When the polynomial P(x) = x3
+ 3x2
– 2Ax + 3,
where A is constant, is divided by x2
+ 1 and
remainder is –5x, then A is
Since this equation must hold for all values of x, we can substitute x = i and x = -i to get two equations: 2A + 3i = -5i=> 2A - 3i = 5i=> A = -3/2Therefore, A is equal to -3/2.
what are polynomials?A polynomial is a mathematical statement with coefficients and uncertainty that uses only additions, subtractions, multiplications, and powers of positive integer variables. There is just one indeterminate x polynomial identified by the formula x2 4x + 7. The term "polynomial" refers to an expression in mathematics that consists of variables (sometimes referred to as "indeterminates") and coefficients that may be added, subtracted, multiplied, and raised to negative integer powers of non-variables. A polynomial is an algebraic expression having variables and coefficients. Only addition, subtraction, multiplication, and non-negative integer exponents are permitted in expressions. The word for these expressions is polynomials.
To find A, we need to perform polynomial long division of P(x) by \(x^2 + 1\)and get the remainder equal to -5x.
x
--------------
\(x^2 + 1 | x^3 + 3x^2 - 2Ax + 3\)
\(x^3 + 0x^2 + x\)
--------------
\(3x^2 - 2Ax\)
\(3x^2 + 0x - 3i\)
------------
\(2Ax + 3i\)
\(2Ax + 0x - 2iA\)
-----------
\(3i + 2iA\)
The remainder of the division is (2A + 3i) when the divisor is \(x^2 + 1\). We know that this remainder is equal to -5x, so we can set up the equation:
2A + 3i = -5x
Since this equation must hold for all values of x, we can substitute x = i and x = -i to get two equations:
2A + 3i = -5i
2A - 3i = 5i
A = -3/2
Therefore, A is equal to -3/2.
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Help me on question 1 please!!!!
pls help I give brainiest
Answer:4
Step-by-step explanation:
what is the sum of 3,3,6
Answer:
12
Step-by-step explanation:
Sum means addition. 3 + 3 + 6 = 12
Answer:
12
Step-by-step explanation:
i hope this is what you meant
imli has 5 bushels of oats she wants to pour all of the oats into boxes that each hold 1 peck how many boxes will she need? ( 4 pecks = 1 bushel)
Answer:
20
Step-by-step explanation:
4 x 5 = 20
Who created Sports Illustrated?
.Joseph Pulitzer
.Michael Jordan
.William Randolph Hearst
.Henry Luce
Answer:
henry lucr did
please brainlist
Answer:
Henry Luce
Step-by-step explanation:
Pine Lakes Country Club opened in Myrtle Beach in 1927. It was here, in 1954, that Sports Illustrated was invented. The man behind it was Henry Luce, who was not a sports fan, but who was the publisher of Life, Time, and Fortune magazines.
Frazer cycles the first 20 miles at an average speed of 21 mph. The second part is more uphill, and he only manages 13mph. By what percentage did the speed decrease
Answer:
38.1% decrease
Step-by-step explanation:
A percentage change is found from ...
% change = (change)/(original amount) × 100%
= (new value - original amount)/(original amount) × 100%
= (13 -21)/21 × 100% = -8/21 × 100% ≈ -38.1%
solve for g:2(g-h)=b+4
Answer:
\(g = \frac{b}{2} + 2 + h\)
Step-by-step explanation:
\(2(g - h) = b + 4 \\g - h = \frac{b}{2} + \frac{4}{2}\\g = \frac{b}{2} + 2 + h\)
Find the value of X that makes lines u and v parallel 7-12
The value of x that makes lines u and v parallel is 6. Option A is correct.
First, let us understand the angles formed by parallel and transversal lines:
The different types of angles are alternate exterior angles, alternate interior angles, corresponding angles, consecutive angles, etc.
From the picture attached,
If the lines u and v are parallel and a third line (transversal) is intersecting these lines at two distinct points,
Both the angles given in the picture will be equal in measure as these angles are alternate exterior angles if u and v are parallel.
