Answer:
55555555546776546567
nter (A,B,C,D)in order below if $A$, $B$, $C$, and $D$ are the coefficients of the partial fractions expansion of $$12\cdot\frac{x^3 4}{(x^2-1)(x^2 3x 2)}
The partial fraction expansion of (x³ + 4)/ ((x² - 1)(x² + 3x + 2)) is -3/ 4(x + 1) + 5/12(x - 1) + 4/3(x + 2) - 3/ 2(x + 1)². So the coefficients A = -3/4, B = 5/ 12, C = 4/3 and D = -3/2.
A partial fraction expansion is a way of expressing a rational function (a function that can be written as the ratio of two polynomials) as the sum of simpler fractions, each with a numerator that is a constant or a simple polynomial. The process of finding the partial fraction expansion of a rational function is also known as partial fraction decomposition.
The denominator is
(x² - 1)(x² + 3x + 2) = (x² - 1)(x² + x + 2x + 2)
(x² - 1)(x² + 3x + 2) = (x + 1)(x - 1)(x + 1)(x + 2)
So by partial fraction expansion
(x³ + 4)/ ((x² - 1)(x² + 3x + 2)) = (x³ + 4)/ ((x + 1)(x - 1)(x + 1)(x + 2))
(x³ + 4)/ ((x + 1)(x - 1)(x + 1)(x + 2)) = A/ (x + 1) + B/(x - 1) + C/(x + 2) + D/ (x + 1)²
A(x - 1)(x + 1)(x + 2) + B(x + 1)²(x + 2) + C(x + 1)²(x - 1) + D(x - 1)(x + 2) = x³ + 4
(A + B + C)x³ + (2A + 4B + C + D)x² + (-A + 5B - C + D)x + (-2A + 2B - C - 2D) = x³ + 4
Thus from coefficients of x³, x², x and 1,
A + B + C = 1
2A + 4B + C + D = 0
-A + 5B - C + D = 0
-2A + 2B - C - 2D = 4
Solving
A = -3/4, B = 5/ 12, C = 4/3 and D = -3/2
--The question is not clear, the question is given below--
"Enter (A,B,C,D) in order below if A, B, C, and D are the coefficients of the partial fractions expansion of
[tex]$$12\cdot\frac{x^3 + 4}{(x^2-1)(x^2 +3x+ 2)}[/tex] "
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answer correct and u get brainliest if u are able to answer this u r a math god
Answer:
184ft^2
Step-by-step explanation:
W have to find the area of triangles and rectangles and add them together to get the total area of the figure:
Area of triangles = 1/2(b)(h)
Area of rectangles = l x w
6 x 10 = 60
1/2(6)(4) = 12 (We can make this 12 a 24 because there are two of these triangles)
5 x 10 = 50 (We can also make this 50 a 100 because there are two of these rectangles)
100 + 24 + 60 = 184ft^2
Can a/the variable in a algebraic expression be a base?
Answer:
yes
Step-by-step explanation:
yes
yes
yes
yes
yeyed
yes
ANSWER BOTH!!!!
A. In a recent year, 22% of all college students were enrolled part-time. If 7.8 million college students were enrolled part-time that year, what was the total number of college students?
Round your answer to the nearest million.
B. Last year, Mai opened an investment account with $6200. At the end of the year, the amount in the account had increased by 24.5%. How much is this increase in dollars? How much money was in her account at the end of last year?
Increase in amount:$
Year-end amount:$
Answer:
A. 35 million
B. $1519 increase
$7719 year end
Step-by-step explanation:
Boxplots are NOT recommended for use with which of the following types of? distributions?
Choose the correct answer below.
a. Symmetric
b. Unimodal
c. Skewed
d. Bimodal or any multimodal distribution
Due to the fact that they obscure bimodality or any multimodality, boxplots are best reserved for distributions with a single mode.
Which distributions are unimodal?The distribution is said to be symmetrical when the box's whiskers are roughly the same on both sides and the median is in the centre of the box. The distribution is positively skewed if the whisker is shorter on the lower end of the box and the median is closer to the bottom of the box (skewed right).
