Answers
Answer:
x−2x4+2x3−7x2−8x+12=x3+4x2+x−6
The rational root theorem suggests that other possible roots may be -6, 6, -3, 3, -2, 2, -1, and 1. It turns out that x=-2x=−2 is a root, since (-2)^3+4(-2)^2+(-2)-6=0(−2)3+4(−2)2+(−2)−6=0 , so x+2x+2 is also a factor and we have
\dfrac{x^4+2x^3-7x^2-8x+12}{(x-2)(x+2)}=x^2+2x-3(x−2)(x+2)x4+2x3−7x2−8x+12=x2+2x−3
Finally, we can factorize the remaining quotient easily:
x^2+2x-3=(x+3)(x-1)x2+2x−3=(x+3)(x−1)
so the other factors are x+2x+2 , x+3x+3 , and x-1x−1 .
Related Questions
What is the equation of a line
that is perpendicular to the line
y = 2x + 1 and passes through the
point (4, 6)?
А y=-2x+6
B y = 2x + 6
c y=-3x+8
D y = 2x + 8
Answers
Answer:
[tex]y =-\frac{1}{2}x + 8[/tex]
Step-by-step explanation:
Given
Perpendicular to [tex]y = 2x + 1[/tex]
Pass through [tex](4,6)[/tex]
Required
Determine the line equation
First, we need to determine the slope of [tex]y = 2x + 1[/tex]
An equation is of the form:
[tex]y = mx + b[/tex]
Where
[tex]m = slope[/tex]
In this case:
[tex]m =2[/tex]
Next, we determine the slope of the second line.
Since both lines are perpendicular, the second line has a slope of:
[tex]m_1 = \frac{-1}{m}[/tex]
[tex]m_1 = \frac{-1}{2}[/tex]
[tex]m_1 = -\frac{1}{2}[/tex]
Since this line passes through (4,6); The equation is calculated as thus:
[tex]y - y_1 = m_1(x - x_1)[/tex]
Where
[tex](x_1,y_1) = (4,6)[/tex]
This gives:
[tex]y - 6=-\frac{1}{2}(x - 4)[/tex]
Open bracket
[tex]y - 6=-\frac{1}{2}x + 2[/tex]
Add 6 to both sides
[tex]y +6- 6=-\frac{1}{2}x + 2+6[/tex]
[tex]y =-\frac{1}{2}x + 8[/tex]
Polly buys 14 cupcakes for the party. the bakery puts them into boxes that hold 4 cupcakes each.
how many boxes will be needed for Polly to bring all the cupcakes to the party? Explain
Answers
Answer:
11 boxes
Step-by-step explanation:
14 didived by 4 is 10.25 so if you round you should get 11 .
Answer:
4, If you round.
Step-by-step explanation:
If you divide the 14 by 4, you get 3.5 and you can't really break the box in half.
So, you would have to use 5.
If the radius is 21 cm and the angle at
center of circle is 140° then the length of
the arc is ?
Answers
Step-by-step explanation:
Given: Radius , r =21 cm
The angle at the center of the circle, n° =140°
Length of an arc =?
W.K.T Formula, Length of an arc = 2πr( n°÷360°) units
= 2*(22/7)*21*(140°/360°)
= 154/3
= 51.33cm
Answer:
2*(22/7)*21*(140°/360°)
= 154/3
= 51.33cm
Step-by-step explanation:
A bank deposit paying simple interest at the rate of 8%/year grew to a sum of $1300 in 6 months. Find the principal. (Round your answer to the nearest cent.)
Answers
Answer:
$1,250
Step-by-step explanation:
The rate is 8%
= 8/100
= 0.08
Time is 6 months
= 1/2 year
Therefore the principal can be calculated as follows
Principal × (1+0.08(1/2) = 1300
Principal × 1+ 0.04 = 1300
Principal × 1.04= 1300
Principal= 1300/1.04
Principal = $1,250
Hence the principal is $1,250
59:41 To build the roof for a paper house, a rectangular paper is cut to form a trapezoid. Which diagram shows the correct cuts? Save and Exit Mark this and return Nes Submn K
Answers
Answer:
Step-by-step explanation:
wheres the diagram?
Answer:B
Step-by-step explanation:
Plz help !!!!!! I don’t understand
Answers
1) The probability that an individual is left-handed is 12%. In a randomly selected class of 30 students, what is the probability of finding exactly 4 left-handed students?
