Given that Ax - 4x² + 3x² + 4 = (x² - 2x + 1)(2x² + B) + C(x-1) + D for all values of x, evaluate A, B, C and D. Hence, deduce the remainder when Ar-4x+3x²+4 is divided by 2x² + B.
Answers
SANA MAKATULONG
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Related Questions
Can someone help me please?
Answers
Answer: a=(3,-4)
B=(3,-1)
C=(5,-2)
Step-by-step explanation:
Is x=−10 a solution to the equation 28x+17=157?
Answers
Answer:
no
Step-by-step explanation:
28x+17=157 Subtract 17 on both sides.
-17 -17
28x=140
x=5
5 does not equal -10, so -10 is not a solution to the equation 28x+17=157.
Hope this helps!! Have a great day :)
A large container in the shape of a rectangular solid must have a volume of 480 m3. The bottom of the container costs $5/m2 to construct whereas the top and sides cost $3/ m2 to construct. Use Lagrange multipliers to find the dimensions of the container of this size that has the minimum cost
Answers
The dimension of the container of this size that has the minimum cost is [tex]x = \sqrt[3]{360}[/tex], [tex]y = \sqrt[3]{360}[/tex] and [tex]z =\frac{4}{3} \sqrt[3]{360}[/tex]
The given parameters are:
Volume = 480m^3Cost: $5 per square meter for the bottom, and $3 per square meter for the sides.Assume the dimensions of the container are: x, y and z.
The volume (V) would be:
[tex]V = xyz[/tex]
Substitute 480 for V
[tex]xyz =480[/tex]
And the objective cost function would be:
[tex]C =8xy + 6xz + 6yz[/tex]
Differentiate the cost function using Lagrange multipliers
[tex]8x + 6z = \lambda xz[/tex]
[tex]8y + 6z = \lambda yz[/tex]
[tex]6x + 6y = \lambda xy[/tex]
Divide equation (1) by (2)
[tex]\frac{8x + 6z}{8y + 6z} = \frac{\lambda xz}{\lambda yz}[/tex]
[tex]\frac{8x + 6z}{8y + 6z} = \frac{x}{y}[/tex]
Factor out 2
[tex]\frac{4x + 3z}{4y + 3z} = \frac{x}{y}[/tex]
Cross multiply
[tex]4xy + 3yz = 4xy + 3xz[/tex]
Evaluate the like terms
[tex]3yz = 3xz[/tex]
Divide both sides by 3z
[tex]y = x[/tex]
Divide the first equation by the third
[tex]\frac{8y + 6z}{6x + 6y} = \frac{\lambda yz}{\lambda xy}[/tex]
[tex]\frac{8y + 6z}{6x + 6y} = \frac{z}{x}[/tex]
Factor out 2
[tex]\frac{4y + 3z}{3x + 3y} = \frac{z}{x}[/tex]
Cross multiply
[tex]4xy+3xz = 3xz + 3yz[/tex]
Cancel out the common terms
[tex]4xy = 3yz[/tex]
Divide both sides by y
[tex]4x = 3z[/tex]
Make z the subject
[tex]z =\frac{4}{3}x\\[/tex]
So, we have:
[tex]y = x[/tex] and [tex]z =\frac{4}{3}x\\[/tex]
Recall that:
[tex]xyz =480[/tex]
Substitute [tex]y = x[/tex] and [tex]z =\frac{4}{3}x\\[/tex]
[tex]x \times x \times \frac 43x = 480[/tex]
So, we have:
[tex]\frac 43x^3 = 480[/tex]
Multiply both sides by 3/4
[tex]x^3 = 360[/tex]
Take the cube roots of both sides
[tex]x = \sqrt[3]{360}[/tex]
Recall that:
[tex]y = x[/tex]
So, we have:
[tex]y = \sqrt[3]{360}[/tex]
Also, we have:
[tex]z =\frac{4}{3}x\\[/tex]
So, we have:
[tex]z =\frac{4}{3} \sqrt[3]{360}[/tex]
Hence, the dimension of the container of this size that has the minimum cost is [tex]x = \sqrt[3]{360}[/tex], [tex]y = \sqrt[3]{360}[/tex] and [tex]z =\frac{4}{3} \sqrt[3]{360}[/tex]
Read more about Lagrange multipliers at:
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on a map where each unit represent one kilometer, two marainas are located at p(4,2) and Q(8,12). if a boat travels in a straight line from one marina to the other, how far does the boat travel?
