Answer
Find out the how much people were at the wedding.
To prove
Let us assume that the people were at the wedding be x .
As given
Joy organised a large wedding .
Guests had to choose their meals from beaf ,chicken or vegetarian .
![\frac{1}{3}\ of\ the\ guests\ chose\ beaf .](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B3%7D%5C%20of%5C%20the%5C%20guests%5C%20chose%5C%20beaf%20.)
![\frac{5}{12}\ of\ the\ guests\ chose\ chicken.](https://tex.z-dn.net/?f=%5Cfrac%7B5%7D%7B12%7D%5C%20of%5C%20the%5C%20guests%5C%20chose%5C%20chicken.)
69 people chose vegetarian .
Than the equation becomes
![x = 69 + \frac{1x}{3} + \frac{5x}{12}](https://tex.z-dn.net/?f=x%20%3D%2069%20%2B%20%5Cfrac%7B1x%7D%7B3%7D%20%2B%20%5Cfrac%7B5x%7D%7B12%7D)
L.C.M of (3,12) = 12
than
12x = 69 × 12 + 4x + 5x
12x - 9x = 828
3x = 828
![x = \frac{828}{3}](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%7B828%7D%7B3%7D)
x = 276
Therefore 276 people were at the wedding.
Given:
X=number of hours
Y=number of tents made
Table of value.
To find:
The slope and its interpretation.
Solution:
Consider any two points from the table, i.e., (0,6) and (1,7).
The slope is
![m=\dfrac{y_2-y_1}{x_2-x_1}](https://tex.z-dn.net/?f=m%3D%5Cdfrac%7By_2-y_1%7D%7Bx_2-x_1%7D)
![m=\dfrac{7-6}{1-0}](https://tex.z-dn.net/?f=m%3D%5Cdfrac%7B7-6%7D%7B1-0%7D)
![m=\dfrac{1}{1}](https://tex.z-dn.net/?f=m%3D%5Cdfrac%7B1%7D%7B1%7D)
![m=1](https://tex.z-dn.net/?f=m%3D1)
Therefore, the slope is 1 and it represent that the number of tents made are increasing by 1 units in each hour.
The coordinates of A', B', C' and D' are
,
,
and ![(5,-2)](https://tex.z-dn.net/?f=%285%2C-2%29)
Explanation:
The coordinates of ABCD from the graph is given by
A is
, B is
, C is
and D is ![(5,2)](https://tex.z-dn.net/?f=%285%2C2%29)
The figure ABCD is reflected across the x - axis.
We need to determine the coordinates of A', B', C' and D' after it is reflected across the x - axis.
Since, we know that the rule to reflect across the x - axis is given by
![(x, y) \rightarrow(x,-y)](https://tex.z-dn.net/?f=%28x%2C%20y%29%20%5Crightarrow%28x%2C-y%29)
Thus, using this rule, we shall determine the coordinates of A', B', C' and D'
![A(2,3) \Rightarrow A^{\prime}(2,-3)](https://tex.z-dn.net/?f=A%282%2C3%29%20%5CRightarrow%20A%5E%7B%5Cprime%7D%282%2C-3%29)
![B(5,5) \Rightarrow B^{\prime}(5,-5)](https://tex.z-dn.net/?f=B%285%2C5%29%20%5CRightarrow%20B%5E%7B%5Cprime%7D%285%2C-5%29)
and
![D(5,2) \Rightarrow D^{\prime}(5,-2)](https://tex.z-dn.net/?f=D%285%2C2%29%20%5CRightarrow%20D%5E%7B%5Cprime%7D%285%2C-2%29)
Thus, the coordinates of A', B', C' and D' are
,
,
and ![(5,-2)](https://tex.z-dn.net/?f=%285%2C-2%29)