Tim has 2 times as luke
t=2l
they have 29 goether
t+l=39
subsitute
2l+l=39
3l=39
divide by 3
l=13
subsitue
t=2l
t=2(13)
t=26
tim has 26 and luke has 13
I don't know how many marble Tim has but probably all of them since alll must die and then the marbles go to Time
A.) f(x) = x^2 because 2 > 1. So f(2) = 4.
A is correct.
B.) f(x) = x^2 because 5 > 1. So f(5) = 25.
B is incorrect.
C.) f(x) = 2x because -2 < 1. So f(-2) = -4.
C is incorrect.
D.) f(x) = 5 because x = 1.
D is correct.
So the answer is A and D.
<span>x^2 + 15x + 56.25 = 105.25
"Completing the square" is one of many different techniques for solving a quadratic equation. What you do is add a constant to both sides of the equation such that the lefthand side can be factored into the form a(x+d)^2. For instance, squaring (X+D) = X^2 + 2DX + D^2. Notice the 2DX term. That is the same term as the 15x term in the problem. So 2D = 15, D = 7.5. And D^2 = 7.5^2 = 56.25.
So we have
x^2 + 15x + 56.25 = 49 + 56.25
Which is
x^2 + 15x + 56.25 = 105.25
Which is the answer desired.
Now the rest of this is going beyond the answer. Namely, it's answering the question "Why does complementing the square help?"
Well, we know that the left hand side of the equation can now be written as
(x+7.5)^2 = 105.25
Now take the square root of each side
(x+7.5) = sqrt(105.25)
And let's use both the positive and negative square roots.
So
x+7.5 = 10.25914226
and
x+7.5 = -10.25914226
And let's find X.
x+7.5 = 10.25914226
x = 2.759142264
x+7.5 = -10.25914226
x = -17.75914226
So the roots for x^2 + 15x - 49 is 2.759142264, and -17.75914226</span>
