The remainder when x³ - 2x²+ X + 1 is divided by X - 1 is 1.
What is Remainder theorem?
The polynomial remainder theorem, also known as little Bézout's theorem, is an algebraic application of Euclidean polynomial division. It says that f is equal to the remainder of dividing a polynomial f(x) by a linear polynomial (x-r) is f(r).
Given:
\(f(x) = x^3 - 2x^2 + x + 1\)
We have to find the remainder of polynomial f(x) when divided by (x - 1).
By using the Remainder theorem, the remainder of f(x) when divided by
(x - r) is f(r).
Here we have to find the value of f(1).
Plug x = 1 is given polynomial f(x).
\(f(1) = (1)^3 - 2(1)^2 + 1 + 1\\f(1) = 1 - 2 + 2\\f(1) = 1\)
Hence, the remainder when x³ - 2x²+ X + 1 is divided by X - 1 is 1.
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Complete question:
Find the remainder when x³-2x²+x+1 is divided by x-1.
Find the greatest odd integer value of x that satisfies the inequality -3x > -105.
Answer:
Step-by-step explanation:
X>35
Answer:
x = -37
Step-by-step explanation:
x < -\(\frac{-105}{3}\)
divide 105 by 3, we get -35
however the question asked for the 'greatest odd' integer 35 which is 37 since x is less than -35
Please answer #1 for me only ! What is my Y for #1 , don't forget to graph !
Please Help I really need this to not get behind in my math class.
I would award more points but I fear people are just gonna answer with no actual answer and just for points….
Answer:
1. 12x+19
2.11x+16
3.54
4.3x+5x+8
Step-by-step explanation:
I first wrote the question and grouped like terms.So after grouping these you will get x+2x+8x +x +7 + 2+10 .When you simplify you wil get 12x+19 . If you don't understand comment me
$2000 was invested for 3 years . it earned $204 in interest. what was the rate
Answer:it is $12,240
Step-by-step explanation:
given: principal=$2000
time=3 years
interest=$204
he genearal formular of RATE = I*P*T/100
from the formular= P*R*T( RATE WITH 100, because the rate is calculated over 100)
=$204*3*$2000/100
=$12,240
Express 7.6109 x 108 in standard form.
A. O 7,610,900,000
B. O 76,109,000
C.O 761,090,000
D. O 0.000000076109
(5) i need help with my math HW I'm stuck with this problem show all ur steps for y & x
A graph of this system of equations on a coordinate plane is shown in the image attached below.
How to graph the solution to this system of inequalities?In order to to graph the solution to the given system of equations on a coordinate plane, we would use an online graphing calculator to plot the given system of equations and then take note of the point of intersection;
y = 2x/5 + 4 ......equation 1.
-2x + 5y = -30 ......equation 2.
Making y the subject of formula in equation 2, we have the following:
5y = 2x - 30
Dividing both sides of the equation by 5, we have:
y = 2x/5 - 30
Based on the graph (see attachment), we can logically deduce that the solution to the given system of equations is non existent because the lines are parallel.
In conclusion, the given system of equations has no solution.
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Please help me with this homework
Answer:sasa
Step-by-step explanation:
Please help! If this pentagon is reflected across the x then rotated 90 degrees about the origin What would be the cords?
Answer:
d (5, 1)
Step-by-step explanation:
after reflection: 1, -5
after rotation: 5, 1
pls mark brainliest :)
The coordinates of B' is (5, 1)
What is Translation?Each point in a figure is moved the same distance in the same direction using a type of transformation known as translation.
There are 4 simple transformations which are; translation, reflection, rotation, and dilation.
Given:
The coordinates of B is (1, 5)
After reflection over x- axis the coordinates of B is (1, -5)
and, After rotation the the coordinates of B is (5, 1)
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Match the system of equations on the left with the appropriate solution on the right: 2x - y = 7 3x + y = 3 No solution (-2, - 3) 2x + 3y = 8 3x - 2y = ~ 14 (=2,4) ~3) 3x - 2y = /2 Infinite number of solutions 6x - 4y = 24 2x - 3y = 6 4x + 6y = 12
To match the system of equations on the left with the appropriate solution on the right, let's analyze each system: 2x - y = 7; 3x + y = 3.
The solution is: No solution; 2x + 3y = 8; 3x - 2y = -14. The solution is: (-2, -3). 3x - 2y = 1/2; 6x - 4y = 24. The solution is: Infinite number of solutions: 2x - 3y = 6; 4x + 6y = 12. The solution is: (2, 4). Therefore, matching the systems of equations with their appropriate solutions, we have: System: 2x - y = 7, 3x + y = 3; Solution: No solution. System: 2x + 3y = 8, 3x - 2y = -14. Solution: (-2, -3).