Due to the fact that they obscure bimodality or any multimodality, boxplots are best reserved for distributions with a single mode.
There is just one peak in a unimodal distribution, two peaks in a bimodal distribution, and three or more peaks in a multimodal distribution. If the data is skewed or symmetric, such information can also be used to characterise the histogram's structure.
Therefore, the correct answer is option b) Unimodal.
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The required correct option for the given question is uni-modal.
Which distributions are uni-modal?The distribution is said to be symmetrical when the box's whiskers are roughly the same on both sides and the median is in the center of the box. The distribution is positively skewed if the whisker is shorter on the lower end of the box and the median is closer to the bottom of the box (skewed right).
Due to the fact that they obscure bi-modality or any multi-modality, box-plots are best reserved for distributions with a single mode.
There is just one peak in a uni-modal distribution, two peaks in a bimodal distribution, and three or more peaks in a multi-modal distribution. If the data is skewed or symmetric, such information can also be used to characterize the histogram's structure.
Therefore, the correct answer is option b) Uni-modal.
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Use I = P R T I=PRT to find the total amount in the savings account. Type in "money form". $1000.00 at 2.365% for 3 years
Answer:
70.95$
Step-by-step explanation:
P = $1000
R = 2.365%
T = 3 years
[tex]\frac{PRT}{100}[/tex] = [tex]\frac{1000*2.365 * 3}{100}[/tex] = [tex]\frac{7095}{100}[/tex] = 70.95$
Por cada 3 quetzales hay cuatro ajolotes y por cada 8 ajolotes hay 5 lobos mexicanos si hay unapoblacion de 150 quetzales ¿cuantos ajolotes hay?Y cuantos lobos mexicanos hay?
Answer:
Step-by-step explanation:
For every 3 quetzals there are four axolotls and for every 8 axolotls there are 5 Mexican wolves, if there is a population of 150 quetzals, how many axolotls are there? And how many Mexican wolves are there?
An 24 m tall statue was carved and the sculptor used a 8 cm. sketch of the statue as a blueprint. What scale did the sculptor use?
Solve. -3 + 9x = 24 (quick)
Answer: x = 3
Step-by-step explanation:
-3 +9x = 24
9x= 24+3
9x=27
9x/9= 27/9
x=3
Answer:
x = 3
Step-by-step explanation:
-3 + 9x = 24
rearrange:
9x - 3 = 24
Add 3 to both sides of the equation:
9x - 3 + 3 = 24 + 3
9x = 27
Divide both sides by 9:
9x/9 = 27/9
x = 3
Have a nice day!
no links, pls help!!
Answer:
look at the photo x is the red and y is the blue
someone help, need the answer asap
Answer:
A : 2x[tex]\sqrt{15}[/tex] b: 23.2
Step-by-step explanation:
How to solve 40 50 90 triangles
The 40 50 90 triangle can be solved using Pythagoras theorem.
What is the 40 50 90 triangle?A triangle in which both legs are congruent, and the length of the hypotenuse is the length of a leg times the square root of 2.
Given:
We have 40 50 90 triangles.
A triangle with two equal legs whose hypotenuse measures one leg's length multiplied by the square root of two.
Because the length of the hypotenuse in the triangle above equals the length of one of its legs times sqrt(2), which is 3, the triangle is a 40-50-90 triangle.
So, Such type of Triangles can be solved using Pythagoras theorem.
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90 minus 10x
ill give 25 points and brainiest
Answer:
80x
Step-by-step explanation:
There is no substitution for the variable so the expression is 80x
The three largest categories of motor vehicles are sedan, SUV, and minivan. Suppose
hat of the buyers in a particular community who now own a minivan, 18% will change to
an SUV and 20% will change to a sedan. Of the buyers who now own a sedan, 35% will
hange to a minivan and 20% will change to an SUV, and of those who now own an
SUV, 12% will buy a minivan and 32% will buy a sedan.
