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Home Question Bank Math Pre Algebra Archive 2024 December 24

Pre-algebra Questions from Dec 24,2024

Browse the Pre-algebra Q&A Archive for Dec 24,2024, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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p. \( \quad \log _{3} \frac{3}{\sqrt[5]{81}} \) Which of the following statement is troe about \( f(x)=x^{2}-6 x+10 \) ? A. The line \( x=1 \) is the axis of symmetry of the graph of \( f \). B. \( f(x) \geq 2 \) for all \( x \) in the domain of \( f \). C. The vertex of the graph of \( f \) is \( (3,1) \). D. The graph of \( f \) opens downward. + 07. The value of \( \left[1^{-2}+2^{-2}+3^{-2}\right] \times 6^{2} \) is \( \begin{array}{ll}\text { (a) } 49 & \text { (b) } 36 \\ \text { (c) } 18 & \text { (d) } 63\end{array} \) 4. Find: \( \begin{array}{llll}\text { (a) } 17-(30) & \text { (b) }-60-(90) & \text { (c) }(-15)-(-18) & \text { (d) }(-25)-(1) \\ \text { (e) } 101-(-101) & \text { (f) }(-56)-(-65) & \end{array} \) 7. A colony of insects was found to have 250 insects at the beginning. Thereafter the number of insects doubled every 2 days. Find how many insects there were after 16 days. \( (3 \) marks (2003 PP2 No. 15 \( \frac{3}{\sqrt{3}} \ \begin{array}{l}\text { ifadesinin eşiti aşağıdakilerden hangisidir? }\end{array} \) (2023) How many four-digit perfect square numbers have 4,5 or 6 in their units place \( \begin{array}{llll}\text { (1) } 42 & \text { (2) } 14 & \text { (3) } 21 & \text { (4) } 35 \text {. } \\ \text { (Hint }:(32)^{2}=1024 \text { and }(99)^{2}=9801 \ldots \text { the perfect square numbers are from } \\ 32 \text { to } 99 \text {. Units place digit should be } 4,5 \text { or } 6 . \therefore \text { the units place diglts of the } \\ \text { two-digit numbers should be } 2,4,5,6 \text { or } 8 \text {. So. numbers are } 32,34,35,36 \\ 38, \ldots, 96,98 \text {. i.e. } 5 \times 7=35 .]\end{array} \) a) \( 3 \frac{1}{2}: 2 \frac{1}{7}=2 \frac{1}{3}: t \); \( \Delta = \left| \begin{array} { c c c } { 3 } & { - 1 } & { 2 } \\ { 1 } & { 4 } & { 1 } \\ { 1 } & { - 1 } & { 2 } \end{array} \right| = \) 2-)(20p) Given that \( A=\left|\begin{array}{ccc}1 & a & 2 \\ -1 & 1 & b \\ a & 2 & 3 b\end{array}\right|=6 \) compute the following deterninant, \( \left|\begin{array}{ccc}2 c & 2 a+2 b c & 4 \\ -c & 1-b c & b \\ a c & 2+a b c & 3 b\end{array}\right| \)
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