Polynomial function R is the difference of two degree-2 polynomial functions P and Q. What are the possible degrees of R? Explain.
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.
What is the probabiWhich value cannot represent the probability of an event occurring?
StartFraction 1 over 100 EndFraction
0.29
85%
Three-halflity of an event that is certain?
Given problem:
Which value cannot represent the probability of an event occurring?
Values:
[tex]\frac{1}{100}[/tex] 0.29 [tex]\frac{85}{100}[/tex] Three-halflity
Probability is the likelihood of an event to occur.
For an event that we are sure of occurring, the probability value is 1, and those that cannot occur have a probability value of 0.
The probability of any event is usually a fraction between 1 and 0.
So we can see that the odd one is the Three-halflity which is clearly greater than 1.
Answer:
D 3/2
Step-by-step explanation:
Pls answer quick, I’ll give brainliest!
Answer:
not sure if I understand the question but a=3,b=0,c=1
Step-by-step explanation:
-2+2(1)-3(-1)=3
-2+1-(-1)=0
2(-2)+2(1)-3(-1)=1
I need help please
Answer:
n=1/3
Step-by-step explanation:
Answer:
There’s no error
Step-by-step explanation:
A line passes through -1,-1and .-3,5
What is the equation of the line in slope-intercept form?
Answer:
y=-3x - 4
Step-by-step explanation:
y2 -y1 = 5- -1 =-4
x2 -x1=-3 - -1=-2
slope is -3
the cell phone cost 271 monthly the water gas and electric cost 1270 what is the yearly total for the water gas and electricity
Answer:
Cell phone monthly 271 X 12 = 2,052
water and gas yearly 1270 + 2,052 =3,320
3,320 is you're answer.
Step-by-step explanation:
A resident of Bayport claims to the City Council that the proportion of Westside residents
(1) with income below the poverty level is lower than the proportion of Eastside residents
(2) The City Council decides to test this claim by collecting a random sample of resident incomes from the Westside of town and a random sample of resident incomes from the Eastside of town. Seventy-six out of 578 Westside residents had an income below the poverty level. Hundred-and-twelve out of 688 Eastside residents had an income below the poverty Specify the hypotheses.
Calculate the value of the test statistic (round to 4 decimal places).
Calculate the p-value (round to 4 decimal places).
Answer:
The test statistics is [tex]z = -1.56 [/tex]
The p-value is [tex]p-value = 0.05938 [/tex]
Step-by-step explanation:
From the question we are told
The West side sample size is [tex]n_1 = 578[/tex]
The number of residents on the West side with income below poverty level is [tex]k = 76[/tex]
The East side sample size [tex]n_2=688[/tex]
The number of residents on the East side with income below poverty level is [tex]u = 112[/tex]
The null hypothesis is [tex]H_o : p_1 = p_2[/tex]
The alternative hypothesis is [tex]H_a : p_1 < p_2[/tex]
Generally the sample proportion of West side is
[tex]\^{p} _1 = \frac{k}{n_1}[/tex]
=> [tex]\^{p} _1 = \frac{76}{578}[/tex]
=> [tex]\^{p} _1 = 0.1315 [/tex]
Generally the sample proportion of West side is
[tex]\^{p} _2 = \frac{u}{n_2}[/tex]
=> [tex]\^{p} _2 = \frac{112}{688}[/tex]
=> [tex]\^{p} _2 = 0.1628 [/tex]
Generally the pooled sample proportion is mathematically represented as
[tex]p = \frac{k + u}{ n_1 + n_2 }[/tex]
=> [tex]p = \frac{76 + 112}{ 578 + 688 }[/tex]
=> [tex]p =0.1485[/tex]
Generally the test statistics is mathematically represented as
[tex]z = \frac{\^ {p}_1 - \^{p}_2}{\sqrt{p(1- p) [\frac{1}{n_1 } + \frac{1}{n_2} ]} }[/tex]
=> [tex]z = \frac{ 0.1315 - 0.1628 }{\sqrt{0.1485(1-0.1485) [\frac{1}{578} + \frac{1}{688} ]} }[/tex]
=> [tex]z = -1.56 [/tex]
Generally the p-value is mathematically represented as
[tex]p-value = P(z < -1.56 )[/tex]
From z-table
[tex]P(z < -1.56 ) = 0.05938[/tex]
So
[tex]p-value = 0.05938 [/tex]
8 less than the product of 7 and -10.
