Conjecture: How many solutions do x3 - 5x2 + 28 = 0 have? Find the real solution(s) of the equation. Then use polynomial long division to find the other solution(s).
Answers
Answer:
x = - 2 is confirmed to be the real solution of the equation.
Step-by-step explanation:
We are tasked with the following activities
Conjecture: How many solutions do have?
Find the real solution(s) of the equation.
Then use polynomial long division to find the other solution(s).
To start with the how many solutions that have
suppose that -2 happens to be a root of the equation, we can easily replace x = - 2 in the given equation. Then , we will have :
-8 - 20 + 28 = 0
-28 - 28 = 0
0 = 0
The equation resulted to 0 = 0 when x = -2 , as such -2 happens to be one root of the equation
So , as x = - 2
x + 2 = 0
x = - 2 is confirmed to be the real solution of the equation.
A picture showing the polynomial long division method used for solving the polynomial equation and other solution(s) can be found in the attached file below.
Related Questions
Help with this problem (20 points)
Sandra calculated the height of a cylinder that has a volume of 576 pi cubic centimeters and a radius of 8 centimeters. Her work is shown below. V = B h Step 1: 576 pi = pi 8 squared h Step 2: 576 pi = 64 pi h Step 3: StartFraction 576 pi Over 64 pi EndFraction = StartFraction 64 pi Over 64 pi EndFraction h Step 4: h = 9 pi cm What error did Sandra make when calculating the height of the cylinder? In step 1, she substituted into the volume formula incorrectly. In step 2, she calculated 8 squared incorrectly. It should be 16 rather than 64. In step 4, the pi should have canceled, making the correct answer 9 cm. Sandra calculated the height of the cylinder correctly.
Distribute 2(-3x+3x)
Write the phrase as an expression. Then evaluate when x=5 .6 more than the product of 8 and a number xExpression: When x=5, the value of the expression is Answer:
Please provide steps
Answers
Answer:
x = 50
Step-by-step explanation:
= a straight line is always equal to 180 degrees
= 180 -30 degrees = 150
= 150/3
=50
Answers
Answer:
Sampling error
Step-by-step explanation:
The answer is sampling error.
The sampling error occurs when the sample does not represent the full population and the result from the sample is not a representation of the results from full sample.
From information given
Population mean = 87.85
Population standard deviation = 118.1
n = 25
Sample mean = 79.07
Sample standard deviation = 129.91
118.2/√25
= 23.62
The standard deviation of the distribution is what is referred to as standard error of m = 23.62
Final answer:
The difference between the population mean and sample mean is likely due to sampling variability, a concept related to the Central Limit Theorem. Given the small sample size in this case, it's not unusual to see this difference.
Explanation:
The difference between the mean of the population (μ) and the mean of the sample (M) is likely attributable to the phenomenon known as sampling variability. This is a concept central to the Central Limit Theorem, which states that when enough random samples are taken from a population, the distribution of the means of these samples will approximate a normal distribution, even if the original population distribution is not normal. The mean of this distribution will be equal to the populating mean, and its standard deviation will be the standard deviation of the population, divided by the square root of the sample size (n).
In this specific case, you've taken a relatively small sample (n=25) from a larger population (N=2,431). Consequently, it is not unexpected that there is some difference between the population mean (μ = 87.85) and the sample mean (M = 79.07). However, as you increase the number of samples you are drawing, according to the Central Limit Theorem, the average of these sample means should converge on the population mean.
Learn more about Central Limit Theorem here:
#SPJ3
Answers
Answers
Given:
The given expression is
We need to evaluate the given expression.
Solution:
The given expression is in the form of general form of geometric sequence
The common ratio is and the first term is a = 4.
The formula to find the sum of the series is given by
Substituting n= 10, a = 4 and , we get;
Thus, the sum of the 10 terms is 5.33
Find each angle measure in the triangle.
Answers
Answer:
sum angle of triangle = 180°
6x°+5x°+9x°=180°
20x° = 180°
x= 180/20=9°
6x° = 54°
5x° = 45°
9x° = 81°
Step-by-step explanation:
a. Write an equation using the information as it is given above that can be solved to answer this problem. Use the variable r to represent the speed of the slower cyclist.
b. What are the speeds of the two cyclists? _______________
Answers
a) The given equation using the information as it is given above that can be solved to answer this problem is 4r + 4(r+3) = 68
b) The speed of both cyclists are 3mi/hr and 10mi/hr respectively
The formula for calculating the distance covered is expressed as:
Distance = speed * time
Let the speed covered by one cyclist be t
If one cycles 3 miles per hour faster than the other, the speed of the other will be t + 3
If both meet after 4 hours of riding, then their time will be 4 hours
Distance covered the first cyclist = 4r
Distance covered by the second = 4(r+3)
If the two cyclists are 68 miles apart, then:
4r + 4(r+3) = 68
a) The given equation using the information as it is given above that can be solved to answer this problem is 4r + 4(r+3) = 68
b) Expand the equation in a to get "r"
4r + 4r + 12 = 68
8r + 12 = 68
8r = 68 - 12
8r = 56
r = 56/8
r = 7miles per hour
Speed of the first cyclist = 7mi/hr
Speed of the second cyclist = 3 + 7mi/hr = 10mi/hr
Hence the speed of both cyclists are 3mi/hr and 10mi/hr respectively
Learn more here: brainly.com/question/19915685
Answer:
4r + 4(r + 3) = 68
r = 7 miles per hour
r + 3 = 10 miles per hour
Step-by-step explanation:
distance = rate * time
a)
4r + 4(r + 3) = 68
Distribute
4r + 4r + 12 = 68
8r + 12 = 68
8r = 56
r = 7 miles per hour
r + 3 = 10 miles per hour