Draw a transition diagram that displays these changes.
On solving the provided question, we can say that - here in the percentage obtained = 40 => so, 40/100X100 = 40%
What is percentage?A percentage in mathematics is a figure or ratio that is stated as a fraction of 100. The abbreviations "pct.," "pct," and "pc" are also occasionally used. It is frequently denoted using the percent symbol "%," though. The amount of percentages has no dimensions. With a denominator of 100, percentages are basically fractions. To show that a number is a percentage, place a percent symbol (%) next to it. For instance, if you correctly answer 75 out of 100 questions on a test (75/100), you receive a 75%. To compute percentages, divide the amount by the total and multiply the result by 100. The percentage is calculated using the formula (value/total) x 100%.
here,
total is = 100
obtained = 40
so, 40/100X100 = 40%
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10 points NO SENDING LINKS JESUS CHRIST
Answer:
387420489
Step-by-step explanation:
I hope this helps if not let me know in the comments
here is the qr code it will show you the steps on how to do it if you click on it
David went shopping for a new phone because of a sale. The price on the tag was $46, but David paid $39. 10 before tax. Find the percent discount
The percent discount on the new phone is 15%.
Discount refers to a reduction in the original price of a product or service. It is a way for businesses to incentivize customers to purchase their products by offering a lower price than the original price.
To find the percent discount, we need to divide the amount of the discount by the original price, and then multiply by 100 to express the answer as a percentage.
Discount = Original Price - Sale Price
Discount = $46 - $39.10
Discount = $6.90
Percent Discount = (Discount / Original Price) x 100
Percent Discount = ($6.90 / $46) x 100
Percent Discount = 15%
Therefore, the percent discount is 15%.
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What are the factors of this quadratic function?
A. (x - 1) and (x - 5)
B. (x + 1) and (x + 5)
C. (x - 1) and (x+5)
D. (x + 1) and (x - 5)
An earth day even will cost 15$ for 3 people to attend. If there are four people attending, how much will the Earth Day fun event cost? Pls, Help me!!!!
Answer: 20$
5$ for each person attending. Hope it helps.
Answer:
$20
Step-by-step explanation:
the unit rate (cost per person) is
$15
-------------- = $5/person
3 people
For four people the total cost would be (4 people) ($5/person) = $20
A cylindrical potato chip container has a diameter of 3.5 inches and a height of 12 inches. What is the volume of the chip container? Use 3.14 for pi. Round your answer to the nearest hundredth.
57.73 in3
115.40 in3
350.65 in3
461.81 in3
Answer:
V = 38.47 in^3
Step-by-step explanation:
The container base radius is half the diameter, that is, 1.75 in, and the height is 12 in. The formula for the volume of a cylinder of radius r and height h is V = (1/3)(pi)(r)^2h, which in this particular case comes out to:
V = (1/3)(3.14)(1.75 in)^2*(12 in), or
V = 38.47 in^3
Answer:
115.40 in3
that is the correct answer to this question.
Please help with math assignment
Answer:
a = 4√2, h = 2√3
Experimental probability is the result of an experiment. Theoretical probability is what is expected to happen.
Answer:
See Explanation
Step-by-step explanation:
The question is incomplete, and it can be interpreted in different ways.
Is the question a true or false question?
If yes, then both statements are true
As a further explanation, we consider a roll of die.
The sample space is:
[tex]S = \{1,2,3,4,5,6\}[/tex]
Because 1 to 6 appear just once on the die, then each have a probability of 1/6
[tex]Pr = \frac{1}{6}[/tex] --- This is referred to as the theoretical probability
But if after rolling the die 6 times, the outcome is:
[tex]Outcome = \{1,1,4,5,1,2\}[/tex]
The experimental probability of (say 1) is, the number of times 1 appeared divided by the number of times the experiment is carried out.
i.e.
