Answer:
[tex]A=5, B=0,C=3[/tex]
Step-by-step explanation:
The partial fraction decomposition is given as:
[tex]\frac{5x^2+3x+54}{(x+3)(x^2+9)} \equiv \frac{A}{x+3}+\frac{Bx+C}{x^2+9}[/tex]
We collect LCD on the RHS to obtain;
[tex]\frac{5x^2+3x+54}{(x+3)(x^2+9)} \equiv \frac{A(x^2+9)+(x+3)(Bx+C)}{(x+3)(x^2+9)}[/tex]
We expand the parenthesis in the numerator of the fraction on the RHS.
[tex]\frac{5x^2+3x+54}{(x+3)(x^2+9)} \equiv \frac{Ax^2+9A+Bx^2+(3B+C)x+3C}{(x+3)(x^2+9)}[/tex]
This implies that:
[tex]\frac{5x^2+3x+54}{(x+3)(x^2+9)} \equiv \frac{(A+B)x^2+(3B+C)x+3C+9A}{(x+3)(x^2+9)}[/tex]
This is now an identity. Since the denominators are equal, the numerators must also be equal.
[tex]5x^2+3x+54=(A+B)x^2+(3B+C)x+3C+9A[/tex]
We compare coefficients of the quadratic terms to get:
[tex]A+B=5\implies B=5-A...(1)[/tex]
Also the coefficients of the linear terms will give us:
[tex]3B+C=3...(2)[/tex]
The constant terms also gives us;
[tex]3C+9A=54...(3)[/tex]
Put equation (1) in to equations (2) and (3).
[tex]3(5-A)+C=3\implies C=3A-12...(4)[/tex]
[tex]3C+9A=54...(5)[/tex]
Put equation (4) into (5).
[tex]3(3A-12)+9A=54[/tex]
[tex]9A-36+9A=54[/tex]
[tex]9A+9A=54+36[/tex]
[tex]18A=90[/tex]
[tex]A=\frac{90}{18} =5[/tex]
Do backward substitution to get:
[tex]C=3(5)-12=3[/tex]
[tex]B=5-5=0[/tex]
[tex]\therefore A=5, B=0,C=3[/tex]
The constants A, B, and C in the partial fraction decomposition are determined to be A = 5, B = 0, and C = 3.
To find the values of A, B, and C in the partial fraction decomposition of the rational function
Therefore, the number of adul, follow these steps:
First, express the function as: [tex](5x^2 + 3x + 54) / ((x+3)(x^2 + 9)) = A/(x+3) + (Bx + C)/(x^2 + 9).[/tex]Multiply both sides by [tex](x+3)(x^2 + 9)[/tex] to eliminate the denominators: [tex]5x^2 + 3x + 54 = A(x^2 + 9) + (Bx + C)(x + 3).[/tex]Expand and combine like terms: [tex]5x^2 + 3x + 54 = Ax^2 + 9A + Bx^2 + 3Bx + Cx + 3C.[/tex]Combine like terms: [tex]5x^2 + 3x + 54 = (A + B)x^2 + (B + C)x + (9A + 3C).[/tex]Match coefficients for corresponding powers of x:For [tex]x^2[/tex]: 5 = A + BFor x: 3 = B + CConstant term: 54 = 9A + 3CSolving these equations:From 5 = A + B, we get B = 5 - A.From 3 = B + C, substitute B: 3 = (5 - A) + C ⟹ C = -2 + A.From 54 = 9A + 3C, substitute C: 54 = 9A + 3(-2 + A) ⟹ 54 = 12A - 6 ⟹ 60 = 12A ⟹ A = 5.Substitute A into B and C: B = 0, C = 3.Thus, the values are A = 5, B = 0, and C = 3.Factorise completely
200y²-18x²
Answer: 2(10y+3x)(10y-3x)
Step-by-step explanation:
2(100y²- 9x²)
2[ (10y+3x)(10y-3x) ]
Find the missing triangle. Leave answer in simplest radical form. Also please explain clearly.
