<span>3.19459 seconds
Since we've been given the equation for how high the ball is at t seconds, all we need to do is solve for a height of 0. So
h = 67 - 5t - 5t^2
0 = 67 - 5t - 5t^2
And you should immediately notice that we have a quadratic equation with A = -5, B = -5, and C=67. Use the quadratic formula to determine the roots of -4.19459 and 3.19459. Since we can't have negative seconds, that means that the ball will hit the ground 3.19459 seconds after it was thrown.</span>
Answer:
18 weeks
Step-by-step explanation:
Create an equation where x is the number of weeks he works
60x - 220 will represent his profit, since he gets $60 a week but spent $220 in equipment.
Set this equal to 860, then solve for x, to find when he will earn $860
60x - 220 = 860
60x = 1080
x = 18
So, it will take him 18 weeks to earn $860
Answer:
3(k - 1)² = 12
Step-by-step explanation:
To complete the square, write the equation standard form and make the a term's coefficient 1.
3k² = 11 + 6k
3k² - 6k - 11 = 0
3(k² - 2k) = 11
Take the middle term -2k and divide the coefficient in 2 and square it. Here it is -2/2 = -1. -1² = 1. Add 1 to both sides.
3(k² - 2k + 1) = 11 + 1
3(k - 1)² = 12
Answer:
Step-by-step explanation:
This is a parabola shaped like a U.
The minimum value is at (-2, -3).
Find the zeroes:
(x + 2)^2 = 3
Find the zeroes:
x + 2 = +/- √3
x = +/-√3 - 2
x = -0.27, -3.73.
So the graph cuts the x axis at (-0.27, 0) and (-3.73, 0)
when x = -4 , f(x) = 1 and when x = 1, f(x) = 6.
So you can now draw the curve through these 5 points and it will be shaped like a U, symetrical about the line x = -2
<h3>Derek used the racquetball courts 47 times</h3>
<em><u>Solution:</u></em>
Given that,
Derek paid a yearly membership fee of $259.99 that covers all the clubs services expect use of the racquetball courts
Derek paid $3.75 each time he used a racquetball court
For the entire year at the health club, Derek paid a total of 436.24
Let "r" represent the number of times Derek used one of the racquetball courts
Therefore,
Amount paid = 259.99 + 3.75r
Derek paid a total of 436.24
Therefore,
436.24 = 259.99 + 3.75r
3.75r = 436.24 - 259.99
3.75r = 176.25
Divide both sides by 3.75
r = 47
Thus Derek used the racquetball courts 47 times