2) Sixty-five percent of men consider themselves knowledgeable football fans. If 10 men are randomly selected, find the probability that exactly six of them will consider themselves knowledgeable fans.
Answers
Answer:
0.2047
0.2377
Step-by-step explanation:
1.
What we have here is a binomial distribution
Probability p = 0.12
N = number of students in the class = 30
Probability of finding 4 left handers
P(x = 4) = 30C4 x (0.12)⁴ x (0.88)²⁶
= 27405 x 0.00020736 x 0.03602047835
= 0.2047
2.
This is also a binomial distribution
N = 10 p = 0.65
P(of 6 knowledgeable fans)
= 10C6 x (0.65)⁶ x (0.35)⁴
= 210 x 0.0754189 x 0.01500625
= 0.2377
At a sports event, Luke scored 8.65 points. Mel scored 9.2 points. How many more points did Mel score than Luke? * PLZ HELP
Answers
Answer:
0.55
Step-by-step explanation:
9.2-8.64=0.55
i hope it helps
Abel Alonzo, Director of Human Resources, is exploring employee absenteeism at the Harrison Haulers Plant. Abel knows that absenteeism varies significantly between departments. For example, workers in the wood shop are absent more than those in the tuning department and the size of the departments ranges from 40 to 120 workers. He orders a random sample of 10 workers from each of the six departments. Abel's sample is a
Answers
Answer:
disproportionate stratified sample
Step-by-step explanation:
Based on the given information we can say that Abel's sample is a disproportionate stratified sample. This is the case mainly because the department worker population ranges from 40 to 120 workers. This changing population makes the 10 workers that were chosen for the sample not proportionate to the entire population. Therefore, under different population sizes workers have different chances of getting selected for the study which ultimately creates different results.
Juan pago $50.00 pesos por 3 cajas de paquetes y 5 cajas de clavos, mientras que Pedro compró 5 cajas de taquetes y 7 cajas de clavos y tuvo que pagar $ 74.00 pesos . ¿ Cual es el precio de cada caja de taquetes y clavos ?
a) ¿ Cuantas incógnitas hay en el problema ?
b) ¿ Cuántas ecuaciones puedes construir según el texto?
c) ¿ Cuales son esas ecuaciones?
Answers
B ) dos
C ) 50 dividida 8, 74 dividida 12
espero que esto haya ayudado!
te agradecería que me dieras un gracias y brainliest (:
As a manager, Mike uses linear programming (LP) to formulate a problem into a series of mathematical expressions. __________ refers to the choices or alternatives Mike selects to minimize or maximize the value of his goals.
a. Objective function
b. Decision variables
c. Optimization
d. Feasible region
Answers
Answer:
b. Decision variables
Step-by-step explanation:
The decision variable is the variable that decides that what would be the output. It presents the final solution.
Since in the given situation it is mentioned that the Mike uses linear programming for formulating a problem now the choices that chose for minimize or maximize the value would be the decision variables
Hence, the correct option is b.
Objective function is a function used in linear programming (LP) so as to maximize or minimize.
Linear programming are system of linear constraints used to optimize or solve a problem. The problem is being solved by selecting the variables that would be used to maximize or minimize the objective function from a list of several objective functions.
Find out more at: https://brainly.com/question/14161814
Which of the following statements is true about the graphs of a linear function (x) = mx + b and that of an exponential function g(x) = a*, where a > 0 and a = 1?
Answers
Answer:
the answer a is the correct answer
PLEASE I NEED HELP WITH MATH
Answers
Answer:
117
Step-by-step explanation:
Hi, If you were to add 75 to 42, you would get 117. Since a triangle's angles all have to add up to 180, the last angle would be 63. However, you are looking for the outside angle, which would then just be 117. Hope this is right!
The surface area of a three-dimensional object is the sum of the area of the faces. If represents the length of the side of a cube, write a formula for the surface area S of the cube.
Answers
Answer:
S = 6e²
I don't know what variable you're using here.
Step-by-step explanation:
There are 6 faces on a cube and they are all the same. Because of this, 6 is the coefficient in this equation.
A square's area can be found by squaring the side length (Which I'll represent with e). So e² is the variable.
Thus, the equation is S = 6e²
42 - 41 – 6 = 30
a
X = 13
X = 13, X=-5
x = 5, x = -13
Answers
Answer:
x=5
Step-by-step explanation:
the temperature at 4 p.m. was -2 °c an hour later the temperature had decreased 3°c what was the temperature at 5:00 pm ?
