There are 19 people total, and groups of four are being asked of us. We can use the formula for permutations or combinations.
Permutations:
Combinations:
Where in both scenarios, there are <em>n</em> objects being chosen at <em>r</em> times.
19 P 4 is 93024
19 C 4 is 3876
It all depends on whether order matters with group placement; if it does, your answer is
93024, if not, then your answer is
3876.:)
<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>
Answer:
−49427112 us the correct answer
A rectangle has a perimeter of length + length + width + width.
L = length of the fence.
W = width of the fence.
so the perimeter will be L+L+W+W or 2L+2W or 2(L+W).
now, we know that 120 ⩽ 2(L+W).
we also know that 168 ⩾ 2(L+W)
and we also know that whatever the length is, is twice the width, or L = 2W.
The answer is :
.0085470085
Hope This Helps!!
:)
