To solve a polynomial inequality, we factor the polynomial
into irreducible factors and find all the real_______polynomial. Then we find the intervals determined by the real__________sign of the polynomial on that interval. Let
$$P(x)=x(x+2)(x-1)$$
Fill in the diagram to find the intervals on which
$P(x) \geq 0$
we see that $P(x) \geq 0$ on the
intervals_______and________.
Answers
Answer:
To solve a polynomial inequality, we factor the polynomial into irreducible factors and find all the real _zeros_ polynomial. Then we find the intervals determined by the real _zeros and use test points in each interval to find the_ sign of the polynomial on that interval.
If P(x) = x(x+2)(x-1)
And P(x) ≥ 0
We see that P(x) ≥ 0 on the intervals (-2, 0) and (1, ∞).
Step-by-step explanation:
The complete question is attached to this solution
To solve inequality of a polynomial, we first obtain the solutions of the polynomial. The solutions of the polynomial are called the zeros of the polynomial.
If P(x) = x(x+2)(x-1)
The solutions of this polynomial, that is the zeros of this polynomial are 0, -2 and 1.
To now solve the inequality that arises when
P(x) ≥ 0
We redraw the table and examine the intervals
The intervals to be examined as obtained from the zeros include (-∞, -2), (-2, 0), (0, 1) and (1, ∞)
Sign of | x<-2 | -2<x<0 | 0<x<1 | x>1
x | -ve | -ve | +ve | +ve
(x + 2) | -ve | +ve | +ve | +ve
(x - 1) | -ve | -ve | -ve | +ve
x(x+2)(x-1) | -ve | +ve | -ve | +ve
The intervals that satisfy the polynomial inequality P(x) = x(x+2)(x-1) ≥ 0 include
(-2, 0) and (1, ∞)
Hope this Helps!!!
Related Questions
It’s a math riddle please help Id appreciate it I need this quickly I’ll give additional points... I’d do need an explanation because the question requires it.
Answers
There are three cloaks, so you have to think, what times what equals 21? 7•3=21 after that you just do that formula through the rest 3•10=30
For the last one you have to figure what added and subtracting itself would equal 15? Well it would be 15
15+15-15=15
After that put it all together and you get 157
7+10•15=157
Hope that helps☀️
The puzzle are: 21, 30, 15, 333.
PuzzleClock:
Clock time=9 o'clock+9 o'clock+3 o'clock
Clock time=21
Calculator:
Calculator 1=1+2+3+4=10
Calculator 2=1+2+3+4=10
Calculator 3=1+2+3+4=10
Calculator=10+10+10
Calculator=30
Bulb:
The 3 bulb has 5 light each which represent the brightness of the 3 bulb.
Bulb=15+(15-15)
Bulb =15+0
Bulb=15
Fourth puzzle
Clock+Calculator×Bulb
9 o'clock+(1+2+2+4)× [3 bulb(3 bulb×4 light)]
9+9×(3×12)
Apply BODMAS
9+9×36
9+324
=333
Inconclusion the puzzle are: 21, 30, 15, 333.
Learn more about puzzle here:https://brainly.com/question/16999211
Please hurry
On each bounce, a ball dropped from 100 feet rises to the height
from which it has fallen. How high does the ball rise, in feet, on the 10th bounce?
Answers
Answer:
D
Step-by-step explanation:
divide 10 times starting with 100.
The answer is 25/256 or 0.09765625
The height of the ball dropped from 100 feet on the 10th bounce is 0.09766 feet
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let y represent the height of the ball after x bounce. Given that the ball rises to the height from which it has fallen, hence:
y = 100(1/2)ˣ
After the 10th bounce:
y = 100(1/2)¹⁰ = 0.09766
The height of the ball dropped from 100 feet on the 10th bounce is 0.09766 feet.
Find out more on equation at: https://brainly.com/question/2972832
Describe the steps you would use to solve the
following inequality
2x - 3
Answers
Answer: No answer
Step-by-step explanation:
Not an inequality, inequalities are of the form 2x - 3 > something.
If it's 2x - 3 > 0 for example, then add both sides by 3 to get 2x > 3, then div by 2 to get x > 3/2.
Hope that helped,
-sirswagger21
A cell phone company is offering 2 different monthly plans. Each plan charges a monthly fee plus an additional cost per minute. Plan A: $ 40 fee plus $0.45 per minute Plan B: $70 fee plus $0.35 per minute a) Write an equation to represent the cost of Plan A b) Write an equation to represent the cost of Plan B c) Which plan would be least expensive for a total of 100 minutes?
