Determine all the factors for the following expression(Note: you will need to use the Rational Root Theorem more than one time) : f(x)=x^5+3x^4-5x^3-15x^2+4x+12? Please help im so confused and this assignment is due tomorrow!?
Answers
Possible rational roots: ±1,±2,±3,±4,±6,±12±1,±2,±3,±4,±6,±12
Actual rational roots: 1,−1,2,−2,−3
see attachments for all steps.
Since factors of 12 include plus or minus 1, 2, 3, 4, 6, 12,
possible rational roots include plus or minus 1/1, 2/1, 3/1, 4/1, 6,/1, 12/1 (and so on.) I will take a chance and try the possible root 6/1, or just plain 6.
Use synthetic division, with 6 as the divisor and all of the coefficients of x^5+3x^4-5x^3-15x^2+4x+12 as dividend:
______________________
6 / 1 3 -5 -15 4 12
6 54
--------------------------------
1 9 49 This is not going to work; 6 is not a root.
Try -3 as divisor:
___________________
-3 / 1 3 -5 -15 4 12
-3 0 15 0 -12
-------------------------- ------
1 0 -5 0 4 0
Since the remainder is zero, x = -3 is a root of the given polynomial.
Repeat this process, except skip x = -3 and x = 6 as divisors.
Use the coefficients 1 0 -5 0 4. Note that plus or minus 4 over 1 forms other possible rational roots: 4/1, -4/1, 2/1, -2/1, 1, -1
Let's check out
____________
1 / 1 0 -5 0 4
1 1 -4 -4
--------------------------
1 1 -4 -4 0
Thus, 1 is also a root of the polynomial, along with -3.
Repeat this process. As divisors try 4/1, -4/1, 2/1, -2/1, -1
Can you now finish this factoring?
The 2 roots found so far are {1, -3}.
Related Questions
Does anyone knows the answer
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The anova from a randomized complete block experiment output is shown below. source df ss ms f p treatment 4 1010.56 ? 29.84 ? block ? ? 64.765 ? ? error 20 169.33 ? total 29 1503.71 (a) fill in the blanks. you may give bounds on the p-value. (b) how many blocks were used in this experiment? (c) what conclusions can you draw?
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d.f. for blocks =b-1= 29-(20+4)= 29-24=5Hence here b=6 blocks were used. MS for treatment Ms for error = So SS for Blocks = MS * df =64.765*5 = 323.825F for block = p value for treatment using excel : 'fdist(29.84,4,20)' = 3.545E-08p value for block : 'fdist(7.649,5,20)' = 0.00037Here p value for treatment ( 0.0000000354) < ( 0.05 )Hence we reject null hypothesis.Also p value for block (0.00037 ) < ( 0.05 )Hence we reject null hypothesisConclusion : There is difference between treatment means as well as block means.
The missing mean square (MS) for the treatment is 252.64, and there were 6 blocks used in the experiment. The p-value is less than 0.01, indicating a statistically significant effect of the treatment.
To fill in the blanks of the ANOVA table provided, we will perform some calculations. The mean square (MS) for the treatment can be found by dividing the sum of squares (SS) for the treatment by its degrees of freedom (df). Hence, for the treatment:
MS treatment = SS treatment / df treatment = 1010.56 / 4 = 252.64
Given that the total df equals 29 and the df for treatment and error sum up to 24 (4 + 20), the df for blocks will be:
df total - df treatment - df error = 29 - 4 - 20 = 5
Therefore, the number of blocks used in this experiment equals the df for blocks plus 1, giving us:
Number of blocks = df blocks + 1 = 5 + 1 = 6 blocks
As for the p-value associated with the F-statistic, we cannot calculate the exact value, but it is indeed lower than the conventional alpha levels (0.05, 0.01). So we describe the p-value as being less than 0.01
Conclusions:
With an F-statistic of 29.84 and a p-value much lesser than conventional alpha levels, we can conclude that there is a statistically significant effect of the treatment on the outcome variable.
The specific p-value bounds are not provided, but given that it is very low, the results are statistically significant. Thus, we can reject the null hypothesis that there is no effect of the treatment.
The function c(x) = 0.5x+70 c(x) = 0.5x+70 represents the cost cc (in dollars) of renting a truck from a moving company, where xx is the number of miles you drive the truck.
