(X+2y)(x-2y) how do I solve this
1 answer:
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Answer: A: (x + 4)² + (y - 5)² = 8
<u>Step-by-step explanation:</u>
The equation of a circle is: (x - h)² + (y - k)² = r² where
- (h, k) is the center of the circle
- r is the radius of the circle
To find the equation of circle A, we need (h, k) and r².
It is given that (h, k) = (-4, 5)
The distance between the center of circles A and B is the radius of circle A.
Let's find the center of circle B by completing the square:
x² - 4x + ____ + y² + 6y + _____ = 12 + ____ + _____
↓ ↓
h = -4/2 k = 6/2
h = -2 k = 3 → Circle B has center (-2, 3)
Now let's find the distance between the center of circles A and B:
= (-4 - (-2))² + (5 - 3)²
= (-2)² + 2²
= 4 + 4
= 8
Now we have the the center (h, k) and the r² for circle A:
(h, k) = (-4, 5) and r² = 8 → (x + 4)² + (y - 5)² = 8
Answer:
She needs a sample size of 25.
Step-by-step explanation:
We have that to find our level, that is the subtraction of 1 by the confidence interval divided by 2. So:
Now, we have to find z in the Ztable as such z has a pvalue of .
That is z with a pvalue of , so Z = 0.995.
Now, find the margin of error M as such
In which is the standard deviation of the population and n is the size of the sample.
The population SD is 2 grams.
This means that
What is the minimum sample size she needs to create a confidence interval that has a width of 0.4 grams?
She needs a sample size of n.
n is found when M = 0.4. So
Rounding up:
She needs a sample size of 25.