System: 3x - 2y = 1/2, 6x - 4y = 24. Solution: Infinite number of solutions; System: 2x - 3y = 6, 4x + 6y = 12. Solution: (2, 4).
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The question is about solving systems of equations to match with their respective solutions. Due to the unclear formatting of the solutions provided in the question, an accurate match cannot be made. The solution to a system of linear equations would typically be in the form of an ordered pair (x, y).
Explanation:The system of equations listed can be matched with their solutions by solving these systems simultaneously to find the values of x and y. Let's proceed to solve the following systems:
2x - y = 7 and 3x + y = 3 2x + 3y = 8 and 3x - 2y = ~14 3x - 2y = /2 and 6x - 4y = 24 2x - 3y = 6 and 4x + 6y = 12
We can solve these systems by either substitution, elimination, or using matrix math. But it's not completely clear what the solutions on the right are, they're not properly formatted, which prevents an accurate solution from being identified. A solution to a linear system would take the form of an ordered pair (x, y).
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prove that a set s of vectors is linearly independent if and only if each finite subset of s is linearly independent.
A set s of vectors is linearly independent if and only if each finite subset of s is linearly independent.
To prove that a set s of vectors is linearly independent if and only if each finite subset of s is linearly independent, we need to prove both directions of the statement.
First, we will prove that if a set s of vectors is linearly independent, then each finite subset of s is linearly independent.
Suppose s is a linearly independent set of vectors. Let F be a finite subset of s. We want to show that F is linearly independent as well.
Assume for contradiction that F is linearly dependent. Then, there exist scalars c1, c2, ..., cn, not all zero, such that:
c1v1 + c2v2 + ... + cnvn = 0
where v1, v2, ..., vn are the vectors in F. Since s contains all the vectors in F and s is linearly independent, it follows that the coefficients c1, c2, ..., cn must all be zero. But this contradicts the assumption that not all the coefficients are zero. Hence, F must be linearly independent.
Next, we will prove that if each finite subset of a set s of vectors is linearly independent, then s itself is linearly independent.
Suppose that each finite subset of s is linearly independent. We want to show that s is linearly independent as well.
Assume for contradiction that s is linearly dependent. Then, there exist scalars c1, c2, ..., cn, not all zero, such that:
c1v1 + c2v2 + ... + cnvn = 0
where v1, v2, ..., vn are the vectors in s. Let F be the finite subset of s consisting of the vectors v1, v2, ..., vm, where m is the smallest index such that c1v1 + c2v2 + ... + cmvm ≠ 0. Then, m ≥ 2, since s is linearly dependent.
Since F is a finite subset of s, it must be linearly independent. Therefore, the coefficients c1, c2, ..., cm in the equation above must all be zero, since m was chosen to be the smallest index such that the equation is non-zero. But this contradicts the assumption that not all the coefficients are zero. Hence, s must be linearly independent.
Therefore, we have proved both directions of the statement, and hence, we have proved that a set s of vectors is linearly independent if and only if each finite subset of s is linearly independent.
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What is a 1-sample t-test used for?
A 1-sample t-test is a statistical method used to determine whether a sample of data is significantly different from a known or hypothesized population mean.
It is a common method used in scientific research and it can be used to test hypotheses in many different fields. The t-test compares the mean of a sample to a population mean, and it uses the t-distribution to calculate the probability that the sample mean is significantly different from the population mean. To perform a 1-sample t-test, you need to have a sample of data and a known or hypothesized population mean, and the test assumes that the data is normally distributed and that the variances between the sample and population are equal.
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can SOMEONE plz HELP!?!?!
Answer:
a. 100 m
b. 900 m
c. 5,100 m
d. 8,800 m
e. -650 m
Step-by-step explanation:
there is a number that if you multiple it by 5 first, and then add 6 to the result, you get 91. what’s the number?
Answer:
Step-by-step explanation:
Do 91-6 which equals 85. Then do 85/5 which equals 17
answer: 17
Answer:
17
Step-by-step explanation:
So first we write an equation
5x+6=91
subtract 6 from both sides
5x=85
divide by 5
so x=17
(plz give me brainliest)
Mrs Nu paid $2083 for 2 smiler laptops and 3 similar earphones. Each laptop cost of each earphones?