The expression is
The value of the expression is 1
Answer:
um i dunna
Step-by-step explanation:
uuuuhhghhhh
What is the product?
Y+5<3 inequality solution
Answer:
y=2
Step-by-step explanation:
y + 5 < 3
- 5 -5
y = 2
.................................
On three consecutive passes, a football team gains yards,9 loses 18 yards, and gains 41 yards. What number represents the total net yardage?
Answer:
Gain:
32 yards
Step-by-step explanation:
+ 9 - 18 + 41
= 41 + 9 - 18
= 50 - 18
= 32
Multiply. Simplify your answer and write as a mixed or whole number.
6 1/3 ⋅ 2
Question is in the picture below please help
Answer:
3
Step-by-step explanation:
3(8)(4)/8(4) = 3
Answer:
3
Step-by-step explanation:
Order of Operations: BPEMDAS
Step 1: Define
a = 8
b = 4
(3ab)/(8b)
Step 2: Substitute and Evaluate
(3 · 8 · 4)/(8 · 4)
(24 · 4)/32
96/32
3
How many combinations are possible if you select one flavor of ice cream and one
topping?
Flavors Toppings
vanilla
chocolate
strawberry
fudge
marshmallow
caramel
Answer:
9
Step-by-step explanation:
A recipe says it produces the best summer drink. The recipe calls for cup of lemonade for every 1 cups of iced tea. If 16 cups of the summer drink are made, how many of those are cups of lemonade? Re-create the table to give your answer.
How can these terms be combined: -2x + 11 + 6x - 5 *
8 points
-8x +16
4x + 6
4x - 6
8x + 6
Problem number 26 of the Rhind Papyrus says:
Find a quantity such that when it is added to StartFraction 1 Over 4 EndFraction of itself the result is a 15.
The modern day equation that models this problem is x plus StartFraction 1 over 4 EndFraction x equals 15..
What is the solution to the equation?
x = 10
x = 12
x = 15
x = 30
Answer:
X=12 on edg
Step-by-step explanation:
Answer:
I can confirm, the answer is 12.
Which postulate or theorem would you use to prove these two triangles congruent?
Answer:
ASA
Step-by-step explanation:
Both triangles are marked on the Angle, a Side, and Another Angle
The square below represents one whole.
Express the shaded area as a fraction, a decimal, and a percent of the whole.
Answer:
Percent 40% Fraction 4/10 or 40/100 Decimal .40
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
التاريخ / /
اليوم
موضوع الدرس
و(
is 82
room )
what is
ده by
و به
the
area
0
the
room?can I translate in English
what’s the answer to this question?
Answer:
the answer is 4/15i think if not sorry I am not 100% sure
The domain of the function f(x)=−3x is restricted to the negative integers. Which values are elements of the range?
answer
[tex]fx = - 3x \\ \frac{fx}{x} = - \frac{3x}{x} \\ f = - 3[/tex]
Answer:
learning only kang po yan
Step-by-step explanation:
basa lang
Which expression is equivalent to (2g^5)^3
Answer:
Your answer should be 8g^15
Step-by-step explanation:
If cubed (power of 3) is on a parenthesis, that means you have to cube every expression inside that parenthesis. In order to distribute exponents, mutliply them. This gives you g^5 times ^3, which is g^15. ^3 has to also be distributed to the 2, which is 2^3 = 8. 8 and g^15 is 8g^15.
