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Home Question Bank Math Algebra Archive 2025 January 11

Algebra Questions from Jan 11,2025

Browse the Algebra Q&A Archive for Jan 11,2025, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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Using the graph of \( f(x) \), graph \( g(x)=\sqrt{3 x+5} \) Write the domain and range of \( g(x) \). Graph \( f(x)=3 x+5 \) Write the domain and range of \( f(x) \) Solve for \( x \) : 1.1.1 \( x^{2}-5 x-50=0 \) \( 1.1 .22 x^{2}-6 x+1=0 \quad \) (correct to TWO decimal places) 1.1.3 \( -x^{2}-3 x>0 \) \( 1.1 .4 x+3-2 \sqrt{5-x}=0 \) 3) \( f(x)-5 x^{2}-3 x-10 \) Solve for \( x \) : 1.1.1 \( x^{2}-5 x-50=0 \) \( 1.1 .2 \quad 2 x^{2}-6 x+1=0 \) (correct to TWO decimal places) (3) \( 1.1 .3-x^{2}-3 x>0 \) (3) 1.1.A \( x+3-2 \sqrt{5-x}=0 \) (5) 2 Solve the following equations timulaneously: \[ 2^{x}-2^{r-2}=0 \text { and } x^{x}+2 x y+y^{2}=36 \] A square has sides \( x \) cm each. If each side of the square is increased by 4 cm , the meas is increased by \( 392 \mathrm{~cm}^{2} \). Calculatex \( x \). (4) [24] QUESTION 1 1.1 Given: \( 2 k=(x-5)(x-k) \), determine: \( 1.1 .1 \cap k \) if \( x=2 \) 1.1.2 \( x \) if \( k=2 \) 1.2 Solve for \( x \) : 1.2.1 \( 2 x^{2}+3=8 x \) (correct to TWO decimal places 1.2.2 \( \sqrt{2(x+10)}-10=x-12 \) 1.2.3 \( 3^{x}(x-5)<0 \) 1.3 Solve the following equations simultaneously: \[ \sqrt{3^{x}} \cdot 9^{y}=27 \quad \text { and } \quad x+4 y^{2}=6 \] 1.4 The solutions of a quadratic equation are given by \[ x=\frac{-2 \pm \sqrt{2 p+5}}{7} \] State, the value(s) of \( p \) for which this equation will have: 1.4.1 Two equal solutions 1.4.2 No real solutions c. \( (2+\sqrt{2}) \times(1+\sqrt{5}) \) \begin{tabular}{l|l} Finding & \( \begin{array}{l}\text { To find the } x \text {-intercept of an equation, set } y \text { equal to } 0 \text { and solve for } x \\ \text { To find the } y \text {-intercept of an equation, set } x \text { equal to } 0 \text { and solve for } y \\ \text { You can use these points to graph the equation. } \\ \text { cepts }\end{array} \) \\ \( \begin{array}{l}\text { Example: Find the } x \text {-and } y \text {-intercepts of the equation } y=-2 x+5\end{array} \) \\ & \end{tabular} \begin{tabular}{l|l} The \( x \)-intercept is also refered to as a \\ or & \( \begin{array}{l}\text { To find the } x \text {-intercept of an equation, set } y \text { equal to } 0 \text { and solve for } x \\ \text { To find the } y \text {-intercept of an equation, set } x \text { equal to } 0 \text { and solve for } y \\ \text { You can use these points to graph the equation. }\end{array} \) \\ \( \begin{array}{l}\text { Tntercepts } \\ \text { Algebraically }\end{array} \) & \( \begin{array}{l}\text { Example: Find the } x \text { - and } y \text {-intercepts of the equation } y=-2 x+5\end{array} \) \\ \hline\end{tabular} jercicio 3 . Verificar si la siguiente ecuacion es homoge indique sugrado de homogenidad \( \frac{x^{3} y-x^{2} y^{2}}{x+8 y} \)
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