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Answer: 5 kilometers.
Step-by-step explanation:
what percent of 81 is 51
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Answer:
62.96%
Step-by-step explanation:
do this
51/81 ×100%
Answer:62.953%
Step-by-step explanation:
81 * (%) = 51
% = 51 / 81
% = 62.953
b) the difference between three and x
Math
Answers
Answer:
3 - x
Step-by-step explanation:
In math, "the difference between A and B" usually means ...
A - B
In English, it often means ...
|A - B| . . . . the positive difference
__
"The difference between 3 and x" can be written as the expression ...
3 - x
please help meeee, thank youuuu
Answers
Answer:
45
Step-by-step explanation:
I think so i dont know
Answer:
45
Step-by-step explanation:
Just do the regular number sequence (1-44) but add 1 since this specific sequence starts with 2.
Hope this helped! ^^Calculate the area of trapezium CDEF.
Answers
Answer:
i think 24 cm² is answer good luck
After Donovan gives Mabel 6 pears, she has
(x + 6) pears. If Mabel gives one-third of her
pears to Nelson, how many pears, in terms
of x, does Nelson have?
Answers
Answer:
see explanation
Step-by-step explanation:
Mabel has (x + 6) pears , then Nelson has
[tex]\frac{1}{3}[/tex] (x + 6) = [tex]\frac{1}{3}[/tex] x + 2
The number of pears that Nelson has in terms of x will be x / 3 + 2.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
After Donovan gives Mabel 6 pears, she has (x + 6) pears.
If Mabel gives one-third of her pears to Nelson. Then the number of pears that Nelson has in terms of x will be calculated as,
⇒ (x + 6) / 3
Simplify the equation, then we have
⇒ (x + 6) / 3
⇒ x / 3 + 2
The number of pears that Nelson has in terms of x will be x / 3 + 2.
More about the Algebra link is given below.
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a cylinder has a radius of 3 feet and a height of 2.1 feet. what is the approximate volume of the cylinder? use 3.14 for pi. 12.6 ftł 59.3 ftł 237.5 ftł 8550.2 ftł
Answers
Answer:
59.3ft³
Step-by-step explanation:
The formula for the volume of a cylinder is V= πr²h, where r is radius and h height.
So in our case, we have r= 3ft and h=2.1 ft and π≅3.14
So from the formula for the volume of a cylinder, we get 3.14*3²*2.1 = 59.3 ft³
The volume of the cylinder is about 59.3 ft³
simplify an expression for the perimeter of the rectangle
Answers
6w+10w-4
16w-4
16w-4
Hope this helps!!
The expression for the Perimeter of rectangle is 16w-4.
What is perimeter of rectangle?The perimeter of a form is the space surrounding its edge. Find the perimeter of various forms by summing the lengths of their sides.
Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Perimeter of the rectangle = 2(length+width)
Given the paramters are;
length = 5w-2
width = 3w
Perimeter of the rectangle = 2(length+width)
Perimeter = 3w+3w+(5w-2)+(5w-2)
= 6w+10w-4
= 16w-4
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this question is hard
Answers
A) Total number of old plans = 3500 + 4700 = 8200
In the new month, the unlimited plans increased by 55%, which adds
0.55 • 3500 = 1925
unlimited plans, while the limited plans decreased by 25%, which subtracts
0.25 • 4700 = 1175
limited plans. Then
Total number of new plans = (3500 + 1925) + (4700 - 1175) = 8950
which corresponds to a percent change of
(8950 - 8200)/8200 ≈ 0.0915 = 9.15%
That is, percent change is given by
(new value - old value) / (old value)
B) The percent change is positive, so it's a percent increase.