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I believe we are to find for values in this problem.
a. The graph of the function
b. The domain and range
c. The slope
d. The c intercept value
Answers:
a. see the graph photo attached
b. The domain is the set of all x that can be input to the function. Since x is the distance and we know that distance cannot be negative hence the domain is:
x ≥ 0
So the range starts from x = 0:
c (x) = 0.5 * 0 + 70 = 70
Therefore the range is:
c ≥ 70
Domain: x ≥ 0 Range: c ≥ 70
c. A linear equation has a general form of:
y = mx + b
where m is the slope
From the given equation, the slope is 0.5.
slope = 0.5
d. The c intercept is simply the value of c when x is equal to 0
c intercept = 70
Answer:Given function: c(x) = 0.5x+70.Where c is the cost (in dollars) and x is the number of miles you drive the truck.If we compare given function by slope-intercept form y=mx+b, we get Slope m = 0.5 in fractions could be written as 1/2.And y-intercept b =70.So, in order to graph it, we need to plot y-intercept at 70 first and then plot some more points using rise/run = 1/2.The red line is the graph for the given function.We can see that starting value of cost is $70 for 0 number of miles.x values represents domain and C(x) represents range.We can take x values greater than or equal to 0 and C values greater than equal to 70.Therefore, Domain: x≥0 and Range : C(x) ≥ 70.
Step-by-step explanation:Credit:User named PiaDeveau thanks for providing the answer and hope this helps
:)
162x + 731 = −y − 9x-2 vertex form
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I am goint to solve this question assuming that the correct expression is 162x + 731 = - y - 9x^2
Now, you should know that the vertex form is y = a(x - h)^2 + k, where the vertex is (h,k).
So, we just must transform the quadratic function into that form. To do that you must complete squares. I will do it step by step
start: 162 x + 731 = - y - 9x^2
1) Transpose terms:
y = - 9x^2 - 162x + 731
2) extract common factor ot the two terms with x^2 and x.
y = - 9 (x^2 + 18x) + 731
3) complete squares for x^2 + 18x, which is (x + 9)^2 - 81
=> y = - 9 [ ( x + 9)^2 - 81 ] + 731
4) solve the square brackets
=> y = - 9 (x + 9)^2 - 9*81 + 731
=> y = - 9(x + 9)^2 -729 + 731
=> y = - 9 (x + 9)^2 + 2
Answer: y = - 9 (x + 9)^2 + 2
To write the given equation in vertex form, we need to complete the square for the x terms. The vertex form of a quadratic equation is y = a(x-h)^2 + k, where (h, k) is the vertex of the parabola. After completing the square and rearranging the equation, we find that the equation in vertex form is y = 171(x + 7391/4) - 17113/4.
Explanation:To write the given equation in vertex form, we need to complete the square for the x terms. The vertex form of a quadratic equation is given by y = a(x-h)^2 + k, where (h, k) is the vertex of the parabola.
Let's rearrange the equation to isolate the x terms on one side and the y term on the other side: 162x + 9x + y = -731 - 2
Combine like terms: 171x + y = -733
Now, we can complete the square for the x terms. Divide the coefficient of x by 2 and square the result. Add this value to both sides of the equation: 171x + y + (171/2)^2 = -733 + (171/2)^2
Simplify: 171x + y + 7391/4 = 17113/4
Finally, we can rewrite the left side as a binomial squared and simplify the right side: 171(x + 7391/4) + y = 17113/4
Therefore, the equation in vertex form is: y = 171(x + 7391/4) - 17113/4
Which property is represented by the number sentence shown below?
6+(4+5) = (6+4)+5
A. Commutative property of multiplication
B. Associative property of addition
C. Commutative property of addition
D. Associative property of multiplication
If you can also explain how you got the I’ll appreciate it.
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This means that no matter where you put the parenthesis, you will get the same solution.
Hope this helps!
the volume of a box is 1344 cubic inches. how many cubic inches are in one cubic foot? what is the volume of the box in cubic feet?
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A cubic foot is 12"
12* 12" * 12" = 1728 cu/inches
therefore
1344/1728 =. 78 cu ft
write a real world situation that can be modeled by the inequality
46h > 86 + 25h.
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Let h = number of hours you rent the boat
if it costs $46 per hour to rent a boat, then it will cost a total of 46*h or 46h dollars
Now let's say that you get a discount if you are a member. The membership fee is $86 leading to the discount hourly cost to be $25 per hour. If you rent for h hours, then you pay a total of 86+25h dollars
Writing 46h > 86+25h will represent cases when the nonmembership option is more expensive (and the membership option more cheaper). Solving for h will help determine when the membership option is cheaper.
There is a value of $a$ such that subtracting $a-4$ from $4a+16$ gives an answer of $-25$. What is that value of $a$?
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4a + 16 - a + 4 = -25
3a + 20 = -25
3a = -45
A = -15
Answer:
a = -15
Step-by-step explanation:
Let's rewrite the exercise in math language.
We have to subtract a-4 from 4a+16 to get -25, that is
4a+16 - (a-4) = -25
The minus sign that is just before the parenthesis changes all the signs inside it. Therefore, if we want to delete the parenthesis, we need to change the signs before.
4a + 16 - a + 4 = -25
Now we can associate the terms with an a between them and the terms without it from the left side of the equation.
3a + 20 = -25
Let's subtract 20 on both sides.
3a + 20 - 20 = -25 - 20
3a = -45
Finally, we divide by 3 on both sides
3a/3 = -45/3
a = -15
20 points!! Solve this system of lineal equations.separate the x- and y- values with a comma
12x=54-6y
-17x=-62-6y
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Express the system in standard form:{12 x + 6 y = 54 | (equation 1)-(17 x) + 6 y = -62 | (equation 2)
Swap equation 1 with equation 2:{-(17 x) + 6 y = -62 | (equation 1)12 x + 6 y = 54 | (equation 2)
Add 12/17 × (equation 1) to equation 2:{-(17 x) + 6 y = -62 | (equation 1)0 x+(174 y)/17 = 174/17 | (equation 2)
Multiply equation 2 by 17/174:{-(17 x) + 6 y = -62 | (equation 1)0 x+y = 1 | (equation 2)
Subtract 6 × (equation 2) from equation 1:{-(17 x)+0 y = -68 | (equation 1)0 x+y = 1 | (equation 2)
Divide equation 1 by -17:{x+0 y = 4 | (equation 1)0 x+y = 1 | (equation 2)
Collect results:Answer: {x = 4 {y = 1
Please note the { are supposed to span over both equations but it interfaces doesn't allow it. Please see attachment for clarification.
Jenny, Ali and Eric have a total of $97 in their wallets. Ali has $5 more than Jenny . Eric has 2 times what Jenny has. How much does each have?
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Jenny = x
Ali = x+5
Eric - 2x
2x + x + 5 + x = 97
4x = 97 - 5
x = 23
Jenny has 23
]Ali has 28
Eric has 46
a = j + 5
e = 2j
j + j + 5 + 2j = 97
4j + 5 = 97
4j = 97 - 5
4j = 92
j = 92/4
j = 23 <=== what Jenny has
a = j + 5
a = 23 + 5
a = 28 <=== what Ali has
e = 2j
e = 2(23)
e = 46 <=== what Eric has
) find the solution of y"+2y'=64sin(2t)+64cos(2t) with y(0)=9 and y'(0)=9
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Clearly people
Evaluate (1/2^-2) + 1/2
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Over the course of a day, you checked 250 total mousetraps and determined that 50 of them were perfectly made. Approximately what percentage of the mousetraps you checked was perfectly made?
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The table shows the heights and weights of a few students in a class.
Height (inches) Weight (pounds)
58 122
59 128
60 126
62 133
63 145
64 136
66 144
68 150
70 152
Complete the following sentences based on your observations.
The data seems to have a correlation coefficient close to .
This indicates that the weight of a student as the height of the student increases.
NextReset
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The data on student heights and weights suggests a strong positive correlation, implying that as a student's height increases, their weight tends to increase as well.
Explanation:The data provided on student's heights and weights suggests a linear relationship. To complete the sentences based on the data:
The data seems to have a correlation coefficient close to positive one. This indicates that the weight of a student increases as the height of the student increases.
In statistics, when we observe that as one variable increases, the other also increases, we describe this as a positive correlation. A positive correlation coefficient closer to +1 implies a strong positive correlation, meaning that generally taller students in the given data set tend to weigh more.
Final answer:
The correlation coefficient for the given data is approximately 0.86, indicating a positive correlation between height and weight.
Explanation:
The data seems to have a correlation coefficient close to 0.86. This indicates that the weight of a student increases as the height of the student increases.
The demand equation for soccer tournament T-shirts is xy − 5,000 = y where y is the number of T-shirts the Enormous State University soccer team can sell at a price of $x per shirt. Find dy dx x = 6 . dy/dx x = 6 = T-shirts per dollar Interpret the result. When the price is set at $6, the demand is by T-shirts per $1 increase in price.
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The given equation is:
x y – 5000 = y
Rewrite this to create an explicit equation:
x y – y = 5000
y ( x – 1) = 5000
y = 5000 / (x – 1)
Derive to get dy / dx:
dy = - 5000 dx / (x – 1)^2
dy / dx = - 5000 / (x – 1)^2
So plugging in x = 6,
dy / dx = - 5000 / (6 – 1)^2
dy / dx = - 200
Answer:
[tex]\frac{dy}{dx}|_{x=6}= -200[/tex]
Step-by-step explanation:
Given : Demand equation [tex]xy − 5,000 = y[/tex]
To Find [tex]\frac{dy}{dx}|_{x=6}[/tex]
Solution :
[tex]xy- y= 5000[/tex]
[tex]y(x-1)= 5000[/tex]
[tex]y= \frac{5000}{x-1}[/tex]
Differentiating with respect to x
[tex]\frac{dy}{dx}= \frac{-5000}{(x-1)^2}[/tex]
Now substitute x = 6
[tex]\frac{dy}{dx}|_{x=6}= \frac{-5000}{(6-1)^2}[/tex]
[tex]\frac{dy}{dx}|_{x=6}= \frac{-5000}{5^2}[/tex]
[tex]\frac{dy}{dx}|_{x=6}= \frac{-5000}{25}[/tex]
[tex]\frac{dy}{dx}|_{x=6}= -200[/tex]
Hence [tex]\frac{dy}{dx}|_{x=6}= -200[/tex] =T-shirts per dollar
What is the mean of 85,89,95,71,80,85,76
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To find the mean of a set of numbers, you can add up the numbers and divide it by the amount of numbers:
85+89+95+71+80+85+76=581
581/7=83
The mean would be 83.
Hope this helps.
-Benjamin
Remember!! To find the mean, simply add up all of the numbers together, then divide it by how many numbers you added together :)
So, :
85 + 89 + 95 + 71 + 80 + 85 + 76 = ?
Simplify.
581 :)
Then, divide this by 7.
Why by 7?
Simply because that's how many numbers that you added together!
581 ÷ 7 = ?
Simplify
83
So, our mean is 83
~Hope I helped!~
After a power failure, the temperature in a freezer increased an average rate of 2.5 Fahrenheit per hour. The total increase was 7.5 Fahrenheit. Right and solve any Quetion to find the number of hours until the power was restored.
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hope this helps!
given that 2/3a=16, which of the following illustrates how the multiplicative inverse property can be used to find the value of a?
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2/3a×3/2 = 16×3/2
a= 8×3 = 24
Step-by-step explanation:
We have been given that [tex]\frac{2}{3}a=16[/tex].
Since multiplicative inverse property states that any number multiplied by its reciprocal is equal to one.
[tex]\frac{2}{3}\times \frac{3}{2} =1[/tex]
To solve for a let us divide 16 by [tex]\frac{2}{3}[/tex].
[tex]a=16\div \frac{2}{3}[/tex]
Since dividing a number by fraction is same as multiplying the number by the reciprocal of fraction. So we will multiply 16 by [tex]\frac{3}{2}[/tex].
[tex]a=16\times\frac{3}{2}[/tex]
[tex]a=8\times 3[/tex]
[tex]a=24[/tex]
We can see that to solve for a we have multiplied 16 by [tex]\frac{3}{2}[/tex] and [tex]\frac{3}{2}[/tex] is reciprocal of [tex]\frac{2}{3}[/tex].
Let us verify our answer by substituting a=24 in our given equation.
[tex]\frac{2}{3}\times 24=16[/tex]
[tex]2\times 8=16[/tex]
[tex]16=16[/tex]
Hence, to find the value of a we used multiplicative inverse property.
P(4,13);Q(13,13) find the slope
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If x = -2 and y = 2, then which of the following statements is false?
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There are 46 kids in the After-school Club. Today they're going to the pool at the Community Center. If each minivan can take 6 kids, they'll need 8 minivans for all the kids. Do you agree or disagree? Explain your thinking.
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you have to have enough buses for each person, and none of them are walking, and so you will need 8 minivans
hope this helps
can anyone help me in pre-cal
tan^2 x = tan x
sin^2 x = sin x
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The quadratic x^2-6x+66 can be written in the form (x+b)^2+c, where b and c are constants. What is b+c?
Please help me!!!!!!!!
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x^2-6x+66
=((x-3)^2-9) + 66
=(x-3)^2+57
so
b=-3, c=57
b+c=-3+57=54
The sum of b and c is equal to 54.
What is quadratic equation?
A quadratic equation is an algebraic equation of the second degree in x. The quadratic equation in its standard form is ax² + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term.
Given is the following quadratic equation -
x² - 6x + 66
x² - 6x + 9 - 9 + 66
x² - 3x - 3x + 9 - 9 + 66
x(x - 3) - 3(x - 3) - 9 + 66
(x - 3)² + 57
The given form of resultant is -
(x + b)² + c
On comparing, we get -
b = - 3
c = 57
Therefore -
b + c = -3 + 57 = 54
Therefore, the sum of b and c is equal to 54.
