Polynomial function R is the difference of two degree-2 polynomial functions P and Q. What are the possible degrees of R? Explain.
Answers
Answer:
D. The possible degrees are 0, 1, and 2 because it cannot be higher than the degree of either P or Q but it can be less depending on which terms cancel.
Step-by-step explanation:
The possible degrees are 0, 1, and 2. Let's explain why by assuming the following is given:
P = 6x² - 3x - 2
Q = 3x² + 2x - 6
Let R = P - Q
Thus:
(6x² - 3x - 2) - (3x² + 2x - 6)
Open parentheses by distributing the factor of -1
6x² - 3x - 2 - 3x² - 2x + 6
Add like terms together
6x² - 3x² - 3x - 2x - 2 + 6
R = 3x² - 5x + 4
The leading term of R has a degree of 2. Therefore, the difference of two degree-2 polynomial functions P and Q can give us a a polynomial function of R with a degree of 2.
Also, let us assume the following:
P = 4x² + 4x - 3
Q = 4x² + x - 8
Let R = P - Q
R = (4x² + 4x - 3) - (4x² + x - 8)
R = 4x² + 4x - 3 - 4x² - x + 8
Collect like terms
R = 4x² - 4x² + 4x - x - 3 + 8
R = 4x + 5 (4x² cancels 4x²)
The leading term of R has a degree of 1. Therefore, the difference of two degree-2 polynomial functions P and Q can give us a a polynomial function of R with a degree of 1.
Also, let us assume the following:
P = x² + 2x - 3
Q = x² + 2x - 8
Let R = P - Q
R = (x² + 2x - 3) - (x² + 2x - 8)
R = x² + 2x - 3 - x² - 2x + 8
Collect like terms
R = x² - x² + 2x - 2x - 3 + 8
R = 5 (x² cancels x², and 2x cancels 2x)
The polynomial R has a degree of 0. Therefore, the difference of two degree-2 polynomial functions P and Q can give us a a polynomial function of R with a degree of 0.
Therefore we can conclude that:
D. The possible degrees are 0, 1, and 2 because it cannot be higher than the degree of either P or Q but it can be less depending on which terms cancel.
Related Questions
The sum of three consecutive integers is 48. What are the three numbers?
Answers
What three consecutive integers have a sum of 48? Which means that the first number is 15, the second number is 15 + 1 and the third number is 15 + 2. Therefore, three consecutive integers that add up to 48 are 15, 16, and 17.
Complete the following equation;
Y=k?
Answers
15 POINTS!
An abandoned lot is to be converted into a community garden. The garden is to consist
of a 7 yard by 20 yard rectangle for planting that is surrounded by a path of uniform
width. The total area of the lot is 198 square yards. What is the width of the path?
SHOW WORK PLS TY
Answers
If g is the midpoint of AB, classify each triangle by its angles and sides
Answers
Each triangle can be classified by its angles and sides in the following ways :
triangle CFE = triangle CFE is a right angle triangle ( as one of its interior angle measures 90° ) . Triangle CFE is also a scalene triangle ( as none of its sides are equal ) .triangle BEC = Triangle BEC is a right angle triangle . It is also a scalene triangle ( as none of its sides or angle are equal ) .triangle BFG = triangle BFG is an equilateral triangle ( all of its sides are equal ) and it is also an acute angle triangle ( all of its angle will be equal to 60° , which is acute ) .triangle GAF = Triangle GAF is an isosceles triangle ( two of its sides - GF and GA are equal ) . It is also an obtuse angled triangle ( one of its angle measures 120° ) .3x+2=11 what is the answer
Answers
x = 3
Step-by-step explanation:Hi there !
3x + 2 = 11
3x = 11 - 2
3x = 9
x = 9/3
x = 3
Good luck !
Plz help ty very much
Answers
Answer:
A fungus breaks down the body of a dead animal or organism.