20x + 10 = 130 degrees
20x = 130 - 10 degrees
x = 120 / 20 = 6
So, the value of x is 6.
Thus, the value of x that makes lines u and v parallel is 6. Option A is correct.
For question please check the below figure:
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Can you please tell me which one it is?? its okay if not
Answer:
estimate
Step-by-step explanation:
BRAINLIEST PLSSSSSSS PSLPSLSSLSSS
Answer:
estimate
Step-by-step explanation:
because when we estimate it will give us a value close to the exact value.
examine the graph below. select the solutions to the graph from the following points. select three that apply.
Answer:
Options (1), (2), (3)
Step-by-step explanation:
Let the equation of the line is,
y = mx + b
Here m = slope of the line
b = y-intercept
Given line on the graph is passing through two points (-3, 0) and (0, 1).
Slope of this line will be,
m = \(\frac{y_2-y_1}{x_2-x_1}\)
= \(\frac{1-0}{0+3}\)
= \(\frac{1}{3}\)
y-intercept of the line 'b' = 1
Equation of the line will be,
y = \(\frac{1}{3}x+1\)
If the points given in the options satisfy the equation, they will be the solution of the line.
Option (1),
For (3, 2),
2 = \(\frac{3}{3}+1\)
2 = 2
True.
(3, 2) is the solution.
Option (2)
For (21, 8),
8 = \(\frac{21}{3}+1\)
8 = 8
True.
(21, 8) is the solution.
Option(3)
For (-15, -4),
-4 = \(\frac{-15}{3}+1\)
-4 = -4
True.
(-15, -4) is the solution.
Option (4)
For (12, 9)
9 = \(\frac{12}{3}+1\)
9 = 5
False
(12, 9) is not the solution.
Option (5)
For (-6, 1)
1 = \(\frac{-6}{3}+1\)
1 = -1
False
(-6, 1) is not the solution.
Therefore, Options (1), (2), (3) are the solutions.
Consider the graph of the function f(x) = 12-49 22 +42-21 Find the x-value of the removable discontinuity of the function. Provide your answer below: The removable discontinuity occurs at x
The function f(x) = 12-49 22 +42-21 has a removable discontinuity at a specific x-value. To find this x-value, we need to identify where the function is undefined or where it has discontinuity that can be removed.
To determine the x-value of the removable discontinuity, we need to examine the function f(x) = 12-49 22 +42-21 and look for any bor points where the function is not defined. In this case, the expression 22 +42-21 involves division, and division by zero is undefined.
To find the x-value of the removable discontinuity, we set the denominator equal to zero and solve for x. In the given function, the denominator is not explicitly shown, so we need to determine the expression that results in division by zero. Without further information or clarification about the function, it is not possible to determine the specific x-value of the removable discontinuity.
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In 2017, the population of a village was 7500. In 2019, the population of the village was 8265. Work out the percentage increase in the population of the village from 2017 to 2019.
Answer:
10.2%
Step-by-step explanation:
The given population of the village in 2017 = 7,500
The given population of the village in 2019 = 8,265
The percentage increase in the population of the village from 2017 to 2019 is given by the following percentage increase formula;
\(Percentage \ increase = 100 \times \dfrac{Final \ value - Initial\ value}{Initial \ value}\)
The final value of the population in 2019 = 8,265
The initial value of the population in 2017 = 7.500
Therefore;
\(Percentage \ increase \ in \ the \ population = 100 \times \dfrac{8,265 - 7,500}{7,500} = 10.2 \%\)
The percentage increase in the population = 10.2%
Kendra watches the moon change from a new moon to a full moon. Which of the following descriptions is accurate? (Select all that apply.)
Responses
The moon is waxing.
The moon is waxing.
The moon is waning.
The moon is waning., ,
The moon appears to get smaller.
The moon appears to get smaller.
The moon appears to get bigger.
The moon appears to get bigger.
The moon does not change.
The correct description is that moon is waxing.
Which of the following descriptions is accurate?The theory used in this question is the lunar cycle, which is the process by which the moon changes its shape and illumination over the course of a month.