Answer:
Pythagorean Theorem
hypotenuse^2 = side^2 + side^2
16^2 = 7^2 + side ^ 2
256 - 49 = side^2
side x = sq root (207)
207 = 9 * 23 Therefore,
side x = 3 * sq root (23)
answer is A
Step-by-step explanation:
The slope of a line is -1/2 . What is the slope of a line that is parallel to it? A. 1/2 B.2 C. -1/2 D. -2
Step-by-step explanation:
We know any line that is parallel to other line has same slope.
Here, m1=m2
So, slope will be -1/2.
For this case we have by definition, that if two lines are parallel then their slopes are equal. That is to say:
[tex]m_ {1} = m_ {2}[/tex]
If we have a line of the form:
[tex]y_ {1} = - \frac {1} {2} x_ {1} + b_ {1}[/tex]
Then a parallel line will be given by:
[tex]y_ {2} = - \frac {1} {2} x_ {2} + b_ {2}[/tex]
That is, the slopes are the same!
Answer:
Option C
Sone for x and y
2x -y = 11
3x – 2y=6
Select one
a. (16.-21)
b. (4, -3)
c. (-3,4)
d. (16,21)
Answer:
d
Step-by-step explanation:
Given the 2 equations
2x - y = 11 → (1)
3x - 2y = 6 → (2)
Multiply (1) by - 2 and adding will eliminate y
- 4x + 2y = - 22 → (3)
Add (2) and (3) term by term
(3x - 4x) + (- 2y + 2y) = (6 - 22)
- x = - 16 ( multiply both sides by - 1 )
x = 16
Substitute x = 16 into (1) or (2) for corresponding value of y
(1) : 32 - y = 11 ( subtract 32 from both sides )
- y = - 21 ( multiply both sides by - 1 )
y = 21
Solution is (16, 21 ) → d
Answer:
It's d. (16,21).
Step-by-step explanation:
2x - y = 11 .............(1)
3x – 2y = 6...........(2)
Multiply the first equation by -2:
-4x + 2y = -22.......(3)
Adding (2) + (3):
-x = -16
x = 16.
Substitute for x in equation (1):
2(16) - y = 11
-y = 11-32 = -21
y = 21.
help me plzzzzzzzzz
Answer:
Whats the question?
Step-by-step explanation:
Please answer this correctly
0.001, 0.014, 0.1, 9.41
6. Simplify:
(1) (37 - (-8)]+[11 - (-30)]
Plz answer
Answer:
86
Step-by-step explanation:
Since something minus a negative is just adding, we get 37-(-8)=37+8 or 45. We can do the same with 11-(-30) which is 11+30 or 41. So 45+41=86
Answer:
86.
Step-by-step explanation:
Work out the 'inner' parentheses first:
(37 - (-8)] + [11 - (-30)]
= (37 + 8) + (11 + 30)
Now the outer parentheses:
= 45 + 41
= 86.
f(X)=-2x-3
g(X)=3X+1
find (fxg)(X)
The value of [tex]f(g(x))=-6x-5[/tex]
Composite function :Given functions are, [tex]f(x)=-2x-3,g(x)=3x+1[/tex]
We have to find composite function [tex]f(g(x))[/tex].
[tex]f(g(x))=f(3x+1)\\\\f(g(x))=-2(3x+1)-3\\\\f(g(x))=-6x-2-3\\\\f(g(x))=-6x-5[/tex]
Learn more about the composite function here:
https://brainly.com/question/10687170
To find (fxg)(X), you need to multiply the two given functions, apply the distributive property, and then combine like terms. The result for (fxg)(X) is -6x² - 11x - 3.
Step-by-step Explanation:
First, write out the functions: f(X) = -2x - 3 and g(X) = 3X + 1.Multiply the two functions together: h(X) = (-2x - 3)(3x + 1).Apply the distributive property: h(X) = -2x * 3x + (-2x) * 1 + (-3) * 3x + (-3) * 1.Simplify each term: h(X) = -6x² - 2x - 9x - 3.Combine like terms: h(X) = -6x² - 11x - 3.Therefore, (fxg)(X) = -6x² - 11x - 3.
The table below represents how Marco feels about chocolate candy bars.
Answer:
The satisfaction level gained when a customer consumes a product is total utility.It calculated by finding the total sum of utility from consumption.
Marginal utility is the rate of change of total utility and quantity consumed.
Here you apply the expression, Marginal utility=change in total utility/change in quantity consumed
Let, Marginal utility=MU
Total utility=TU
Quantity consumed=QC
Then MU=ΔTU ÷Δ QC
Given the table
Chocolate Candy Bars Total Utility(utils) Marginal Utility(utils)
0 0 -
1 25 x
2 y 17
3 54 z
4 a b
5 66 4
6 c -1
Here you have assigned the missing areas with letter, hence finding the real values of the letters;
Apply MU=ΔTU÷ΔQC
[tex]1.17=\frac{y-25}{1}\\\\17=y-25\\\\y=17+25=42\\\\\\2.x=\frac{25-0}{1} \\\\x=25-0=25\\\\\\3.z=\frac{54-42}{1} \\\\z=54-42=12\\\\\\4.\frac{66-a}{1} =4\\\\66-a=4\\\\66-4=a\\a=62\\\\5.b=\frac{62-54}{1} =8\\\\\\6.\frac{c-66}{1} =-1\\\\\\c-66=-1\\\\c=-1+66=65[/tex]
Answers
y=42,x=25,z=12,a=62,b=8,c=65
Replace the letters with the real numbers in filling the table.
What is the formula to find the Lateral Area of a pyramid
Answer: The general equation for the lateral area of a pyramid is LSA=(1/2)pl
P is the perimeter
L is the slant
HELP! What type of association does the graph show between x and y? (5 points)
A graph shows scale on x axis and y axis from 0 to 12 at increments of 1. Dots are made at ordered pairs 1, 1 and 2, 1.1 and 3, 1.3 and 4, 1.7 and 5, 2 and 6, 2.5 and 7, 3.1 and 8, 4.2 and 9, 6 and 10, 10.
Select one:
a. Linear positive association
b. Nonlinear positive association
c. Linear negative association
d. Nonlinear negative association
The dots do not form a straight line, there is a small curve.
The dots do move up and to the right which makes it a positive curve.
The answer would be B. nonlinear positive association.
What is the length of QR?
Answer:
C
Step-by-step explanation:
Since the triangle is right with hypotenuse QR
Use Pythagoras' identity to solve for QR
The square on the hypotenuse is equal to the sum of the squares on the other two sides, that is
QR² = 8² + (8[tex]\sqrt{3}[/tex] )²
= 64 + 192
= 256 ( take the square root of both sides )
QR = [tex]\sqrt{256}[/tex] = 16
Final answer:
The length of QR is approximately 2.25 units. Since qr and qs are similar, the length of QR is also approximately 2.25 units.
Explanation:
The length of QR can be determined based on the given information about the vectors near S, R, and T. The vectors near S start at about 6 units away, while vectors near R and T start at about 4 units. Using the equation qr|d² = qs|D², we can find that as|¶R = D² / d² = 36 / 16 = 2.25. Since qr and qs are similar, the length of QR is also approximately 2.25 units.
what is the y-intercept for the equation 3x+5y=30?