Answers
Answer:
Step-by-step explanation:
3 degrees Celsius
It says at 4 p.m. was -2 degrees C. Then an hour later which would be 5 pm the temperature was 3 degrees C.
Debra needs to make a total of 40 deliveries this week. So far she has completed 6 of them. What percentage of her total
deliveries has Debra completed?
Answers
A book publisher found that the cost to produce 1000 calculus textbooks is $26,300, while the cost to produce 2000 calculus textbooks is $52,900. Assume that the cost C(x) is a linear function of x, the number of textbooks produced. What is the marginal cost of a calculus textbook?
Answers
Answer:
$26.60
Step-by-step explanation:
Calculation for the marginal cost of a calculus textbook
Marginal cost =($52,900-$26,300)/(2,000-1,000)
Marginal cost=$26,600/1,000
Marginal cost=$26.60
Or
First step
$52,900=2,000x +c equation (1)
$26,300= 1,000x+c equations (2)
Second step is to subtract equation (1) from equation (2)
$52,900=2,000x +c equation (1)
-$26,300= 1000x+c equations (2)
$26,600=1,000x
Third step is to find the marginal cost
$26,600=1,000x
x=26,600/1,000
x=$26.60
Therefore the marginal cost of a calculus textbook will be $26.60
LeShawn is arranging a display of shirts at a department store. He wants to dress two mannequins in different colored shirts
Answers
Answer:
ok so he needs to buy two different collored shirts
Step-by-step explanation:
What is the estimated sum of 2/5 + 13/20 ?
Answers
Answer:
1.05 as a fraction 21/20
Answer:
Step-by-step explanation:
the answer is 1
Please help me answer this:)
I will give you braisnlt
Answers
Answer:
B, E, F
Step-by-step explanation:
they are linear because there are no fractions or exponents
Answer:
B, E, F
Step-by-step explanation:
For a linear function, you can have x multiplied by a number, but you cannot have x multiplied by a variable. Also you can't have x in denominator or an exponent on x other than 1.
For a linear equation, y must equal a first degree polynomial or a constant.
Answer: B, E, F
3,3 x,y 6,9 what is x,y 
Answers
answer:
answer:
answer:
15 points theres an image to help you guys out too i need it ASAP though.. please
Answers
Answer:
16
Step-by-step explanation:
8-1+9
7+9=16
the answer is=16
Answer:
16
Step-by-step explanation:
(8-1) = 7 + 9
= 16
D ......
Ben is solving a problem and his final units need to be in square centimeters. His
current answer is 12 meters?. What is the equivalent measurement in square
centimeters?
Answers
Answer:
Step-by-step explanation:
1 metre = 100cm
12m = 12 x 100 = 1200cm
CE
Debra paid $12.16 for a 4.07-pound bag of shrimp at one store. The following week, she paid $14.99 for a 5.11 -pound bag at another store.
Find the unit price for each bag. Then state which bag is the better buy based on the unit price.
Bound your answers to the nearest cent.
Answers
Answer:
the better buy is that from the second store as it is cheaper than that purchased from the first store
Step-by-step explanation:
Given that :
First store :
Amount paid = $12.16
Pounds of shrimps = 4.07
Unit price :
Amount paid / pounds of shrimps
$12.16 / 4.07 = $2.9877
= $2.99 = 299 cents
second store :
Amount paid = $14.99
Pounds of shrimps = 5.11
Unit price :
Amount paid / pounds of shrimps
$14.99 / 5.11 = $2.933
= 2.93 = 293 cents
Hence, the better buy is that from the second store as it is cheaper than that purchased from the first store
Jared has $12.82 in his wallet, and $46.99 in his bank account.
Answers
Answer:
59.81 in all
Step-by-step explanation:
A chain letter starts when a person sends a letter to five others. Each person who receives the letter either sends it to five other people who have never received it or does not send it to anyone. Suppose that 10,000 people send out the letter before the chain ends and that no one receives more than one letter. How many people receive the letter, and how many do not send it out?
Answers
Answer:
50,001 people sent out the letter.
40,001 did not send it out
also can i get brainliest???
Step-by-step explanation:
780 people receive the letter before the chain ends.
9,220 people do not send out the letter.
We have,
In the given scenario, the chain letter starts with one person sending it to five others.