IS IT VALID OR NOT (explaining would be helpful) you want to determine how many students consider math to be their favorite school subject. you randomly survey 75 students. thirty-three students consider math to be their favorite subject while forty-two does not. so, you conclude that 40% of students at your school consider math to be their favorite subject.
Answers
Answer:
I would say not valid
Step-by-step explanation:
well, it would actually be 44% since 33/75= 0.44 to represent the number of ppl hat consider math their favorite subject
Cans of peas are on sale at 2 for $1.19 how much would 12 cans cost
Answers
Answer:uh 2 divide 1.19 and add 12 i think
Step-by-step explanation:
3. Avery noticed that of the apples in a basket are red. There are 45 red apples in the basket.
(a) Represent the situation with an equation. Use a for the variable.
(b) Solve the equation in Part (a). Show your work.
(c) What does the solution of the equation represent in the situation?
Answers
Answer:
Step-by-step explanation:
Something missing in "noticed that of the apples." Perhaps "that 40% of . . .?"
But I'll try to answer, using an example:
Avery noticed that 30% of the apples in a basket are red. There are 45 red apples in the basket.
To find the total number of apples, X:
(0.30)X = 45
X = 150 apples total. 45, or 45/150, is 0.3 0r 30%.
AMIGOS AND AMIGAS PLS HELP MY POOR BRAIN ILY FAM:
1) 8+ 9p = 9p - 7
2) 2(3x + 6) = 3(2x - 6)
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1. 9p - 9p = -8 - 7
0 = - 15
2. 6x + 12 = 6x - 18
6x - 6x = - 18 - 12
0 = - 30
That's what I got
Kyle was playing archery and shot 20 arrows. 30% of them hit the bullseye. how many of the arrows hit the bullseye?
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0.2 = 1%
6 = 30%
6 arrows hit the bullseye
Slope= -1/2 Y-intercept =4
Answers
Answer:
no I'm pretty sure it's wrong
Step-by-step explanation:
the y intercept for that to right us -4
Solve the inequality f – 4 ≤ 9 for f
help me.
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Answer:
13
Step-by-step explanation:
Have a great day!! :)
Translate and solve. The quotient of m and 6/7 is 5/6
Answers
Answer:
m / 6/7 = 5/6
m = 35
Step-by-step explanation:
Answer:
m = 5/7Step-by-step explanation:
The quotient of m and 6/7 is 5/6:
m ÷ 6/7 = 5/6m = 5/6 × 6/7m = 5/7What is the number of solutions to the system of
equations?
Infinitely Many
Solutions
No Solution
One Solution
Two Solutions
Answers
Answer:
infinitely many solutions
Step-by-step explanation:
The lines over lap
The minute hand of a clock has a length of 12 cm, and the hour hand has a length of 8 cm
a) How far does the tip of the minute hand travel in one hour?
b) How far does the tip of the hour hand travel in 12 hours?
c) How far does the tip of each hand travel in one week?
Answers
Answer:
I have no any ideas
Step-by-step explanation:
sorry
how do i tell if an angel is comolentery, supplmentsry, or neither? I was not at school the day they showed me this?
Answers
Answer:
supplementary angles - two angles are supplementary when they add up to 180 degrees (a straight line)
complementary angles - two angles are complementary when they add up to 90 degrees (a right angle)
hopefully this helps! :)
Answer:
1. complementary
2. neither
3. supplementary
4. complementary (x = 6)
10x + 30 = 90 x + 3 = 9 x = 6
5. supplementary (x = 20)
4x + 40 + 3x = 180 7x = 140 x = 20
6. x = 50.5
2x + 79 = 180 2x = 101 x = 50.5
Step-by-step explanation:
When the measurement of the angles adds up to 90 degrees, the angles are complementary. When the sum of the angles is 180 degrees, then they are supplementary.
3,408 divided by 41
Explanation in traditional method
52 POINTS PLS HELP
Answers
Answer:
83.1219512195
Step-by-step explanation:
Hope this helps!