7 more than 3 times a number is 49.What is the number?
Answer:
14
Step-by-step explanation:
Let x be the missing number
3x + 7 = 49 [Given equation]
3x = 42 [Subtract 7 from both sides of the equal sign]
x = 14 [Simplify]
Hope this helps! I apologize if I get this incorrect.
Answer:14
Step-by-step explanation: I hope this helps plz tell me if its wrong so i can fix it :)
Write the equation of the line that passes through (1, -4) and (-4, 5). Put your answer in fully reduced point slope form unless it is a vertical or horizontal line.
Mike sold half of his comic books and then bought 8 more. He now has 18. How many did he begin with?
Answer: 20
Step-by-step explanation:
Answer:
20.
Step-by-step explanation:
If he sold half of them, bought 8 more, and now has 18, he had 20 to begin with.
What is 8x - 6x + 4 +5 = 19
Answer: x = 5
The step-by-step explanation is below.
Combine like terms
8x-6x = 2x
4+5=9
2x+9=19
Subtract 9
2x=10
Divide by 2
x = 5
Hope this helps!
Refer to the Newsela article "The Lakota Tribe Wants to Educate People Through Music Project."
Part A
What is an implied idea about the Lakota Music Project in the article?
It was created to unite Native American musicians and their diverse ideas.
It was established with the intent to increase human connectivity.
It was intended to celebrate the uniqueness of Native American music and not to limit it.
It was viewed as an idea that covered all areas of the human experience.
Part B
Which two sentences from the text that best support the answer in Part A?
“Gier was eager to develop community programs, and he learned about tensions in his new community between Native and non-Native Americans.”
“‘I find the Lakota Music Project a visionary undertaking, and I feel it deserves to be more widely known,’ said Joseph Horowitz.”
"The Lakota Music Project's focus remains on building bridges through music."
“Some of the orchestra's musicians and the Porcupine Singers, a drumming circle on the reservation, met to exchange ideas and play music for one another.”
Answer: part A
It was established with the intent to increase human connectivity.
part B
"The Lakota Music Project's focus remains on building bridges through music."
“Gier was eager to develop community programs, and he learned about tensions in his new community between Native and non-Native Americans.”
Step-by-step explanation: I took the test ok k12 sooo...
Answer for part A
It was established with the intent to increase human connectivity.
Answer for part B
"The Lakota Music Project's focus remains on building bridges through music."
AND
“Gier was eager to develop community programs, and he learned about tensions in his new community between Native and non-Native Americans.”
Note
I also took the K12 test, and got it correct! :D (Note: I forgot to click on the "Gier was eager to develop'... thats why it's yellow.)
You are permitted to use your calculator to solve an equation, find the derivative of a function at a point, or calculate the value of a definite integral. However, you must clearly indicate the setup of your question, namely the equation, function, or integral you are using. If you use other built-in features or programs, you must show the mathematical steps necessary to produce your results. Your work must be expressed in standard mathematical notation rather than calculator syntax.
Show all of your work, even though the question may not explicitly remind you to do so. Clearly label any functions, graphs, tables, or other objects that you use. Justifications require that you give mathematical reasons, and that you verify the needed conditions under which relevant theorems, properties, definitions, or tests are applied. Your work will be scored on the correctness and completeness of your methods as well as your answers. Answers without supporting work will usually not receive credit. Unless otherwise specified, answers (numeric or algebraic) need not be simplified. If your answer is given as a decimal approximation, it should be correct to three places after the decimal point.
Unless otherwise specified, the domain of a function f is assumed to be the set of all real numbers x for which f(x) is a real number.
x -3 0 3 6
f(x) -5 4 1 7
f'(x) -1 2 -2 4
The table above gives values of a twice-differentiable function f and its first derivative f' for selected values of x. Let g be the function defined by
g(x)= f(x^3-x )
Required:
What is the value of g (3)?
Answer:
17
Step-by-step explanation: