9514 1404 393
Answer:
- real: -1, 2; complex: +i, -i
- 1, 3, 4
Step-by-step explanation:
1. The graph (red) shows the only real zeros to be -1 and 2. When the corresponding factors are divided from the function, the remaining factor is the quadratic (x^2 +1), which has only complex roots. The quadratic is graphed in green.
The linear factorization is ...
f(x) = (x +1)(x -2)(x -i)(x +i)
The roots are -1, 2, -i, +i.
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2. The graph (blue) shows the zeros are 1, 3, 4.
You observe that the sum of coefficients is zero, so x=1 is a root. Factoring that out gives the quadratic (x^2 -7x +12), which you recognize factors as
(x -3)(x -4) . . . zeros of 3 and 4
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I have attached a spreadsheet that does synthetic division. There are web sites that will do this, too. The tables shown correspond to f1(x)/(x-2) and f2(x)/(x-1). When you fill in the zero and coefficients, the built-in formulas do the rest.
Answer:
Theoretical probability
Step-by-step explanation:
The theoretical probability is defined as:
In this case we look for the probability of taking a 2 out of the bag. As there is only one paper with the number 2 in the bag then:
number of desired results = 1
The amount of paper in the bag is equal to 7, so:
number of possible results = 7
Thus:
This is a theoretical probability, since we do not need to perform the experiment to calculate the probability.
To calculate the experimental probability we must perform the following experiment:
Take a paper out of the bag, record the number obtained and then return the paper to the bag.
Now repeat this experiment n times. (Perform n trials)
So:
To calculate a theoretical probability you always need to perform an experiment with n trials.
Distributive property then additive inverse
Okay. So by looking at this and doing mental math, it takes her 15 minutes to walk 1 mile. So for her to walk 7 miles, it will take her 105 minutes or 1 hour 45 minutes to do so. Here’s the double line diagram to support my answer (forgive me for the terrible writing).
We will use the similarity of the triangles:
100 : 20 = x : 2,500
20 x = 2,500 * 100
20 x = 250,000
x = 250,000 : 20
x = 12,500 ft
Answer: She is 12,500 feet away from the bluffs.
