Answer:
The image of (2,3) after a reflection over the given line will be: (-3,-2)
Step-by-step explanation:
The given point is (2,3)
Let (x,y) be a point, when it will be reflected over the line y=-x the coordinates are exchanged and are negated i.e. point (x,y) becomes (-y,-x)
When a point is reflected over a line the distance between the image of point and the line remains the same as the distance between original point and line.
Given point will become: (-3,-2)
Hence,
The image of (2,3) after a reflection over the given line will be: (-3,-2)
The average height of the 5 members is 179.8 cm
She might've put 1.232*4 ml of pepper sauce instead of 1.232*3 ml of pepper sauce
let's bear in mind that an absolute value expression is in effect a piece-wise expression, namely it has a ± versions of the same expression.
![\bf 5|3x-4| = x+1\implies |3x-4|=\cfrac{x+1}{5}\implies \begin{cases} +(3x-4)=\cfrac{x+1}{5}\\[1em] -(3x-4)=\cfrac{x+1}{5} \end{cases} \\\\[-0.35em] ~\dotfill\\\\ +(3x-4)=\cfrac{x+1}{5}\implies 3x-4=\cfrac{x+1}{5}\implies 15x-20=x+1 \\\\\\ 14x-20=1\implies 14x=21\implies x = \cfrac{21}{14}\implies \boxed{x=\cfrac{3}{2}} \\\\[-0.35em] ~\dotfill\\\\ -(3x-4)=\cfrac{x+1}{5}\implies -3x+4=\cfrac{x+1}{5}\implies -15x+20=x+1 \\\\\\ 20=16x+1\implies 19=16x\implies \boxed{\cfrac{19}{16}=x}](https://tex.z-dn.net/?f=%5Cbf%205%7C3x-4%7C%20%3D%20x%2B1%5Cimplies%20%7C3x-4%7C%3D%5Ccfrac%7Bx%2B1%7D%7B5%7D%5Cimplies%20%5Cbegin%7Bcases%7D%20%2B%283x-4%29%3D%5Ccfrac%7Bx%2B1%7D%7B5%7D%5C%5C%5B1em%5D%20-%283x-4%29%3D%5Ccfrac%7Bx%2B1%7D%7B5%7D%20%5Cend%7Bcases%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20%2B%283x-4%29%3D%5Ccfrac%7Bx%2B1%7D%7B5%7D%5Cimplies%203x-4%3D%5Ccfrac%7Bx%2B1%7D%7B5%7D%5Cimplies%2015x-20%3Dx%2B1%20%5C%5C%5C%5C%5C%5C%2014x-20%3D1%5Cimplies%2014x%3D21%5Cimplies%20x%20%3D%20%5Ccfrac%7B21%7D%7B14%7D%5Cimplies%20%5Cboxed%7Bx%3D%5Ccfrac%7B3%7D%7B2%7D%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20-%283x-4%29%3D%5Ccfrac%7Bx%2B1%7D%7B5%7D%5Cimplies%20-3x%2B4%3D%5Ccfrac%7Bx%2B1%7D%7B5%7D%5Cimplies%20-15x%2B20%3Dx%2B1%20%5C%5C%5C%5C%5C%5C%2020%3D16x%2B1%5Cimplies%2019%3D16x%5Cimplies%20%5Cboxed%7B%5Ccfrac%7B19%7D%7B16%7D%3Dx%7D)