Each recipient of the letter has the option to either send it to five new recipients or not send it to anyone.
Let's analyze the chain letter progression:
The first person sends the letter to 5 recipients.
Each of those 5 recipients has the choice to send the letter to 5 new recipients or not send it.
If each of the 5 recipients sends the letter to 5 new recipients, we have a total of 5 x 5 = 25 new recipients.\
If any of the 5 recipients choose not to send the letter, they are out of the chain.
Now, we have 25 recipients who received the letter and have the same choice: send it to 5 new recipients or not send it.
If each of the 25 recipients sends the letter to 5 new recipients, we have a total of 25 * 5 = 125 new recipients.
If any of the 25 recipients choose not to send the letter, they are out of the chain.
This process continues until the chain ends.
To determine how many people receive the letter and how many do not send it out, we can observe the pattern:
After the first step, there are 5 recipients.
After the second step, there are 5 + (5 * 5) = 30 recipients.
After the third step, there are 5 + (5 * 5) + (5 * 5 * 5) = 155 recipients.
After the fourth step, there are 5 + (5 * 5) + (5 * 5 * 5) + (5 * 5 * 5 * 5) = 780 recipients.
We can see that the number of recipients follows a geometric progression with a common ratio of 5.
The formula for the sum of a geometric progression is:
[tex]Sum = a (r^n - 1) / (r - 1)[/tex]
Where:
a = initial term = 5
r = common ratio = 5
n = number of steps
We are given that the chain ends after 10,000 people send out the letter. Let's calculate the number of recipients:
[tex]Sum = 5 (5^4 - 1) / (5 - 1)[/tex]
= 5 (625 - 1) / 4
= 5 624 / 4
= 780
Therefore, 780 people receive the letter before the chain ends.
To find the number of people who do not send it out, we subtract the number of recipients from the total number of people who sent out the letter:
Number of people who do not send it out = Total number of people - Number of recipients
= 10,000 - 780
= 9,220
Therefore, 9,220 people do not send out the letter.
Thus,
780 people receive the letter before the chain ends.
9,220 people do not send out the letter.
Learn more about geometric sequence here:
https://brainly.com/question/2321576
#SPJ2
3f+2.9=4.4
Please help.
Answers
Answer:
f =0.5
Isolate the variable by dividing each side by factors that don't contain the variable.
______________________________
1.) Subtract 2.9 from both sides:[tex]2.9-2.9=[/tex] Cancels Out. [tex]4.4-2.9=1.5[/tex].- We subtract 2.9 from both sides because we need to get rid of any extra numbers on the opposite side of the equal sign. To do so, you do the opposite of what you see: We have a positive 2.9, so we subtract.
Equation at the end of Step 1:
[tex]3f=1.5[/tex].2.) Divide both sides by 3.[tex]3f[/tex] ÷ [tex]3=f[/tex].[tex]1.5[/tex] ÷ [tex]3=0.5[/tex].- We divide 3 from both sides because the 3 is attached to the variable and we need to get the variable alone. So to do so we have to divide by 3 on each side.
3.) Turn the decimal into a fraction: [tex]0.5=\frac{1}{2}[/tex].- 0.5 is equal to [tex]\frac{1}{2}[/tex] as a fraction.
______________________________
Select two ratios that are equivalent to 2:9
Choose 2 correct answers 40 points
Answers
Answer:
4:18 6:27 8:36
Step-by-step explanation:
The null hypothesis for an ANOVA is that all treatments/samples come from populations with the same mean. The alternative hypothesis is best stated as:____________
Answers
Answer:
At least one of the population means is different from the others.
Step-by-step explanation:
ANOVA is a short term or an acronym for analysis of variance which was developed by the notable statistician Ronald Fisher. The analysis of variance (ANOVA) is typically a collection of statistical models with their respective estimation procedures used for the analysis of the difference between the group of means found in a sample. Simply stated, ANOVA helps to ensure we have a balanced data by splitting the observed variability of a data set into random and systematic factors.
In Statistics, the random factors doesn't have any significant impact on the data set but the systematic factors does have an influence.
Basically, the analysis of variance (ANOVA) procedure is typically used as a statistical tool to determine whether or not the mean of two or more populations are equal through the use of null hypothesis or a F-test.
Hence, the null hypothesis for an ANOVA is that all treatments or samples come from populations with the same mean. The alternative hypothesis is best stated as at least one of the population means is different from the others.