diff --git a/Grade 10/Math/MPM2DZ/Quiz #2.md b/Grade 10/Math/MPM2DZ/Quiz #2.md index 5d18e6e..0599cf8 100644 --- a/Grade 10/Math/MPM2DZ/Quiz #2.md +++ b/Grade 10/Math/MPM2DZ/Quiz #2.md @@ -1,2 +1,65 @@ - **1. Solve for** $`x`$ **if** $`\dfrac{2x+3}{4} - \dfrac{3x-1}{3} = \dfrac{5x - 2}{2}`$ + +- $`3(2x+3) - 4(3x-1) = 6(5x-2)`$ + +- $`6x+9 - 12x + 4 = 30x - 12`$ +- $`-6x + 13 = 30x - 12`$ +- $`36x = 25`$ +- $`x = \dfrac{25}{36}`$ + +**2. Determine the length of** $`AB`$ **for** $`\triangle ABC`$, **where** $`D`$ **is on segment** $`AC`$, and $`AD = 7, DC = 3,BC = 5`$ +- $`\because 3^2 + 4^2 = 5^2 `$ +- $`\therefore BD = 4`$ +- $`\because \angle{ADB} = 90\degree`$ +- $`\therefore BA = BD^2 + 7^2`$ +- $`\therefore BA = \sqrt{4^2 + 7^2}`$ +- $`BA = \sqrt{65}`$ +- The length of $`AB`$ is $`\sqrt{65}`$ + +**3. Line 1 goes through the points** $`(-3, -7)`$ **and** $`(9, 1)`$. **Line 2 is perpendicular to** $`3x-4y+8 = 0`$ **and has a y-intercept of** $`7`$. **Determine the point of intersection of line 1 and line 2**. +- $`m_1 = \dfrac{1-(-7)}{9-(-3)}`$ + +- $`m_1 = \dfrac{8}{12}`$ + +- $`m_1 = \dfrac{2}{3}`$ + +- $`1 = \dfrac{2}{3}(9) + b`$ + +- $`1 = 6 + b`$ + +- $`b = -5`$ + +- $`y_1 = \dfrac{2}{3}x - 5`$ + +- $`3x - 4y + 8 = 0 `$ + +- $`4y = 3x + 8`$ + +- $`y = \dfrac{3}{4}x + 2`$ + +- $`m_{\perp} = \dfrac{-4}{3}`$ + +- $`y_2 = \dfrac{-4}{3}x + 7`$ + +- $`\begin{cases} y = \dfrac{-4}{3}x + 7 \quad (1) \\ \\y = \dfrac{2}{3}x - 5 \quad (2) \end{cases}`$ + +- **sub** $`(1)`$ **into** $`(2)`$ + +- $`\dfrac{2}{3}x - 5 = \dfrac{-4}{3}x + 7`$ + +- $`\dfrac{6}{3}x = 12`$ + +- $`2x = 12`$ + +- $`x = 6 (3)`$ + +- **sub** $`(3)`$ **into** $`(2)`$ + +- $`y = \dfrac{-24}{3} + 7`$ + +- $`y = -8 + 7`$ + +- $`y = -1`$ + +- $`\therefore`$ the Point of Intersection is $`(6, -1)`$ +