The waxing phase of the lunar cycle is when the moon is gradually getting bigger and more illuminated.
The waning phase is when the moon is gradually getting smaller and less illuminated.
The moon is waxing:
This is an accurate description because when the moon changes from a new moon to a full moon, it is said to be waxing.
This means that the moon is gradually getting bigger, and its illuminated side is increasing.
This process is called the waxing phase of the moon's cycle.
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When finding all the unknown values in similar right triangles you
have choices: you can use Proportional Relationships or the Pythagorean
Theorem. Which would you use for each of these examples, and why?
Find all the missing sides!
Answer:
sffsffrdffffgtgttgfftggggfhfffddgddgff
What is an example of a obtuse triangle?.
Answer:
A triangle where the angles in the inside are 100 degrees, 40 degrees, and 40 degrees.
Step-by-step explanation:
The angles inside a triangle always add up to 180 degrees
And an obtuse triangle is a triangle whose biggest angle is bigger than 90 degrees
100 is biggest angle out of the three angles we're using to make the triangle and 100 is bigger than 90.
Adding the three angles we're using also makes 180 (100 + 40 + 40)
Which expression is equivalent to x^2+5x-36
(x-4)(x+9) is equivalent to x^2+5x-36
all you need to do is factor the equation
histograms are used to a. determine the distribution of nonresponse errors. b. investigate the relation between two variables. c. construct cumulative distribution functions. d. construct cross tabulation tables. e. determine the empirical distribution of a variable.
Histograms are used to determine the empirical distribution of a variable. Therefore, option (e) is the correct one.
Histogram is used to summarize discrete or continuous data measured on an interval scale. It is often used to describe key features of the distribution of data in a practical way.
A histogram divides the range of possible values in a data set into different classes or groups. For each group, a rectangle is created with a base length equal to the range of values in that particular group and a length equal to the number of observations that fall into that group.
Histograms are similar to column charts, but there are no gaps between the bars. Histograms generally have equal width bars.
Thus, it can be concluded that histograms are used to determine the empirical distribution of a variable. Therefore, option (e) is the correct one.
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Hello, just checking my work. First right answer will be brainiest
Irwin rode his bicycle from one end of a trail to another and back at a speed of 20 miles per hour. If the trail is 4 miles long, for how many hours was Irwin riding?
0.2 hours
0.4 hours
2.5 hours
5.0 hours
Answer:
0.4
Step-by-step explanation:
how many minutes are in 4 miles
Answer:
I believe it’s C. 2.5
Step-by-step explanation:
Solve for x someone please help
The value of x = 9 in given figure.
What is the value of x?
In given figure, there three perpendicular lines.
By using given figure, we can write as,
49/28 = \(\frac{24+3x+5}{3x+5}\)
(49*3x) + 49*5 = 24*28 +3x*28 + 5*28
147x + 245 = 672 + 84x + 140
63x = 567
x = 9
What are perpendicular lines?
Perpendicular lines are two lines that intersect at a 90-degree angle, forming a right angle. They are commonly found in geometry and have important properties such as bisecting each other and being useful in constructing right angles. Perpendicular lines are fundamental in practical applications such as architecture, engineering, and construction. They are important for ensuring structures are stable and secure.
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\(\sqrt{25} is an irrational
Answer:
Is Square Root of 25 Rational or Irrational?
Step-by-step explanation:
A rational number can be expressed in the form of p/q. Because √25 = 5 and 5 can be written in the form of a fraction 5/1. It proves that √25 is rational.
The answer is:
⇨ √25 is a rational numberWork/explanation:
What are rational numbers?
Rational numbers are integers and fractions.
Irrational numbers are numbers that cannot be expressed as fractions, such as π.
Now, \(\bf{\sqrt{25}}\) can be simplified to 5 or -5; both of which are rational numbers.
Hence, √25 is rational.A phone is regularly priced at $350. If you get it on sale for 15% off, how much do you pay?
