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Home Question Bank Math Algebra Archive 2024 December 10

Algebra Questions from Dec 10,2024

Browse the Algebra Q&A Archive for Dec 10,2024, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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4. A magician oharges a \( \$ 30 \) fee to cover travel and expenses, plus \( \$ 19.99 \) per hour. Write an equation to represent the relationship between th, the number of hours, and t, the total charge for magician. 10. \( \left\{\begin{array}{l}6 x-3 y=12 \\ 4 x+3 y=24\end{array}\right. \) 3. Mia has \( \$ 50 \) on a gift card to her favorite coffee shop. Each time she visits the coffee shop she spends \( \$ 3.75 \) on her favorite drink. Write an equation to represent the relationshis between \( n \), the number of times she visits the coffee shop, and \( b \), the total balance on he gift card. Solve the logarithmic equation \( \log _{5}(x+10)+\log _{5}(x-10)=3 \) 3. Consurean nulai \( x_{1} \) dan \( x_{2} \) lan \( 5 x^{2}+11 x+6=0 \) 1. \( 3 y^{2}-18 x=0 \) 9. \( \left\{\begin{array}{l}3 x-4 y=-14 \\ 3 x+2 y=-2\end{array}\right. \) 1. (a) Expand \( (1+2 y)^{10} \) in ascending powers of \( y \), up to and including the term \( y^{3} \). Hence evaluate \( (1.002)^{10} \) correct to 6 decimal places. (b) Express each of the following in the form \( \frac{x}{y} \), where \( x, y \in Z, y \neq 0 \) (i) \( 1.6666 \ldots \) (ii) \( \quad 2 . \overline{4} \overline{5} \) (c) If \( \alpha \) and \( \beta \) are the roots of the equation \( 6 x^{2}+2 x-3=0 \), find the value of \( \frac{a}{\beta}+\frac{\beta}{\alpha} \). 2. (a) Given that \( f(x)=\frac{x-1}{2 x^{2}+2 x-3} \) find (i) \( f(-1) \) and \( f\left(\frac{1}{2}\right) \) (ii) what values of \( x \) must be excluded from the domain? (2) (b) Given that the determinant of the matrix \( \left(\begin{array}{cc}2 & -5 \\ 1 & 5\end{array}\right) \) is equal to the determinant of the matrix \( \left(\begin{array}{cc}5 & x \\ 5 & 8\end{array}\right) \) find the value of \( x \). (3) (c) \( (x-1) \) and \( (x+1) \) are the factors of the expression \( f(x)=x^{3}+a x^{2}+b x+c \) Solve the exponential equation \( 5^{2x-1} = 25 \) and express your answer in terms of logarithm. 18. \( 2 x^{2}+71=-163 \)
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