Solve the equation using the distributive property and properties of equality.5(a+ 3) = -55
1 answer:
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<u>Given</u>:
The quadratic equation is
We need to determine the solutions of the quadratic equation.
<u>Solution</u>:
Let us solve the equation to determine the value of x.
Adding both sides of the equation by 5x and 3, we get;
The solution of the equation can be determined using quadratic formula.
Thus, we get;
Thus, the two roots of the equation are and
Hence, the solutions of the equation are and
a) You are told the function is quadratic, so you can write cost (c) in terms of speed (s) as
... c = k·s² + m·s + n
Filling in the given values gives three equations in k, m, and n.
Subtracting each equation from the one after gives
Subtracting the first of these equations from the second gives
Using the next previous equation, we can find m.
Then from the first equation
[tex]28=100\cdot 0.01+10\cdot (-1)+n\\\\n=37[tex]
There are a variety of other ways the equation can be found or the system of equations solved. Any way you do it, you should end with
... c = 0.01s² - s + 37
b) At 150 kph, the cost is predicted to be
... c = 0.01·150² -150 +37 = 112 . . . cents/km
c) The graph shows you need to maintain speed between 40 and 60 kph to keep cost at or below 13 cents/km.
d) The graph has a minimum at 12 cents per km. This model predicts it is not possible to spend only 10 cents per km.