The function f(x) = 454 + 0.9x gives the cost, in dollars, of manufacturing x vinyl records. select all the true statements. the initial cost for manufacturing records depends on the quantity ordered. the initial cost for the manufacturing is $454, regardless of the number of records ordered. in addition to the initial cost, each record costs $0.90 to manufacture. in addition to the initial cost, each record costs $454 to manufacture. each record costs a total of $454.90 to manufacture.
The true statements are:
The initial cost for manufacturing records is $454, regardless of the number of records ordered.
In addition to the initial cost, each record costs $0.90 to manufacture.
Each record costs a total of $454.90 to manufacture.
As according to the question the function f(x)= 454+0.9x gives the cost, in dollars, of manufacturing x vinyl records.
Hence the incorrect statements are:
"The initial cost for manufacturing records depend on the quantity ordered".
"in addition to the initial cost, each record costs $454 to manufacture".
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Point Pis on line segment OQ.Given OQ = 4s – 10, OP = 23, and PQ = I,determine the numerical length of OP.
P
OQ = 4S - 10
OP = 23
PQ = 1
Equation
OQ = OP + PQ
Substitution
4S - 10 = 23 - 1
Simplification
4S = 22 + 10
4S = 32
S = 32/4
S = 8
Determine OP
OQ = 4(8) - 10
OQ = 32 - 10
OQ = 22
From the list of Al-alloy series below, select those that are considered age-hardenable. Only select answers you are sure are correct. Partial credit is available for each correct answer but negative marking is applied within this question it is not possible to score a negative mark for the question overall). O 1000 O 2000 O 3000 0 4000 O 5000 O 6000 7000
From list of Al-alloy series, age-hardenable aluminum alloy series are 2000, 6000, and 7000. These makes precipitation hardening.Other alloy series are not considered age-hardenable and have different properties
A process that involves the formation of fine precipitates within the alloy matrix, resulting in increased strength and hardness. The 2000 series alloys are known for their high strength and excellent mechanical properties, making them suitable for aerospace and structural applications.
The 6000 series alloys are widely used due to their good combination of strength, formability, and corrosion resistance, and are commonly employed in automotive and architectural applications. The 7000 series alloys offer exceptional strength and toughness and are frequently used in high-performance aerospace and defense applications.
The other alloy series listed (1000, 3000, 4000, and 5000) are not typically considered age-hardenable and have different properties and applications.
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Need help with 20 and 22
24
Because it we have to find x....
John is x years old now. five years ago,he was hal as old as he is now.how old is he now?
Answer:
Not enough information.
Geometry, dont need explanation. Just those 3 questions.
Answer:
1. B
2. A
3. C
Step-by-step explanation:
Liz is shipping a package to her friend. The maximum weight of a medium flat rate box is 20 pounds , including the box which weighs 6 ounces Write and solve an inequality to describe the possible weight in pounds , wof the contents that will ship to her friend she must medium flatrate box Use the drop-down menus to explain your answer
Answer:
19.625 pounds. i think
Step-by-step explanation:
HELP PELASE ASAPppppp
Answer:
Part 1 d/a = a/f
d/b = b/c
e/c = c/f
Explanation:
The triangles are similar.
This is about equal proportion. Look at the relationship between the short leg to the hypotenuse, short leg to long leg, and long leg to hypotenuse.
Part 2:
78
Explanation:
Calculate x, then substitute to get the lengths of the sides. Given equal angles, the two sides are equal.
5x –19 = 2x +11
3x = 30
x= 10
5(10) –19 = 31
2(10) + 11 = 31
Add the three sides: 31 +31 +16 = 78
Part 3:
Sin A= Cos B. both are a/b
Sin C= Cos A both are c/b
Sin C = c/b
Explanation:
Remember S=o/h, C=a/h , T=o/h
Look at the relationship of the sides to the angles given. If the sides match, the statement is true.
Sine of angle A is side a to side b. This is opposite/hypotenuse
Cosine of angle B is side a to side b This is adjacent/hypotenuse.
The lengths a and b are used in both. The hypotenuse don't change, but whether a side is considered an opposite or an adjacent depends on which angle you are looking at.
This can be confusing, but the more you practice, the easier it gets.
I hope this helps!