*Please Show Work*
Answers
Answer:
Plan A would be the least expensive
Step-by-step explanation:
Plan A= $0.45x100= 45, 45+40=$85
Plan B= $0.35x100= 35, 35+70= %105
(Each plan is for 100 minutes)
The cost of producing x soccer balls in thousands of dollars is represented by h(x) = 5x + 6. The revenue is represented by k(x)
= 9x - 2. Which expression represents the profit, (k-h(x), of producing soccer balls?
Answers
Answer:
4x - 8
Step-by-step explanation:
k - H(x)
(9x -2) - (5x + 6)
4x -8
Use the distributive property to remove the parentheses .
-8(y-v-3)
Answers
Answer:
-8y +8v +24
Step-by-step explanation:
-8(y-v-3)
Multiply each term inside the parentheses by -8
-8y -v*-8 -3*-8
-8y +8v +24
___________________________________
Hey!!!
solution,
-8(y-v-3)
= -8y+8v+24
_________________________________
Here,
You have to remember these things:
(+)*(+)=(+)(+)*(-)=(-)(-)*(-)=(+)(-)*(+)=(-)Hope it helps.
Good luck on your assignment
(TEKS 2A.) EF has endpoints E (8,3) and F(-4,9). What is the distance of the given segment?
A 8.544
C 11.250
B 10.345
D 13.416
Answers
Maybe D, I’m learning this same subject
find the slope of the line (-5,2) and (4,2)
Answers
Answer:
The answer is 0
Step-by-step explanation:
Having integrated with respect to ϕ and θ, you now have the constant 4π in front of the integral and are left to deal with ∫[infinity]0A21(e−r/a)2r2dr=A21∫[infinity]0r2(e−r/a)2dr.
What is the value of A21∫[infinity]0r2(e−r/a)2dr?Express your answer in terms of A1 and a.
Find the unique positive value of A1.
Express your answer in terms of a and π.
Answers
Answer:
Step-by-step explanation:
[tex]\int\limits^{\infty}_0 {A^2_1} (e^{-r/a})r^2dr= {A^2_1}\int\limits^{\infty}_0r^2(e^{-r/a})^2\, dr)[/tex]
[tex]=A_1^2\int\limits^{\infty}_0 r^2e^{-2r/a}\ dr[/tex]
[tex]=A_1^2[\frac{r^2e^{2r/a}}{-2/a} |_0^{\infty}-\int\limits^{\infty}_0 2r\frac{e^{-2r/a}}{-2/a} \ dr][/tex]
[tex]=A^2_1[0+\int\limits^{\infty}_0 a\ r\ e^{-2r/a}\ dr][/tex]
[tex]=A^2_1[\frac{a \ r \ e^{-2r/a}}{-2/a} |^{\infty}_0-\int\limits^{\infty}_0 \frac{a \ e^{-2r/a}}{-2/a} \ dr][/tex]
[tex]=A_0^2[0-0+\int\limits^{\infty}_0 \frac{a^2}{2} e^{-2r/a}\ dr\\\\=A_1^2\frac{a^2}{2} \int\limits^{\infty}_0 e^{-2r/a}\ dr\\\\=A_1^2\frac{a^2}{2} [\frac{e^{-2r/a}}{-2/a} ]^{\infty}_0[/tex]
[tex]=\frac{A_1^2a^2}{2} -\frac{a}{2} [ \lim_{r \to \infty} [e^{-2r/a} -e^0]\\\\=\frac{A_1^2a^2}{2} -(\frac{a}{2}) (0-1)[/tex]
[tex]=\frac{A_1^2a^3}{4}[/tex]
[tex]\therefore A_1^2\int\limits^{\infty}_0 r^2(e^{-r/a}) \ dr =\frac{A_1^2a^3}{4}[/tex]
Find the unique positive value of A1
[tex]=4\pi (\frac{A_1^2a^3}{4} )\\\\=A_1^2a^3\pi\\\\A_1^2=\frac{1}{a^3\pi} \\\\A_1=\sqrt{\frac{1}{a^3\pi} }[/tex]
If you found that the 95% confidence interval to estimate the true proportion of visitors to Niagara Falls that are from the United States was (0.5216, 0.6784), does this provide evidence that a majority of visitors to Niagara Falls are from the United States
Answers
Answer:
The lower end of the interval is above 0.5, which means that it provides evidence that a majority of visitors to Niagara Falls are from the United States
Step-by-step explanation:
We want to see if the majority of Niagara Falls visitors are from the United States.
Looking at the confidence interval
We have to see if the lower end of the interval is higher than 0.5.
In this question:
The 95% confidence interval to estimate the true proportion of visitors to Niagara Falls that are from the United States was (0.5216, 0.6784).