83.12195
traditional method is either long division or short division
What is the common denominator of StartFraction 1 Over a EndFraction StartFraction 1 Over b EndFraction in the complex fraction StartFraction 1 Over a EndFraction minus StartFraction 1 Over b EndFraction divided by StartFraction 1 Over a EndFraction 1 Over b EndFraction?.
Answers
The common denominator is 1
Given the expression:
[tex]\frac{1/a-1/b}{1/a1/b}[/tex]Find the LCM of the numerator to have:
[tex]\dfrac{\frac{b-a}{ab} }{\frac{1}{a} \frac{1}{b} }[/tex]Simplify both the numerator and the denominator to have:
[tex]= \dfrac{\frac{b-a}{ab} }{\frac{1}{ab} }\\= \frac{b-a}{ab} \times ab\\=\frac{b-a}{1} \times 1 \\=\frac{b-a}{1}[/tex]
From the result, we can see that the common denominator is 1
Learn more about fractions here: https://brainly.com/question/17743912
Answer:
here is the correct answer for edge2022
Step-by-step explanation:
What is the probability that a student took AP Chemistry, given they did not get into their first-choice college? Enter
your answer as a decimal to the ten thousandths place.
Answers
Using conditional probability, it is found that there is a 0.2273 = 22.73% probability that a student took AP Chemistry, given they did not get into their first-choice college.
Conditional Probability
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened. [tex]P(A \cap B)[/tex] is the probability of both A and B happening. P(A) is the probability of A happening.In this problem:
Event A: Did not get into their first-choice college.Event B: Took AP chemistry.According to the chain given, the percentages associated with not getting into their first-choice college are:
0.1375(chemistry).0.1575(physics).0.24(Env Sci).0.07(Biology).Hence:
[tex]P(A) = 0.1375 + 0.1575 + 0.24 + 0.07 = 0.605[/tex]
The probability of both not getting into their first-choice college and taking chemistry is 0.1375, hence [tex]P(A \cap B) = 0.1375[/tex]
Then, the conditional probability is:
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.1375}{0.605} = 0.2273[/tex]
0.2273 = 22.73% probability that a student took AP Chemistry, given they did not get into their first-choice college.
To learn more about conditional probability, you can take a look at https://brainly.com/question/14398287
Answer: 0.2273
Step-by-step explanation: because it says so <3
PLEASE SHOW YOUR WORK !!! I REALLY NEED HELP
Answers
I did the math in the link below
After the first four games of a professional football season, three players scored a total of 80 touchdowns.
Duke Johnson scored 14 of the touchdowns.
Josh McCown scored 40% of the touchdowns.
Andre Roberts scored the remaining touchdowns.
How many touchdowns did Andre Roberts score?
A.20 touchdowns
B.28 touchdowns
C.32 touchdowns
D.52 touchdowns
Answers
Answer:
b
Step-by-step explanation:
Andre Roberts scored a total of 34 touchdowns
An equation is an expression that shows the relationship between two or more variables and numbers.
The total touchdowns is 80.
Duke Johnson scored 14 of the touchdowns.
Josh McCown scored 40% of the touchdowns. = 40% of 80 = 0.4 * 80 = 32
Let x represent the number of touchdowns scored by Andre Roberts, hence:
x + 14 + 32 = 80
x + 46 = 80
x = 34
Andre Roberts scored a total of 34 touchdowns
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HELLPPPP MEEEEE ASAPPPPPPP PLEASEEEEEEEEEEEEWEEEEEEEE
Answers
Answer:SORRY CANT HELP U THERE
Step-by-step explanation:
Find the slope of the line segment shown.
A) -1/2
B -1
C 1/3
D 1
Answers
Answer:
D)
Step-by-step explanation:
The answer would be D. The slope of a line is how fast it climbs. Height divided by base. Up divided by over. Thus, if it goes across 3 and up 1, its slope would be 1/3. If it goes across 1 and up 2, the slope is 2. If it goes across 1 and up -1, the slope is -1.
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