Answer:
Step-by-step explanation:
The information given is incomplete :
Answer:
x = 1/2(2083 - 3y)
y = 1/3(2083 - 2x)
Step-by-step explanation:
Let
Laptop cost = x
Earpiece cost = y
Number of laptops= 2
Number of earpiece = 3
2x + 3y = $2083
The cost per laptop :
2x = 2083 - 3y
Divide both sides by 2
x = (2083 - 3y) / 2
x = 1/2(2083 - 3y)
Or
3y = 2083 - 2x
y = (2083 - 2x) / 3
y = 1/3(2083 - 2x)
If x = -2, what is y = ?
Y = ?
Answer:
y = 2
Step-by-step explanation:
locate x = - 2 on the x- axis, go vertically up to meet the graph at (- 2, 2 )
that is when x = - 2 then y = 2
Answer:
y = 2
Step-by-step explanation:
Solve the following initial value problem. y' (t) - 2y = 6, y(2) = 2 Show your work for solving this problem and your answer on your own paper. y(t) = (Type an exact answer in terms of e.)
The solution to the initial value problem. y' (t) - 2y = 6, y(2) = 2 is y(t) = -3 + (5/e^4)e^(2t)..
To solve the initial value problem y'(t) - 2y = 6 with y(2) = 2,
we will use an integrating factor and the given initial condition. Here's the step-by-step solution:
1. Identify the integrating factor: The integrating factor is e^(-2t).
2. Multiply the equation by the integrating factor: e^(-2t)y'(t) - 2e^(-2t)y = 6e^(-2t).
3. Observe that the left side of the equation is the derivative of the product y(t)e^(-2t): (y(t)e^(-2t))' = 6e^(-2t).
4. Integrate both sides with respect to t: ∫(y(t)e^(-2t))' dt = ∫6e^(-2t) dt.
5. Integrate: y(t)e^(-2t) = -3e^(-2t) + C.
6. Solve for y(t): y(t) = -3 + Ce^(2t).
7. Apply the initial condition y(2) = 2: 2 = -3 + Ce^(4).
8. Solve for C: C = (5/e^4).
9. Substituting C back into the solution for y(t): y(t) = -3 + (5/e^4)e^(2t).
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Drag and drop the range of each data set into the boxes. Team 1 Team 2 Range Two line plots aligned vertically so that their labels match. The first line plot is from 72 to 82, is labeled Team 1, and shows the following values that appear as x marks above the line. One x mark above 73. Two x marks above 74. Two x marks above 75. Three x marks above 76. Two x marks above 77. One x mark above 78. One x mark above 80. The second line plot is also from 72 to 82, is labeled Team 2, and shows the following values that appear as x marks above the line. One x mark above 74. Two x marks above 75. Four x marks above 76. Two x marks above 77. One x marks above 78. One x mark above 79. One x mark above 80. 6 7 10 76?
The range of data for Team 1 is 72 to 82, while the range for Team 2 is also 72 to 82. The range represents the span between the lowest and highest values in a dataset.
In the given scenario, there are two line plots representing Team 1 and Team 2. Both line plots are aligned vertically, with labels matching the respective teams. The range for both datasets is from 72 to 82, indicating that the data points range from the lowest value of 72 to the highest value of 82.
For Team 1, the line plot displays x marks above the line for different values. There is one x mark above 73, two x marks above 74, two x marks above 75, three x marks above 76, two x marks above 77, one x mark above 78, and one x mark above 80.
Similarly, for Team 2, the line plot also shows x marks above the line for different values. There is one x mark above 74, two x marks above 75, four x marks above 76, two x marks above 77, one x mark above 78, one x mark above 79, and one x mark above 80.
Therefore, the range of the data for both Team 1 and Team 2 is the same, from 72 to 82. The range represents the full span of values covered by the dataset, indicating the extent of variability in the data.
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can someone please help me
The measure of the angle formed at the center of anoxygen atom in a water molecule is about 105. The angles formed at each hydrogen atom are congruent. What is the size of the angle at each hydrogen atom?
