The sum of two numbers is 51 and the greater number is twice the smaller number. Find the numbers.
1 answer:
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Answer:
See below.
Step-by-step explanation:
1)
So we have the equation:
To change into the slope-intercept form, we need to isolate the y-variable. Thus, subtract 2x from both sides:
The left side cancels:
Now, divide both sides by 3. The left side cancels:
The slope-intercept form is:
Where m is the slope and b is the y-intercept.
Thus, the slope is -2/3 and the y-intercept is 490.
2)
So, since we already know the y-intercept is 490, plot a point at (0,490).
The slope is too small to use. Thus, multiply the fraction by 100. It is now (-200/300). This means that we move <em>down</em> 200 for every 300 (recall that the slope means rise over run. Thus, we move down 200 for every 300 to the right). Thus, another possible point would be (0+300,490-200) or (300,290). Plot that. Then, connect them.
3)
To write in in function notation, simply substitute the y-variable for the function notation. Our independent variable here is x so we'll use that.
This means that for every x sandwiches made, there is f(x) wraps made for the total sum to be $1,470.
For example, if 105 sandwiches were made, then f(105)=-2/3(105)+490=420 wraps were made for the total profit to be $1,470.
4)
Please refer to the attached graph.
5)
First, since the total profit has now increased, the graph above and to the right of the old graph. This is because Sal needs to sell more sandwiches and wraps. Likewise, because of this, the x- and y-intercepts will also be different. Nevertheless, if converted into the slope-intercept equation, the slope will remain the same.