Answer:
the y-intercept is -6
Step-by-step explanation:
3x+5y=30
-5y -5y
(30-)3x=30-5y(-30)
3x-30=5y/y
3/5x-6=y
how many nickels does it take to make $4.85
Answer is:
37 nickels
Answer:
it takes 97 nickels
Step-by-step explanation:
4.85÷0.05=97
Let y = safe load in pounds and x = length in feet of a horizontal beam. A constant of proportionality k exists such that y=k/x . y varies inversely as x. Determine the constant k for a beam with y = 2,000 pounds and x = 15 feet. a. 133.3 b. 3,000 c. 30,000
Answer:
Option c. 30,000
Step-by-step explanation:
we know that
A relationship between two variables, x, and y, represent an inverse variation if it can be expressed in the form [tex]y*x=k[/tex] or [tex]y=k/x[/tex]
Let
y ----> safe load in pounds
x ----> length in feet of a horizontal beam
we have
For [tex]x=15\ feet, y=2,000\ pounds[/tex]
Remember that
[tex]k=y*x[/tex]
substitute
[tex]k=2,000*15=30,000[/tex]
Find the area of the triangle.
24 square units
12 square units
11 square units
Area of a triangle is 1/2 x base x height.
The base is 6 units long and the height is 4 units.
Area = 1/2 x 6 x 4 = 12 square units.
Are these fractions equivalent or nonequivalent?
xy/4y x/4
Answer:
They are equivalent
Step-by-step explanation:
x/4 multiplied by y/y equals to xy/4y. Therefore, they are equivalent
Let f(x) = 8x and g(x) = x - 3. What's
the smallest number that is in the domain of
fog?
Answer:
The smallest number that is in the domain of fog is 3
Step-by-step explanation:
f(x) = [tex]\sqrt{8x}[/tex] (as corrected in comments)
g(x) = x-3
we need to find fog = f(g(x))
For finding f(g(x)) we put the value of g(x) inside the f(x)
f(g(x))=[tex]\sqrt{8(x-3)}[/tex]
The domain of this function is x ≥ 3
because if value of x is less than 3 than the result would be negative and we know √f(x) ≥ 0
So, the smallest number that is in the domain of fog is 3
4(x)+6+3=17 what does x equal
Hello There!
X=2
To solve this, we first need to understand that when we see an X in parentheses, we multiply the number before it in this case 4 by X.
The answer is 2 because we multiply 4 by 2 which is the x value so 4*2 is equal to 8 and they we add 9 to it because the sum of 6 and 3 is 9.
Finally, our answer we get is 17 so our X value is 2.
Have A Great Day!
Determine whether the three segment lengths will produce a triangle. Type yes or no in the space provided.
20, 20, 30 = ?
Answer:
20 , 20 , 30 will produce a triangle
Step-by-step explanation:
* Lets study how to know if the lengths of the three segments
can formed a triangle
- It is a fact that in any triangle the sum of the smallest two sides
must be greater than the largest side
- Lets study some examples
# If the lengths of the three segments are 5 , 6 , 7
∵ 5 and 6 are the smallest
∴ 5 + 6 = 11
∵ 11 > 7 ⇒ the sum greater than the 3rd side
∴ 5 , 6 , 7 can formed a triangle
# If the lengths of the three segments are 5 , 7 , 12
∵ 5 and 7 are the smallest
∴ 5 + 7 = 12
∵ 12 = 12 ⇒ the sum equal the 3rd side
∴ 5 , 7 , 12 can not formed a triangle
# If the lengths of the three segments are 10 , 12 , 24
∵ 10 and 12 are the smallest
∴ 10 + 12 = 22
∵ 22 < 24 ⇒ the sum less than the 3rd side
∴ 10 , 12 , 24 can not formed a triangle
* Now lets solve the problem
∵ The length of the three segments are 20 , 20 , 30
∵ 20 and 20 are the smallest
∴ 20 + 20 = 40
∵ 40 > 30 ⇒ the sum greater than the 3rd side
∴ 20 , 20 , 30 will produce a triangle
There are 1,379 souvenir paperweights that need to be packed in boxes. Each box will hold 15 paperweights. How many boxes will be needed?