btw you cant be in college I did this years ago in fourth grade
A fungus breaks down the of a dead animal
g The average lifespan for a certain type of vehicle is 8 years and follows an exponential distribution. A lot contains 200 of these vehicles, brand new. What is the probability that 50 or more of them fail in the first 2 years
Answers
Answer:
The probability is [tex]P(A \ge 50 ) = 0.14321[/tex]
Step-by-step explanation:
The average life span is [tex]\pi = 8[/tex]
The sample size is n = 200
Generally we are told that average lifespan for a certain type of vehicle follows an exponential distribution
i.e
[tex]X \~ \ \ \ exp(8)[/tex]
Gnerally the probability distribution function for exponential distribution is
[tex]f(x) = \left \{ {{\lambda * e^{-\lambda * x }\ \ \ x\ge 0 } \atop {0 \ \ \ \ \ \ \ \ \ \ x < 0}} \right.[/tex]
Now [tex]\lambda[/tex] is the constant which is evaluated as
[tex]\lambda = \frac{1}{\pi}[/tex]
=> [tex]\lambda = \frac{1}{8}[/tex]
=> [tex]\lambda = 0.125[/tex]
Generally the that the vehicles will fail in less than 2 years is mathematically represented as
[tex]P(X \le 2 )= p= \int\limits^2_0 {\lambda e^{- \lambda * x} } \, dx[/tex]
[tex]P(X \le 2 )= p= [ {0.125 * - \frac{1}{0.125 } e^{- 0.125 * x} } ]|\left 2 } \atop {0}} \right.[/tex]
[tex]P(X \le 2 )= p= [ {0.125 * - \frac{1}{0.125 } e^{- 0.125 * 2} } ] - [ {0.125 * - \frac{1}{0.125 } e^{- 0.125 * 0} } ][/tex]
[tex]P(X \le 2 )= p= -0.77880 + 1[/tex]
[tex]P(X \le 2 )= p= 0.2212[/tex]
Generally the probability that the vehicle will fail in the first 2 years follows a binomial distribution with the mean evaluated as
[tex]\mu = n * p[/tex]
=> [tex]\mu = 200 * 0.2212[/tex]
=> [tex]\mu = 44.24[/tex]
The standard deviation is
[tex]\sigma = \sqrt{np(1 - p)}[/tex]
[tex]\sigma = \sqrt{200 * 0.2212 (1 - 0.2212)}[/tex]
[tex]\sigma = 5.86[/tex]
Using normal approximation of binomial distribution the probability that 50 or more of them fail in the first 2 years is mathematically represented as
[tex]P(A \ge 50 ) = 1 - P(A < 50 )[/tex]
Applying continuity correction
[tex]P(A \ge 50.5 ) = 1 - P(A < 50.5 )[/tex]
Here
[tex]P(A < 50.5 ) = P(\frac{A - \mu }{\sigma} < \frac{50 - 44.24}{5.87} )[/tex]
Generally
[tex]\frac{A - \mu }{\sigma} = Z (The \ standardized \ value \ of A )[/tex]
=> [tex]P(A < 50.5 ) = P( Z < 1.0664 )[/tex]
From the z-table the probability value of ( Z < 1.0664 ) is
[tex]P( Z < 1.0664 ) = 0.85679[/tex]
So
[tex]P(A \ge 50 ) = 1 - 0.85679[/tex]
=> [tex]P(A \ge 50 ) = 0.14321[/tex]
Solve the inequality 3x + 4 < 22
Answers
Answer:
3х<18
х<6
хє(-infinity ;6);
Answer:
x<6
Step-by-step explanation:
3x+4<22
First, subtract 4 from both sides of the inequality.
3x-4<22-4
This cancels out the 4, so the 3x is isolated
3x/3<18/3
Finally, simplify to get the answer.
x<6
please mark as brainliest!!
volume of 29 mL and has a mass of 53 g what’s is the density
Answers
Answer: 1.82
Step-by-step explanation:
Density = [tex]\frac{mass}{volume}[/tex] *Divide the mass by volume.
= 1.82
Maggie bought a pound of bananas and 4 boxes of cereal for $10.11. If each box of cereal cost $2.40, what was the price of a pound of bananas?
$0.51
$0.61
$1.51
$2.91
Answers
Answer:
$0.51
Step-by-step explanation:
If each box of cereal is $2.40, $2.40 multiplied by 4 is $9.60. $10.11 is the total, so $10.11 - $9.60 = $0.51.
Answer:
$0.51
Step-by-step explanation:
the person above me was correct
Triangle EFG is graphed below. If the triangle is translated 4 units to the right and 3 units down, what will be the coordinates of G’ ? A. (3,-2) B. (3,4) C. (2, -3) D. (2,2)
Answers
Answer:
A) (3,-2)
Step-by-step explanation:
A) (3,-2)
A=4 b= -5 and c=-8
HELLPPPPPP
Answers
Hope this helps
since b = -5, that cancels out the negative and makes b=5.
5+-8 is -3.
2x+ 8y = -3
3x+ 6y = -4
Choose all answers that apply
Answers
multiply the top equation by 3, multiply the bottom equation by 4, then subtract the bottom equation from the top equation
multiply the top equation by 3, multiply the bottom equation by -2, then add the equations
The American Society of PeriAnesthesia Nurses (ASPAN; www.aspan.org) is a national organization serving nurses practicing in ambulatory surgery, preanesthesia, and postanesthesia care. The organization's membership is listed below.
State/Region Membership
Alabama 114
Arizona 261
Maryland, Delaware, DC 319
Connecticut 183
Florida 654
Georgia 313
Hawaii 58
Maine 98
Minnesota, Dakotas 335
Missouri, Kansas 324
Mississippi 52
Nebraska 125
North Carolina 342
Nevada 66
New Jersey, Bermuda 321
Alaska, Idaho, Montana, Oregon, Washington 893
New York 690
Ohio 798
Oklahoma 201
Arkansas 74
Illinois 632
Indiana 216
Iowa 76
Kentucky 155
Louisiana 161
Michigan 304
Massachusetts 530
California 1,110
New Mexico 93
Pennsylvania 631
Rhode Island 75
Colorado 344
South Carolina 264
Texas 1,120
Tennessee 122
Utah 45
Virginia 304
Vermont, New Hampshire 192
Wisconsin 316 West Virginia 63
Use statistical software to answer the following questions.
a. Find the mean, median, and standard deviation of the number of members per component. (Round your answers to 1 decimal places.)
Mean?
Median?
Standard deviation?
b-1. Find the coefficient of skewness, using the software method? (Round your answer to 2 decimal places.)
Coefficient of skewness?
b-2. What do you conclude about the shape of the distribution of component size?
Mild positive skewness or Mild negative skewness
(d-1) Are there any outliers?
One, Zero, Three, Four, Two
(d-2) What are the limits for outliers? (Round your answers to 1 decimal place. Negative amounts should be indicated by a minus sign.)
Answers
Answer:
Kindly check explanation
Step-by-step explanation:
Given the data :
114, 261, 319, 183,654,313,58,98,335,324,52,125,342,66,321,893,690,798,201,74,632,216,76,155,161,304,530,1110,93,631,75,344,264,1120,122,45,304,192,316,63
USING CALCULATOR :
The mean(m) of the data: = ΣX/n
n = sample size = 40
m = 12974/40
m = 324.4
Median = ((n + 1)/2) th term = 41/2 = (20 + 21)th term / 2
= (261 + 264) / 2 = 262.5
Standard deviation (s) = sqrt(Σ(x - m)²/n))
s = 281. 74
B.) Coefficient of skewness (Ks) :
3(mean - median) / standard deviation
3(324.4 - 262.5) / 281.74
= 0.66
Mild positive skewness Given a positive skew Coefficient value.
(d-1) Are there any outliers?
Yes
Four outliers
(d-2) What are the limits for outliers? (Round your answers to 1 decimal place. Negative amounts should be indicated by a minus sign.)
Lower bound = Q1 - (1.5 * IQR)
Upper bound = Q3 + (1.5 * IQR)
IQR = Q3 - Q1
Q3 = upper quartile = 343 ; Q1 = 106 ; Q2 = 262.5
IQR = 343 - 106 = 237
Lower bound = 106 - (1.5 * 237) = - 249.5
Upper bound = 343 + (1.5 * 237) = 698.5
-249.5 ≤ X ≤ 698.5
Need help ASAP please! Simplify these.
Answers
Answer:
x³/2
8x³/7
5x²/3
3/4x³
What is the equation of the line in slope-intercept form? the line perpendicular to y = x + 2 through (-7, -8)
Answers
Answer:
[tex]y=-x-15[/tex]
Step-by-step explanation:
Point-slope formula: [tex]y-y_1=m(x-x_1)[/tex], where [tex](x_1, \ y_1)[/tex] are the coordinates of a point on the line, and [tex]m[/tex] is the slope of the line.
You are given a point that the line you are trying to find passes through, and a slope. The slope is less obvious than the point, but you can find the slope using the given information.
The line perpendicular to y = x + 2 will have the opposite reciprocal slope of this line. The slope of y = x + 2 is 1, so the opposite reciprocal of 1 is:
[tex]m=-\frac{1}{1} =-1[/tex]Now that you have both a point and the slope of the line you are trying to find, you can substitute these values into the point-slope formula (Notice: the name of this formula contains both "point" and "slope").
