline{27} \) ? Mark all that apply. \( \begin{array}{ll}\text { A. } \frac{9}{7} & \text { D. } \frac{28}{19} \\ \text { B. } \frac{12}{5} & \text { O. } \frac{42}{33} \\ \text { C. } \frac{14}{11} & \text { O F. } \frac{60}{27}\end{array} \)
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