It takes 213 yards of denim to make one pair of jeans. How many yards would it take to make 5 pairs of jeans?
1 answer:
You might be interested in
Answer:
see attached for a graph
Step-by-step explanation:
It looks like you want to plot a graph of the function. For a piecewise function like this one, the effort is divided into pieces. The "or equal to" part of the comparison symbol tells you the end value is included in that interval.
__
For the piece between x=-8 and x=-6, you can find the y-values by evaluating the function for those x-values.
For x = -8: y = -1/2(-8) = 4.
For x = -6: y = -1/2(-6) = 3.
So, the left piece can be plotted by drawing a line segment between points (-8, 4) and (-6, 3).
__
For the piece between x=-6 and x=1, you can do the same thing:
For x=-6: y = -(-6) -3) = 6-3 = 3
For x=1: y = -(1) -3 = -4
So, the right piece can be plotted by drawing a line segment between points (-6, 3) and (1, -4). We notice that (-6, 3) is already the end point of the first piece, so the function is continuous at x=-6. (Sometimes there is a discontinuity between pieces. Not here.)
You can also plot the right piece by recognizing it is a line with a y-intercept of -3 and a slope of -1. That is, point (0, -3) will be on that line, and it will have a "rise" of -1 for each "run" of 1 (to the right).
__
A graph is shown. We have made the pieces different colors, so you can see what they are. And we have plotted a filled dot at (-6, 3) to indicate that point is part of the function definition. (The dot is unnecessary.)
Part A
Let y = a + b*x
where
x = number of days
y = cost
When x = 2, y =$225. Therefore
a + 2b = 225 (1)
When x = 5, y = 480. Therefore
a + 5b = 480 (2)
Subtract (1) from (2).
3b = 480-225 = 255
b = 85
From (1), obtain
a = 225 - 2*85 = 55
Answer:
y = 55 + 85x
where x = the number of days
y = the cost (dollars)
Part B.
The cost is
f(x) = 55 + 85x
Part C
To graph y = 55 + 85x,
The y-intercept is 55
The x-intercept occurs when y = 0. That is
55 + 85x = 0
x = -55/85 = -11/17
The graph is shown below.
Let y = a + b*x
where
x = number of days
y = cost
When x = 2, y =$225. Therefore
a + 2b = 225 (1)
When x = 5, y = 480. Therefore
a + 5b = 480 (2)
Subtract (1) from (2).
3b = 480-225 = 255
b = 85
From (1), obtain
a = 225 - 2*85 = 55
Answer:
y = 55 + 85x
where x = the number of days
y = the cost (dollars)
Part B.
The cost is
f(x) = 55 + 85x
Part C
To graph y = 55 + 85x,
The y-intercept is 55
The x-intercept occurs when y = 0. That is
55 + 85x = 0
x = -55/85 = -11/17
The graph is shown below.