Please I need helppppll
Answer:
4 cases of oil
Step-by-step explanation:
Answer:
qwerty ur mother
Step-by-step explanation:
Pls solve with all steps
The results of the expressions involving logarithms are listed below:
Case 1: 1 / 2
Case 2:
Subcase a: 0
Subcase b: 11 / 2
Subcase c: - 11 / 2
How to simplify and evaluate expressions involving logarithmsIn this problem we have a case of an expression involving logarithms that must be simplified and three cases of expressions involving logarithms that must be evaluated. Each case can be solved by means of the following logarithm properties:
㏒ₐ (b · c) = ㏒ₐ b + ㏒ₐ c
㏒ₐ (b / c) = ㏒ₐ b - ㏒ₐ c
㏒ₐ cᵇ = b · ㏒ₐ c
Now we proceed to determine the result of each case:
Case 1
㏒ ∛8 / ㏒ 4
(1 / 3) · ㏒ 8 / ㏒ 2²
(1 / 3) · ㏒ 2³ / (2 · ㏒ 2)
㏒ 2 / (2 · ㏒ 2)
1 / 2
Case 2:
Subcase a
㏒ [b / (100 · a · c)]
㏒ b - ㏒ (100 · a · c)
㏒ b - ㏒ 100 - ㏒ a - ㏒ c
3 - 2 - 2 + 1
0
Subcase b
㏒√[(a³ · b) / c²]
(1 / 2) · ㏒ [(a³ · b) / c²]
(1 / 2) · ㏒ (a³ · b) - (1 / 2) · ㏒ c²
(1 / 2) · ㏒ a³ + (1 / 2) · ㏒ b - ㏒ c
(3 / 2) · ㏒ a + (1 / 2) · ㏒ b - ㏒ c
(3 / 2) · 2 + (1 / 2) · 3 + 1
3 + 3 / 2 + 1
11 / 2
Subcase c
㏒ [(2 · a · √b) / (5 · c)]⁻¹
- ㏒ [(2 · a · √b) / (5 · c)]
- ㏒ (2 · a · √b) + ㏒ (5 · c)
- ㏒ 2 - ㏒ a - ㏒ √b + ㏒ 5 + ㏒ c
- ㏒ (2 · 5) - ㏒ a - (1 / 2) · ㏒ b + ㏒ c
- ㏒ 10 - ㏒ a - (1 / 2) · ㏒ b + ㏒ c
- 1 - 2 - (1 / 2) · 3 - 1
- 4 - 3 / 2
- 11 / 2
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A pair of designer sneakers was purchased for $120. Since they were purchased, their price has decreased by 15%
Complete question :
A pair of designer sneakers was purchased for $120. Since they were purchased, their price has increased by 15%. What is the new price?
Answer:
$138
Step-by-step explanation:
Given that :
Initial price = $120
Percentage increase in price = 15%
The new price of sneakers:
Initial price + (percentage increase in price * initial price)
New price :
$120 + (15% * $120)
New price :
$120 + (0.15 * $120)
New price of sneakers :
$120 + $18
New price of sneakers = $138
need help with algerba 2
F(4)4 is the x value 4. Find where the line is on th y axis at x = 4
The dot is between 60 and 70 so the answer would be 64
Answer: D. 64
Answer:
the answer is d
Step-by-step explanation:
if you look on the graph where the x-value equals 4, the y-value of that point is your answer and d is the only value in that range
Question 5 of 9Which of the expressions are equivalent to the one below? Check all thatapply.6.(2+8)I A. (8 + 2). 6OB. 6. (8 + 2)O C. 6. 2) + 8O d. 6.2 + 6.8SUBMIT
We have the expression:
\(6\cdot(2+8)\)We can solve the parenthesis and then multiply or we can apply the distibutive property before the addition.
1) Solving the parenthesis first:
\(6\cdot(2+8)=6\cdot10=60\)2) Applying the distributive property:
\(6\cdot(2+8)=6\cdot2+6\cdot8=12+48=60\)If we look at each of the expressions, we can find if they are equivalent of not.
A) Equivalent. In this case, we are applying the commutative property of the multiplication (you can multiply in any order).
\(6\cdot(2+8)=(2+8)\cdot6\)B) Equivalent. In this case, the commutative property of the addition is applied, as we can sum in any order.
\(6\cdot(2+8)=6\cdot(8+2)\)C) Not equivalent. Is the distributive property but applied wrong: the 6 has to also multiply the 8.
\(6\cdot(2+8)\neq(6\cdot2)+8\)D) Equivalent. This is the application of the distributive property.
\(undefined\)Draw the image of Quadrilateral ABCD translated -2 units horizontally and 5 units vertically. Label the image points using prime notation. (in other words Rule: (x, y) --> (x-2, y+5) )
The image of Quadrilateral ABCD after transformation is shown in graph with coordinates A' (0, 2), B' (2, 4), C' (5, 4) and D' (4, 3).
What is Transformation?
Transformation is the act or process of changing completely.