To solve more questions on quadratic equation, visit the link below-
https://brainly.com/question/1863222
#SPJ2
which simplified fraction is equal to 0.17...?
A. 9/17
B. 8/45
C. 17/9
D. 16/90
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8/45 = .17777 (the seven repeats)
17/9 = 1.8888 (the eight repeats)
16/90 = .17777 (the seven repeats)
While B and D both equal approximately 1.7. B is the simplified form, So B is the answer
Brainliest would be fantastic :) Have a nice day.
In order to find the simplified fraction that equals to 0.17, we need to take all the options given and start dividing them until we find the one that equals to 0.17
So, let's get started....
A) 9/17 = 0.52 So this NOT the answer
B) 8/45 = 0.17 This is the answer
C) 17/9 = 1.88
D) 16/90 = 8/45 = 0.17
Here is where the trick is. You see that B and D has the same final answer. Well, they ask for the simplified fraction. D or 16/90 was not simplified until we simplified it. But the others were already simplified. So, that's why we eliminated D.
So, the correct answer is option B
Good luck!
Samuel order four did from an online music stores. Each dvd cost 9.99$. He has a 20% discount code and sales tax is 6.75%. What is the total cost of the order
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Then you need to remember the 20% discount $39.96 - 20%= $39.96 x .20= 7.99 (if you need to show your work) Then subtract $7.99 from $39.96=$31.97
Next you have to factor in the tax. $31.97 + 6.75% = $31.97 + 2.16= $34.13 for Samuel's total order
multiply 4 by 9.99 for cost of the 4 dvd's
9.99 *4 = 39.96
20% discount is: 39.96 *0.20 = 7.99
39.96 - 7.99 = 31.97
now add the sales tax:
31.97 * 1.0675 = 34.13
total cost is $34.13
How do I solve this promblem
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Let's look at what we've been given:
[tex]\log_3{(x^{20}\cdot \sqrt[3]{y^6} )[/tex]
We can start by using the property that [tex]\log_n(a\cdot b) = \log_na+\log_nb[/tex] to separate our single logarithm into the sum of two:
[tex]\log_3x^{20}+\log_3\sqrt[3]{y^6}[/tex]
Next, let's simplify the term [tex] \sqrt[3]{y^6} [/tex] into something a little more workable. We can turn the radical [tex] \sqrt[3]{\ } [/tex] into the rational exponent 1/3, which lets us obtainin a new form for the y term:
[tex]y^{6(1/3)}=y^{6/3}=y^2[/tex]
We now have:
[tex]\log_3x^{20}+\log_3y^2[/tex]
We can now use the property that [tex]\log_na^x=x\log_na[/tex] to bring the exponents on the x and the y out front and obtain our final answer:
[tex]\log_3x^{20}+\log_3y^2=20\log_3x+2\log_3y[/tex]
Where 20 is our A and 2 is our B
What is the answer to this question?
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2A on 2A + 3B + 3C = 8 pieces
The probability:
[tex]\dfrac{2}{8}=\dfrac{2:2}{8:2}=\dfrac{1}{4}[/tex]
[tex]\dfrac{1}{4}=\dfrac{1}{4}\cdot100\%=25\%[/tex]
Answer: 25%colorado often experiences snowstorms resulting in multiple inches of snow. During the last snowstorm, the snow accumulated at 4/5 inch snow per hour. If snows continue at this rate for 10 hours how much snow will accumulate?
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multiply 4/5 by 10
4/5 * 10 = 40/5 = 8 inches total
A presidential candidate plans to begin her campaign by visiting the capitals in 44 of 4343 states. what is the probability that she selects the route of fourfour specific capitals? is it practical to list all of the different possible routes in order to select the one that is best?
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If the 4 states have to be in a specific order say ABCD, then the total number of different possible routes is:
43P4 = 2,961,840
So the probability is:
1 / 2,961,840 = 3.38 x 10^-7
But if the 4 states can be in any order such as DBAC, ACBD etc, then the total number of different possible routes is:
43C4 = 123,410
So the probability is:
1 / 123,410 = 8.1 x 10^-6
No I don’t think it is practical to list all the different possible routes to select the one that is best. We can simply use mathematical models to solve for that one.
Find the greatest common factor of 36 and 72
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Answer:
36
Step-by-step explanation:
36 is a factor of both numbers
_____
If the smaller divides the larger with no remainder, then the smaller number is the greatest common factor.
If there is a remainder, replace the larger number with that and repeat the process.