<span> Direct-substituting x = -2 gives 0/0, so we know that by the factor theorem, both the numerator and denominator have a factor of x + 2. From there, we can cancel out the conflicting factors and apply the limit.
We can factor the numerator and denominator to get:
x^3 - x^2 - x + 10 = (x + 2)(x^2 - 3x + 5)
x^2 + 3x + 2 = (x + 2)(x + 1).
So we have:
lim (x-->-2) (x^3 - x^2 - x + 10)/(x^2 + 3x + 2)
= lim (x-->-2) [(x + 2)(x^2 - 3x + 5)]/[(x + 2)(x + 1)]
= lim (x-->-2) (x^2 - 3x + 5)/(x + 1), by canceling out x + 2
= [2^2 - 3(-2) + 5]/(-2 + 1)
= (4 + 6 + 5)/(-1)
= -15.
I hope this helps! </span>
Answer:
The metric system is an alternative system of measurement used in most countries, as well as in the United States. The metric system is based on joining one of a series of prefixes, including kilo-, hecto-, deka-, deci-, centi-, and milli-, with a base unit of measurement, such as meter, liter, or gram.
Hi, I was able to find the full context for this one from another source:
<span>"Juanita has a storage closet at her shop with extra bottles of lotion and shower gel. Some are scented and some are unscented. If she reaches into the closet and grabs a bottle without looking, she has a 42% chance of grabbing a bottle of shower gel."
For the "shower gel" and "scented" to be independent given the situation above, we need to show that P(A | B) = P(A). You can get this equation from the definition of "independence" where P(A </span>∩ B) = P(A)*P(B) and the formula for conditional probability P(A | B).
We only have the given P(shower gel) = 42% therefore the event "shower gel" must be the variable A.
ANSWER: To show independence of the two events, P(shower gel | scented) = 42% must be true.
Answer:
The line equation of the line is:
Step-by-step explanation:
Given the two points
Finding the slope between (0,3) and (8,0)
Therefore, the slope of the line: m = -3/8
Using the point-slope form of the line equation
where m is the slope of the line and (x₁, y₁) is the point
substituting the values m = -3/8 and the point (0,3)
Add 3 to both sides
Simplify
Therefore, the line equation of the line is:
