For a two-tailed test we need to halve 0.01, giving 0.005. Then we need to sutract 0.005 from 0.5, giving 0.5 - 0.005 = 0.495. Looking up the p value of 0.495 in an inverse normal probability table we obtain the value z = 2.5758. Therefore the critical values are -2.5758 and 2.5758.
<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:
It would be a
Step-by-step explanation:
the difference is 4/8 but simplified it is 1/2
Answer:
Step-by-step explanation:
A
<em>Answer:</em>
<em>The answer for this question will be 324 square roots</em>
<em>Step-by-step explanation:</em>
<em>The length and width of a rectangle are interchangeable, however we usually use the longer side for the length.
</em>
<em>If that's the case, </em><em>then the square is 18 x 18 = 324 square units.
</em>
<em>On the other hand, the square could also be 10 x 10 square units. You choose ! In reality, the length and width, like I said, are interchangeable.</em>
