Among the following choose the wrong statementa. According to geo-centric theory, earth is the centre of universe b. Copernicus proposed helio-centric theory of the universe c. Ptolemy proposed geo-centric theory of the universe d. According to helio-centric theory, earth is the centre of the universe

Certainly! Here are some sample solutions with step-by-step explanations: #### Example 1: **Problem:** Solve the equation $2x+5=13$. **Solution:** Step 1: Subtract 5 from both sides of the equation: $\begin{array}{rl}2x+5-5& =13-5\\ 2x& =8\end{array}$ Step 2: Divide both sides of the equation by 2: $\begin{array}{rl}\frac{2x}{2}& =\frac{8}{2}\\ x& =4\end{array}$ Therefore, the solution to the equation $2x+5=13$ is $x=4$. #### Example 2: **Problem:** Simplify the expression $\frac{3x^2-9x}{6x}$. **Solution:** Step 1: Factor out $3x$ from the numerator: $\begin{array}{rl}\frac{3x^2-9x}{6x}& =\frac{3x(x-3)}{6x}\end{array}$ Step 2: Simplify the fraction by canceling out common factors: $\begin{array}{rl}\frac{3x(x-3)}{6x}& =\frac{3(x-3)}{6}\\ & =\frac{1}{2}(x-3)\end{array}$ Therefore, the simplified expression is $\frac{1}{2}(x-3)$. #### Example 3: **Problem:** Find the slope and y-intercept of the line with equation $y=2x-3$. **Solution:** Step 1: Identify the slope and y-intercept from the equation. The equation is in slope-intercept form ($y=mx+b$), where $m$ is the slope and $b$ is the y-intercept. Therefore, the slope is 2 and the y-intercept is -3. Step 2: Write the slope and y-intercept in the form $y=mx+b$: $\begin{array}{rl}y& =2x-3\\ & =2x+(-3)\\ & =2x+b\end{array}$ Therefore, the slope-intercept form of the line is $y=2x-3$, which shows that the slope is 2 and the y-intercept is -3.