The equation y = 11x describes the amount of money Louis earns, where x is the number of hours he works and y is the amount of m
oney he earns.
The table shows the amount of money Carl earns for different numbers of hours worked.
(a) How much money does Carl earn per hour? Show your work on how you found the constant of proportionality for both.
(b) Who earns more per hour? Justify your answer by comparing the two. Please use complete sentences.
(c) Draw a graph that represents Carl’s earnings over time in hours. Remember to label the axes with the real world quantities that x and y represent. Please use the graph that has been provided
The table shows the amount of money Carl earns for different numbers of hours worked.
(a) How much money does Carl earn per hour? Show your work on how you found the constant of proportionality for both.
(b) Who earns more per hour? Justify your answer by comparing the two. Please use complete sentences.
(c) Draw a graph that represents Carl’s earnings over time in hours. Remember to label the axes with the real world quantities that x and y represent. Please use the graph that has been provided
1 answer:
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*I am assuming that the hexagons in all questions are regular and the triangle in (24) is equilateral*
(21)
Area of a Regular Hexagon: square units
(22)
Similar to (21)
Area = square units
(23)
For this case, we will have to consider the relation between the side and inradius of the hexagon. Since, a hexagon is basically a combination of six equilateral triangles, the inradius of the hexagon is basically the altitude of one of the six equilateral triangles. The relation between altitude of an equilateral triangle and its side is given by:
Hence, area of the hexagon will be: square units
(24)
Given is the inradius of an equilateral triangle.
Substituting the value of inradius and calculating the length of the side of the equilateral triangle:
Side = 16 units
Area of equilateral triangle = square units
Formula #1: 0.15x + 22
Formula #2: 0.19x
0.15x + 22 = 0.19x
So x = 550.
I hope this helps! :)