The lower end of the interval is above 0.5, which means that it provides evidence that a majority of visitors to Niagara Falls are from the United States
Identify the predictor variable and the response variable. A farmer has data on the amount of precipitation crops received and the harvest of the crops. The farmer wants to determine the harvest of his crop based on the amount of precipitation his crop received.
Answers
Answer:
The Predictor variable is the amount of precipitation received while the Response variable is the crop harvest.
Step-by-step explanation:
The Response variable in an experiment is the factor being measured or studied. They are also known as the dependent variables. Predictor variables are those values that explain the changes in the Response variable. They are also known as the independent variables.
In the question above, the amount of precipitation provides an explanation for the harvest of his crops. Therefore, the amount of precipitation can be rightly described as the predictor or independent variable, while the harvest of his crops is described as the response or dependent variable.
Reflect on the concept of function. What concepts (only the names) did you need to accommodate the concept of function in your mind? What is the simplest function you can imagine? In your day to day, is there any occurring fact that can be interpreted as a function? Is it possible to view a function? What strategy are you using to get the graph of a function?
Answers
Answer:
Step-by-step explanation:
For this kind of question you'd be better off if you'd write down and share your own answers to these conceptual questions and then ask for Brainly feedback on what you have written. You'll need to understand the concept of "function" often in algebra and beyond.
What concepts (only the names) did you need to accommodate the concept of function in your mind? input, output, rule, domain, range, mapping, variation (direct and inverse)
Simplest function: y = c (there's only one x-value and y equals that value)
In your day to day, is there any occurring fact that can be interpreted as a function? An electronic parking meter: the amount of time you can park at the meter without risking getting a ticket is dependent upon the number of quarters you insert into the meter, e. g, 15 minutes for 25 centers, 30 minutes for 50 cents, and so on.
Is it possible to view a function? Sure. Graph the function.
What strategy are you using to get the graph of a function? Set up a coordinate plane. Label the horizontal axis "x" and the vertical axis "y". Choose x (input) values that are included in the domain of the function. If the domain includes '0' you will be finding the 'y-intercept' of the function. Write the input and output as a point: (x, y). Plot that point. Choose other x values within the domain and calculate the corresponding y value for each. Plot several more points and draw a line or a curve through them. Of course there are more sophisticated strategies for graphing functions. Remember: If you're working with a function, there is never more than one output or y value for any particular input value.
According to the Bureau of Labor Statistics, 7.1% of the labor force in Wenatchee, Washington was unemployed in February 2019. A random sample of 100 employable adults in Wenatchee, Washington was selected. Using the normal approximation to the binomial distribution, what is the probability that 6 or more people from this sample are unemployed
Answers
Answer:
73.24% probability that 6 or more people from this sample are unemployed
Step-by-step explanation:
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The standard deviation of the binomial distribution is:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
Normal probability distribution
Problems of normally distributed samples can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
When we are approximating a binomial distribution to a normal one, we have that [tex]\mu = E(X)[/tex], [tex]\sigma = \sqrt{V(X)}[/tex].
In this problem, we have that:
[tex]n = 100, p = 0.071[/tex]
So
[tex]\mu = E(X) = np = 10*0.071 = 7.1[/tex]
[tex]\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{100*0.071*0.929} = 2.5682[/tex]
What is the probability that 6 or more people from this sample are unemployed
Using continuity correction, this is [tex]P(X \geq 6 - 0.5) = P(X \geq 5.5)[/tex], which is 1 subtracted by the pvalue of Z when X = 5.5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{5.5 - 7.1}{2.5682}[/tex]
[tex]Z = -0.62[/tex]
[tex]Z = -0.62[/tex] has a pvalue of 0.2676
1 - 0.2676 = 0.7324
73.24% probability that 6 or more people from this sample are unemployed
WRITING BOOK
Personal Writing
AD 1
NUMBERS
Which of the following cannot be an integer?
A. 0.8
B. -3
C. 4
D. 25
Answers
Answer:
A
Step-by-step explanation:
Integers are negative and positive whole numbers
Answer: A. 0.8
Step-by-step explanation:
An integer is a whole number (not a fractional number) that can be positive, negative, or zero. Examples of integers are: -5, 1, 5, 8, 97, and 3. Examples of numbers that are not integers are: -1.43, 1 3/4, 3.14
Please answer this correctly
Answers
Answer:
41-60 => 5
Step-by-step explanation:
41-50 => 2
51-60 => 3
So 2+3 =5
Answer:
5
Step-by-step explanation:
Add up the number of children between 41 and 60
41-50: 2
51-60: 3
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total 5