Substitute [tex](-7, \ -8)[/tex] for [tex](x_1,\ y_1)[/tex] and [tex]m=-1[/tex] into the point-slope formula.
[tex]y-(-8)=-1(x-(-7))[/tex]Simplify this equation.
[tex]y+8=-1(x+7)[/tex]Distribute -1 inside the parentheses.
[tex]y+8=-x-7[/tex]Subtract 8 from both sides of the equation.
[tex]y=-x-15[/tex]This line is in slope-intercept form ([tex]y=mx+b[/tex]), so we are done.
The graph shows the linear relationship between the balance in a student school lunch account and the number of lunches purchased
Answers
Answer:
Step-by-step explanation:
Simplify -√36 please
Answers
Answer:
-6
Step-by-step explanation:
djhcjici4n c rncinr
for the question the answer will be -6
ve spent the whole weekend grading math assignments. I graded 30 students
work this weekend, which is 40% of my class. How many students do I have in
my class?
Answers
Answer:
75
Step-by-step explanation:
How many students is 1% of the class, 30/40=0.75, so you could do 0.75x100=75, or you could do 0.75x60=45, and 45+30=75.
CAN SOMEONE PLEASE DOUBLE CHECK IF THIS IS RIGHT!!! Please
Answers
Answer:
yes yesss yessssssssssssssssssssssssssssssssssss
HELP ILL GIVE BRAINLIEST HELPPPP
Answers
Db = 6
Ac = 9
IJKL-
Db = 2
Ac = 3
I hope this helps
-45 x (-2) solve please
Answers
Answer:
-90x Mark Me Brainlest Please
Step-by-step explanation:
A bucket is leaking. After 3 hours the bucket has leaked 6 gallons. How many gallons per hour is the bucket leaking?
Answers
Answer:
2 gallons
Step-by-step explanation:
divide 6 by 3 because that's the amount
Answer:
2 gallons
Step-by-step explanation:
If f(x) = 8x+9 and g(x) = 4x-3, what is (f+g)(x)?
O A 4x-12
B. 4x+12
0
C 12x+6
D. 32x-27
Answers
Steve said that [5, 12) is the interval notation that represents the set of all real numbers greater than or equal to 5 and less than 12. Joe says that (5, 12] is correct interval notation. Who is correct and justify why? HEPLLLL!!!!!
Answers
Answer:
Steve
Step-by-step explanation:
Because it means greater than or equal to
What is the average speed of a baseball that is thrown 90 feet in 2 seconds?
A. 180 feet/second
B. 45 feet/second
C. 92 feet/second
D. A variable most often found on the y-axis
Answers
To find out how fast it can go in 1 second, we divide it by 2
90 divided by 2 is 45, so the average speed of a baseball that is thrown 90 feet in 2 seconds is 45 feet/second
Round 47.58051 to the nearest thousandths
Answers
Answer:
47.581
Step-by-step explanation:
can't explain I just know how to do it
Can anyone help me solve for x and y
Answers
x = 24, y = 120
if you disagree tell me, I just substituted values.
Step-by-step explanation:
10. (6x - 7)° + (3x - 29)° = 180°
i.e they are co-interior angles:
6x + 3x - 7 - 29 = 180°
9x - 36° = 180°
9x = 216°
x = 24.
(6x - 7)° = (8y + 17)°
i.e they are vertically opposite angles;
but x = 24.
6(24) - 7 = 8y + 17
144 - 7 = 8y + 17
120 = 8y
y = 15
11. (9x + 25)° = (13x - 19)°
i.e they are corresponding angles;
25 + 19 = 13x - 9x
44 = 4x
x = 11
(13x - 19)° + (17y + 5)° = 180°
i.e they are adjacent angles;
but x = 11
13(11) - 19 +5 + 17y = 180
17y = 180 - 129
17y = 51
y = 3
Determine which sides of the given quadrilateral are parallel. Q (0, 4), R (4, 0), S (0, −4), T (−4, 0)
Answers
Answer:
The answer is QR and TS are parallel. QT and RS are parallel
Step-by-step explanation:
You can find the slope of each line using the formula y2-y1/x2-x1 and to help organize your ideas or understand better, you can graph the points in a cardinal plane.
1/2 mi = 880 yd
O True
O False
Help
Answers
Answer:
True
Step-by-step explanation:
1,760 yds = 1 mile, 1,760 ÷ 2 = 880