To complete the square:
we take the coefficient ox "x" (which in this problem is -20)
we divide it by 2
square that number
then add it to both sides of the equation
-20 / 2 = -10
-10^2 = 100
then we add 100 to both sides of the equation:
x^2 -20x
x^2 -20x +100 = 100
******************************************************
To get the roots of the equation, we take the square root of both sides:
(x -10) * (x-10) = 10
(x-10) = square root (10)
x-10 =
<span>
<span>
<span>
3.1622776602
</span>
</span>
</span>
x1 =
<span>
<span>
<span>
13.1622776602
</span>
and don't forget that square root of 10 also equals </span></span><span><span><span> -3.1622776602
</span>
</span>
</span>
x2 = 10
-<span>
<span>
<span>
3.1622776602
x2 = </span></span></span>
<span>
<span>
<span>
6.8377223398
</span>
</span>
</span>
Answer:
7, 8, 9, 10
Step-by-step explanation:
If Zoe worked 4 hours of babysitting at $7 per hour, she earned $28. Therefore, she must earn another $102 to earn at least $130. At $15 per hour, she must work a minimum of 7 hours clearing tables to make at least $102. This is fine since she can work another 10 hours before reaching her maximum of 14 total hours. Therefore, all possible values for the number of whole hours clearing tables that she must work to meet her requirements are 7, 8, 9, 10.
Answer:
y = 3x -18 ( where y = balls sent back by Rudolf; x= balls given to Rudolf)
Step-by-step explanation:
x (Balls given) y( Balls sent back)
8 6 Δy/Δx = (27-6)/(15-8) = 3
15 27
25 57 Δy/Δx = (57-27)/(25-15) = 3
Observing the number sequence shows constant gradient and as such we can use equation of a straight line to relate the two variables.
Using the equation of a straight line we have:
(y-y1)/(x-x1) = (y2-y1)/(x2-x1)
y-6/x-8 = (27-6)/(15-8)
y-6/x-8 = 3
y-6 = 3(x-8)
y-6 = 3x - 24
y = 3x-18
