Answer:
20 miles
Step-by-step explanation:
I'm not sure if that is exactly how you solve it but
If its
8x+4 as the equation and x is the number of hours run
the total number of miles run should be 20 miles
8(2)+4=20
4/6=2/3 (divide both numerator and denominator by 2 (gcd)).
Hope this helps.
Answer:
39.0625 ft
Step-by-step explanation:
Since the function is a quadratic representing height, and the coefficient of the t² is negative, the vertex of the parabola will be the maximum height achieved by the ball.
The general form for a quadratic equation is ax² + bx + c, here a is -16, and b is 50
To find the x coordinate of the vertex, use x = -b/(2a)
We have x = -50/[2(-16)]
x = -50/-32
x= 25/16
Now plug that into the equation to find the y value, which will be the height...
y = 50(25/16) - 16(25/16)²
y = 1250/16 - 16(625/256)
y = 1250/16 - 625/16
y = 625/16
y = 39.0625
Answer:
9.1 minutes.
Step-by-step explanation:
Let t represent time taken to fill the tank.
We have been given that a cold water faucet can fill a sink in 12 min, so the part of sink filed in 1 minute would be 
.
The hot-water faucet can fill it in 15 min, so the part of sink filed in 1 minute would be 
.
The drain can empty the sink in 25 min, so the part of drain emptied in 1 minute would be 
.
The part of 1 full tank filled in t minutes, when both faucets are on and the drain is open would be:
Make a common denominator:
Therefore, it will take 9.1 minutes to fill the sink.
The answer is: x = 7 - √53 or x = 7 + √53
The general quadratic equation is: ax² + bx + c =
0.
But, by completing the square we turn it into: a(x + d)² + e = 0, where:<span>
d = b/2a
e = c - b²/4a
Our quadratic equation is x² - 14x -4 = 0, which is
after rearrangement:
So, a = 1, b = -14, c = -4
Let's first calculate d and e:
d = b/2a = -14/2*1 = -14/2 = -7
e = c - b²/4a = -4 - (-14)</span>²/4*1 = -4 - 196/4 = -4 - 49 = -53<span>
By completing the square we have:
a(x + d)² + e = 0
1(x + (-7))</span>² + (-53) = 0
(x - 7)² - 53 = 0
(x - 7)² = 53
x - 7 = +/-√53
x = 7 +/- √53
Therefore, the solutions are:
x = 7 - √53
or
x = 7 + √53
