Answer:
Step-by-step explanation:
Theorm-The Fundamental Theorem of Algebra: If P(x) is a polynomial of degree n ≥ 1, then P(x) = 0 has exactly n roots, including multiple and complex roots.
Let's verify that the Fundamental Theorem of Algebra holds for quadratic polynomials.
A quadratic polynomial is a second degree polynomial. According to the Fundamental Theorem of Algebra, the quadratic set = 0 has exactly two roots.
As we have seen, factoring a quadratic equation will result in one of three possible situations.
graph 1
The quadratic may have 2 distinct real roots. This graph crosses the
x-axis in two locations. These graphs may open upward or downward.
graph 2
It may appear that the quadratic has only one real root. But, it actually has one repeated root. This graph is tangent to the x-axis in one location (touching once).
graph 3
The quadratic may have two non-real complex roots called a conjugate pair. This graph will not cross or touch the x-axis, but it will have two roots.
Answer:
Step-by-step explanation:
To find the gradient (slope) of the given <u>linear relation</u>, use <u>arithmetic operations</u> to isolate y:
Given relation:
Add 5x to both sides:
Divide both sides by 3:
<u>Slope-intercept form of a linear equation</u>
where:
- m is the slope (gradient)
- b is the y-intercept
Comparing the rewritten equation with the slope-intercept formula, the gradient (slope) of the given linear relation is ⁵/₃.
Learn more about linear equations here:
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Answer:
0≥x<4
Step-by-step explanation:
first, let's look at this number line.
there is a closed circle at 0 and an open circle at 4. this means that 0 is included (≤ or ≥) and that 4 is not included (< or >).
these are the endpoints, meaning that in this compound inequality, the numbers next to the symbols are 0 and 4.
x is in the middle of this compound inequality.
0 x 4
now, we have to figure out the symbols in between. i wrote out our choices above for each number. the highlighted portion is greater than or equal to 0 and less than 4, so we can write this compound inequality as the following:
0≥x<4
x is greater than or equal to 0, but less than 4
Answer:
a range of values such that the probability is C % that a rndomly selected data value is in that range
Step-by-step explanation:
complete question is:
Select the proper interpretation of a confidence interval for a mean at a confidence level of C % .
a range of values produced by a method such that C % of confidence intervals produced the same way contain the sample mean
a range of values such that the probability is C % that a randomly selected data value is in that range
a range of values that contains C % of the sample data in a very large number of samples of the same size
a range of values constructed using a procedure that will develop a range that contains the population mean C % of the time
a range of values such that the probability is C % that the population mean is in that range
