Two cars at the same point on I-75. One heads north going 75mph and one heads south going 60mph. How long will it take for the c
1 answer:
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Answer:
length of rectangle = 5
width of rectangle = 5
Area of rectangle = 25
Step-by-step explanation:
Since the length of the rectangle is "x", and the value of the area is given by the product of the length "x" times the width "10-x", indeed, the area "y" of the rectangle is given by the equation:
Now, they tell us that the area of the rectangle is such that coincides with the maximum (vertex) of the parabola this quadratic expression represents. So in order to find the dimensions of the rectangle and therefore its area, we find the x-coordinate for the vertex, and from it, the y-coordinate of the vertex, which is the rectangle's actual area.
Recall that the formula for the x of the vertex of a quadratic of the form :
is given by the formula:
which in our case gives:
Therefore, the length of the rectangle is 5, and its width (10-x) is also 5.
The area of the rectangle is therefore the product of these two values: 5 * 5 = 25
Which should coincide with the value we obtain when we replace x by 5 in the area formula:
Answer: 560
Step-by-step explanation:
There are [20, 22, 24, 26, 28]: 5 even integers for each ten numbers.
The 20's set can be written as 5*20 + (2+4 + 6 + 8) = 5*20 + (20) = 120
The 30's can be written: 5*30 + 20 = 170
40's: 5*40+20 = 220
50's: 5*50+20 = 270
60's: 5*60+20 = 320
Each set is incremented by 50
We want the sets for 20, 30, and 40, plus the number 50.
(120+170+220+50) = 560
You can also do this in Excel (attached). Set the first cell to 20, the next cell below equal to the cell above plus 2. Then draw the second cell down until you've reached 50. Then sum the cells to arrive at 560.
Answer:
The function is non-proportional.
Step-by-step explanation:
If the function was proportional, when the number of hours spent riding the bicycle is equal to 0, the total cost of renting the bicycle would also be 0. In other words, the function would be proportional if y=0 when x=0. However, this is not the case.
Plug 0 into the equation as x
When 1 bicycle has been rented for 0 hours, the customer still has to pay 10 dollars just for renting it. When x=0, y=10. This means that the function is non-proportional.
I hope this helps!