Jeff is playing a racing game. The game awards him an initial $4,000 of virtual money. In addition, he gets $100 of virtual mone
y for each race he wins. In the end, he calculates average earnings $200 of for each race he won. If x represents the number of races he won, which equation can be used to find the number of wins?
1 answer:
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Answer:
Accelerating to top speed, deaccelerating to finish line.
Step-by-step explanation:
If the runner kept a constant speed of 11 mph for the whole duration of his run (32 minutes), the distance he would have covered is:
This means that, in order to run the full 6.2 miles, the runner needs to reach a speed over 11 mph. Assume he starts from rest, while accelerating the runner reaches, and the surpasses, the 11 mph mark. Since his speed at the finish line is zero, the runner has to deaccelerate from his current running speed (which should be higher than 11 mph), passing through 11 mph and reaching zero at the finish line.
see the image to better understand the problem
we have that
sin(15)=6800/L -------> by opposite side divided by the hypotenuse
solve for L
L=6800/sin(15)
<h2>L=26,273 ft</h2>
Answer:
B. -2, 2
Step-by-step explanation:
Apparently, we're to presume that f(x) is the line that is graphed. It has a y-intercept of +1 and a slope (rise/run) of 1/2. Its equation is ...
f(x) = 1/2x +1
If we want points of intersection, we want to solve the equation f(x) = g(x) for the values of x that make it so.
1/2x +1 = √(x +2)
Squaring both sides, we get ...
1/4x² +x + 1 = x +2
1/4x² = 1 . . . . . . . . . . . . subtract x+1 from both sides
x² -4 = 0 . . . . . . . . . . multiply by 4, subtract 4
(x -2)(x +2) = 0 . . . . factor the difference of squares
x = -2, 2 . . . . . . . . . values of x that make the factors zero
The solutions to f(x) = g(x) are x = -2 and x = 2.
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<em>Additional comment</em>
The attached graph shows the x- and y-values at the points of intersection. The solutions to f(x) = g(x) are only the x-values, -2 and 2.
The square of (ax +b) is ...
(ax +b)² = a²x² +2abx +b²
The point-slope equation of a line is ...
y = mx + b . . . . . line with slope m and y-intercept b
