Using the Factor Theorem, it is found that yes, it is possible for a sixth degree polynomial function with integer coefficients to have no real zeroes, as they can have three complex-conjugate pairs.
<h3>What is the Factor Theorem?</h3>
The Factor Theorem states that a polynomial function with roots is given by:
In which a is the leading coefficient.
If a complex number is a root of a function, it's conjugate will also be a root. Thus, with three pairs of complex-conjugate roots, for example, , a sixth degree function with no real zeros is formed, so the answer is Yes.
More can be learned about the Factor Theorem at brainly.com/question/24380382
Answer:
a
Step-by-step explanation:
subtract 6 from both sides
A dilation can elongate or diminish a figure. It can
create an image the same as the original by using a scale factor. The scale
factor of a dilation is the ratio of corresponding side lengths. To
dilate a polygon, multiply the coordinates of each vertex by the scale
factor k and connect the vertices.
(a)
The binomial distribution can be used because the current situation satisfies all of the following:
1. The probability of success (p=85%) is known and remains constant during the whole experiment
2. The number of trials (n=40) is known and constant.
3. Each trial is a bernoulli trial (success or failure only)
4. All trials are (assumed) independent of each other.
The probability of x successes is therefore
P(X=x)=C(n,x)(p^x)(1-p)^(n-x)
(b) P(X=35) means the probability of 35 successes out of 40 trials at p=0.85
and
P(X=35)=C(40,35)*0.85^35*0.15^5=658008*0.003386*0.00007594
=0.16918
(c) P(X>=35)=∑ P(X=i) for i=35 to 40
=0.16918+0.13315+0.08157+0.03649+0.01060+0.00150
=0.4325
(d) P(X<20)=∑ P(X=i) for i=0 to 19
=0.00000003513 (individual probabilities are very small).
Note that m∠4 and m∠1 are vertical angles, and so they would have the same measurements (same for m∠3 & m∠2). Note that m∠1 and m∠2 are supplementary angles (going to have a total measurement of 180°)
m∠2 = 50° (given)
m∠1 + m∠2 = 180
m∠1 + 50 = 180
Isolate m∠1. Note the equal sign. What you do to one side you do to the other. Subtract 50 from both sides
m∠1 + 50 (-50) = 180 (-50)
m∠1 = 180 - 50
m∠1 = 130°
m∠1 = 130° is your answer
hope this helps