The rule of transformation is given as;
(x, y) --> (x-2, y+5)
Now, The coordinates of Quadrilateral ABCD are;
A (2, -3) , B (4, -1), C (7, -1) and D (6, -2)
Apply the rule of transformation to find the coordinates of the image of Quadrilateral ABCD as;
A' (2-2, -3+5) = (0, 2)
B' (4-2, -1+5) = (2, 4)
C' (7-2, -1+5) = (5, 4)
D' (6-2, -2+5) = (4, 3)
Hence, The coordinates of image of Quadrilateral ABCD are;
A' (0, 2), B' (2, 4), C' (5, 4) and D' (4, 3).
And, The image of Quadrilateral ABCD after transformation is shown in graph.
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What are some of the factors to take into consideration when opening a savings account and what information do you
need to provide?
Answer:
The factors we might take into consideration when opening a savings account is how accessible are the banks, the types of services the bank provides, customer services, and what types of rates the bank provides.
Step-by-step explanation:
Some of the factors to take into consideration when opening a savings account are;
- Interest Rate
- Minimum Cash Balance
- Wide reach of bank
- Service Charge
Some of the factors to consider when opening a savings account are;
1) Interest Rate; Savings accounts usually pay the lowest interest rates when we compare to other investment means. This is because some pay interest rate of around 6% annually while others pay lesser. Thus, it is very important to choose the bank wisely.
2) Minimum Cash Balance; Some banks require a particular minimum balance to open a savings account. Thus, it will be wise to look for a bank that doesn't require too much initial minimum opening balance.
3) Wide reach of bank; Although many transactions can now be done online but yet there are times we have to go to the banks physically and so it will be good to go with a bank that has many branches.
4) Service Charges; Banks usually have some charges which are called service charge and they range from ATM card charges, SMS charges, transaction charges. Thus, it will be good to have an idea of these charges before opening an account.
The information required to be provided to open savings account are;
- Government issued Identification Card
- Social Security Number
- Date of birth
- Address
- Contact Information like phone number, email e.t.c
- Bank account information
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Find the area of hexagon DEFGHI.
Step-by-step explanation:
Break it up into two trapezoids as shown
area = trap1 + trap2
= 2 * (7+3) / 2 + 3 * ( 7 + 3) / 2 = 10 + 15 = 25 units^2
A company offers four plans for customers who want to rent DVDs and video games. The cost of the plans can be modeled by a linear function that combines a one time membership fee with a per disc rental rate. The table shows the total cost, including membership fees, for a person who rents 1,2 and 5 discs in a month
Discs rented plan A B C D
1. $14. $12. $10. $12
2. $17. $16. $15. $21
5. $26. $28. $30. $48
The plan with the smallest one-time membership fee is Plan D.
The point-slope formula will be used to determine the equation that models the cost of each plans.
(y - y₁) = [(y₂ - y₁)/(x₂ - x₁)](x - x₁)
where (x₁, y₁) is the coordinates of point 1
(x₂, y₂) is the coordinates of point 2.
For the equation y = mx + b,
let x = number of discs rented
y = total cost
m = rental rate per disc
b = one-time membership fee
Plan A
(y - 14) = [(17 - 14)/(2 - 1)](x - 1)
y - 14 = 3x - 3
y = 3x + 11
Plan B
(y - 12) = [(16 - 12)/(2 - 1)](x - 1)
y - 12 = 4x - 4
y = 4x + 8
Plan C
(y - 10) = [(15 - 10)/(2 - 1)](x - 1)
y - 10 = 5x - 5
y = 5x + 5
Plan D
(y - 12) = [(21 - 12)/(2 - 1)](x - 1)
y - 12 = 9x - 9
y = 9x + 3
Hence, the plan with the smallest one-time membership fee, b, is Plan D.
Your question is incomplete, but most probably you are asking
"...Which plan has the smallest one-time membership fee?"
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Pls, Help I'll do brainiac!!!
Solve for y. Write the answer as a complete equation using no spaces.
6x+3y=12
A concrete pillar has the shape of a cylinder. It has a radius of 4 meters and a height of 7 meters. If concrete costs $94 per cubic meter, how much did the concrete cost for the pillar? Use 3.14 for π , and do not round your answer.
Answer:
C = $33,057.92
The cost of the pillar is $33,057.92
Step-by-step explanation:
Given;
Radius of the concrete r = 4 m
Height h = 7 m
Cost per volume R = $94 per cubic meter
π = 3.14
The volume of the cylinder shape concrete is;
V = πr^2 h
Substituting the given values;
V = 3.14×4^2 × 7
V = 351.68 m^3
The cost of the pillar is C;
C = Volume × cost per volume
C = V × R
C = 351.68 m^3 × $94 per cubic meter
C = $33,057.92
The cost of the pillar is $33,057.92
Giving brainly for answer correctly uwu:)<3