[tex]Pr(1) = \frac{3}{6}[/tex]
How many solutions
y=10x+2
y=8x+2x+2
Answer:
Infinutely many solutions
Step-by-step explanation:
y = 10x + 2 --------- (1)
y = 8x +2x +2
=> y = 10x + 2---------- (2)
(1) -> 10x -y + 2 = 0
(2) -> 10x -y + 2 = 0
a1=10 ; b1=-1 ; c1 = 2
a2=10 ; b2=-1 ; c2= 2
a1/a2 = 10/10 = 1
b1/b2 = -1/-1 = 1
c1/c2 = 2/2 = 1
therefore, a1/a2 = b1/b2 = c1/c2
Therefore the line coincides and there are infinitely many solutions.
Hello. Please answer!
A triangle has sides with lengths of 12 feet, 16 feet, and 18 feet. Is it a right triangle?
Answer:
Step-by-step explanation: If the sides are a,b,c (in ascending order) and c squared = the sum of the squares of a and b, then it's a right triangle.
Answer:
No, it is not a right triangle.
Step-by-step explanation:
Right triangle fulfill the pythagorean theorem:
[tex]a^2+ b^2 = c^2[/tex]
Where, c is the hypothenuse or the longest side, and b and a are the remaining two sides.
[tex]12^{2} = 144\\16^2 = 256\\256 + 144 = 400\\\sqrt {400} = 20 \neq 18[/tex]
Find the midpoint of A and B where A has coordinates (2,3) and B has coordinates (8,9)
Step-by-step explanation:
[tex]midpoint = ( \frac{(2 + 8)}{2} , \frac{(3 + 9)}{2} ) \\ = (5,6)[/tex]
Answer:
√(x2-x1)²+(y2-y1)²
√(8-2)²+(9-3)²
√6²+6²
√36+36
√72
8.48528137424≈8.5
Step-by-step explanation:
vanessa will sell yogurt for $2.50 a cup fill in the table to show how much money Vanessa will make if she sells 19 cups of vanilla yogurt
answer: 47.5 cups
Step-by-step explanation:
2.50 x 19 = answer
Solve this problem
Step by step
The measure of the missing length of the trapezoid is equal to 3√39 units.
How to determine the missing length of a trapezoid
Trapezoids are quadrilaterals with only one pair of congruent sides and two pairs of congruent angles. The relationship between the longest and shortest legs (D, d) in a trapezoid is defined below:
D = d + 2 · c
Where c is the length of the horizontal leg of the right triangle in a trapezoid.
And the missing leg can be found by means of Pythagorean theorem:
x = √(r² - c²)
Where:
r - Hypotenusec - Shortest legx - Longest legFirst, determine the length of shortest leg: (D = 40, d = 26)
40 = 26 + 2 · c
14 = 2 · c
c = 7
Second, find the longest leg by Pythagorean theorem:
x = √(20² - 7²)
x = 3√39
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where is the vertex located on the graph of y=(x+7)(x+1)
Answer:
The vertex is (-4, -9)
Step-by-step explanation:
The two roots are located at x = -7 and x = -1, which come from (x + 7) and (x + 1). The axis of symmetry is located halfway between these values, at x = -4. This axis passes through the vertex. The y-value at the vertex is (-4 + 7)(-4 + 1), or -9. The graph is a parabola that opens up. The vertex is (-4, -9).
What is the range of this function?
(-9, 10) (19, 18) (0,7) (20,3)
Point lies on the diagonal of square with . Let and be the circumcenters of triangles and respectively. Given that and , then , where and are positive integers. Find .
Point P lies on the diagonal AC of square ABCD with AP > CP. Let [tex]$O_1$[/tex] and [tex]$O_2$[/tex] be the circumcenters of [tex]$\triangle \mathrm{ABP}$[/tex] and [tex]$\triangle \mathrm{CDP}$[/tex] respectively. Given that AB = 12 and [tex]$\angle \mathrm{O}_1 \mathrm{PO}_2=120^{\circ}$[/tex], then [tex]$\mathrm{AP}=\sqrt{\mathrm{a}}+\sqrt{\mathrm{b}}$[/tex],
where a and b are positive integers.
The value of a + b is 96.
Let mid-point of DC be E and mid-point of AB be F.
Since [tex]$\mathrm{O}_1$[/tex] and [tex]$\mathrm{O}_2$[/tex] are circumcenters, therefore both lie on the perpendicular bisectors of DC and AB passing through E and F.
Now, [tex]$\mathrm{O}_1 \mathrm{P}=\mathrm{O}_1 \mathrm{~B}$[/tex] and [tex]$\mathrm{O}_2 \mathrm{P}=\mathrm{O}_2 \mathrm{D}$[/tex]
Also [tex]$\angle \mathrm{CAB}=\angle \mathrm{ACD}=45^{\circ}$[/tex]
Therefore [tex]\angle \mathrm{BO}_1 \mathrm{P}=2 \times 45^{\circ}=90^{\circ}=\angle \mathrm{DO}_2 \mathrm{P}$[/tex]
Angle subtended by an arc of a circle at its center = 2 × the angle subtended at its circumference
Therefore [tex]\angle \mathrm{O}_1 \mathrm{~PB}$[/tex] and [tex]$\angle \mathrm{O}_2 \mathrm{PD}$[/tex] are isosceles right triangles.
Using the above information and symmetry,
[tex]$\angle \mathrm{DPB}=120^{\circ}$[/tex]
Also, [tex]$\triangle[/tex]ABP is congruent to [tex]$\triangle[/tex]ADP (SAS)
and [tex]$\triangle[/tex]CPB is congruent to [tex]$\triangle[/tex]CPD (SAS)
Therefore [tex]\angle \mathrm{APB}=\angle \mathrm{APD}=60^{\circ}[/tex]
And [tex]\angle \mathrm{CPB}=\angle \mathrm{CPD}=120^{\circ}[/tex]
Now, [tex]$\angle \mathrm{ABP}=(180-60-45)^{\circ}=75^{\circ}$[/tex]
[tex]\Rightarrow \angle \mathrm{O}_1 \mathrm{BF}=30^{\circ}[/tex]
And [tex]$\angle \mathrm{PDC}=(180-120-45)^{\circ}=15^{\circ}$[/tex]
[tex]\Rightarrow \angle \mathrm{O}_2 \mathrm{DE}=30^{\circ}[/tex]
Therefore [tex]\triangle \mathrm{O}_1 \mathrm{BF}$[/tex] and [tex]$\triangle \mathrm{O}_2 \mathrm{DE}$[/tex] are right angled triangles.
BF = DE = [tex]\frac{12}{2}[/tex] = 6
[tex]\Rightarrow O_1 B=O_2 D=4 \sqrt{3}[/tex]
And PB = PD = [tex]\frac{4 \sqrt{3}}{\cos 45^{\circ}}=4 \sqrt{6}[/tex]
Now, Let x = AP
Using law of cosine on [tex]$\triangle[/tex]ABP, we have
[tex]& 96=x^2+144-24 x \times \frac{1}{\sqrt{2}} \\[/tex]
[tex]& \Rightarrow x^2-12 \sqrt{2} x+48=0 \\[/tex]
[tex]& \Rightarrow x=\sqrt{72} \pm \sqrt{24}[/tex]
Taking the positive root, AP = [tex]\sqrt{72}+\sqrt{24}$[/tex]
Therefore a + b = 72 + 24 = 96
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Point P lies on the diagonal AC of square ABCD with AP > CP. Let [tex]$O_1$[/tex] and [tex]$O_2$[/tex] be the circumcenters of [tex]$\triangle \mathrm{ABP}$[/tex] and [tex]$\triangle \mathrm{CDP}$[/tex] respectively. Given that AB = 12 and [tex]$\angle \mathrm{O}_1 \mathrm{PO}_2=120^{\circ}$[/tex], then [tex]$\mathrm{AP}=\sqrt{\mathrm{a}}+\sqrt{\mathrm{b}}$[/tex], where a and b are positive integers. Find a + b. (correct answer +5, wrong answer 0 )