92 boxes
1379/15=91.93 but u need a full box so 92
Answer:
92
Step-by-step explanation:
Given:
Number of Paperweights = 1,379
Number of Paperweights that each box can hold = 15
Number of boxes needed = 1379 ÷ 15 = 91.933 boxes
Because 0.933 of a box is of no use to anyone, we simply round this number up to the next whole box and just have the last box partially full.
This gives us 92 boxes.
17x - 6 + 3x - 5 = x + 11 + 4x
Answer:
I believe it's 22/15
Step-by-step explanation:
17x -6 + 3x - 5 = 1x + 11 + 4x first you add the 17x and 3x and 1x and the 4x
which it would be: 20x - 6 -5 = 5x + 11;
20x - 11 = 5x + 11,
-5 -5
15x - 11 = 11
+11 +11
15x = 22
15 15 Divide
x = 22/15
Hope my answer has helped you if not i'm sorry.
What is the fiftieth term of the arithmetic sequence 3, 7, 11, 15, ... ?
Answer:
199
Step-by-step explanation:
For this problem, you have to write an formula.
a(n)=a(1)+(n-1)d
n is the term you are trying to find (in this case it's 50).
a(1) is the first term in the sequence (in this case it's 3).
d is the common difference (in this case it's 4).
Plug those in, and you get:
a(50)=3+(50-1)4
And you can easily solve that and get a(50)=199.
Answer:
199
Step-by-step explanation:
The product of three consecutive numbers is 990. What is the sum you f the 3 whole numbers?
Answer:
20
Step-by-step explanation:
If the three numbers are x, x+1, and x+2, then:
x (x+1) (x+2) = 990
x (x² + 3x + 2) = 990
x³ + 3x² + 2x - 990 = 0
(x - 9) (x² + 12x + 110) = 0
Since x must be a whole number, x = 9. You can also use simple trial and error to find that the three numbers are 9, 10, 11.
The sum is:
9 + 10 + 11 = 20
Triangle ABC is translated 2 units right and 5 units down to form triangle A′B′C′. This triangle is then translated 5 units right and 4 units up to form triangle A″B″C″. If vertex A is at (-4, 2), what are the coordinates of vertex A″?
Answer:
The coordinates of vertex A" is (3 , 1)
Step-by-step explanation:
* Lets revise The translation of a point
- If the point (x , y) translated horizontally to the right by h units
then the new point = (x + h , y)
- If the point (x , y) translated horizontally to the left by h units
then the new point = (x - h , y)
- If the point (x , y) translated vertically up by k units
then the new point = (x , y + k)
- If the point (x , y) translated vertically down by k units
then the new point = (x , y - k)
* Now lets solve the problem
∵ Δ ABC has a vertex A = (-4 , 2)
∵ The Δ ABC is translated 2 units right and 5 units down to form
triangle A′B′C′
- From the rule above the x coordinate id added by 2 and the
y-coordinate is subtracted by 5
∴ A' = (-4 + 2 , 2 - 5) = (-2 , -3)
∴ The image of vertex A is A' = (-2 , -3)
∵ Δ A'B'C' is then translated 5 units right and 4 units up to form
triangle A″B″C″
- From the rule above the x coordinate is added by 5 and the
y-coordinate is add by 4
∴ A" = (-2 + 5 , -3 + 4) = (3 , 1)
* The coordinates of vertex A" is (3 , 1)
Answer:
it is a
Step-by-step explanation:
What is the discriminant of 3х^2 + 6x = 2?
Answer:
Δ = 60
Step-by-step explanation:
Given a quadratic in standard form : ax² + bx + c = 0 : a ≠ 0
Then the discriminant
Δ = b² - 4ac
Given
3x² + 6x = 2 ( subtract 2 from both sides )
3x² + 6x - 2 = 0 ← in standard form
with a = 3, b = 6 and c = - 2
b² - 4ac = 6² - (4 × 3 × - 2) = 36 - (- 24) = 36 + 24 = 60
Factor.
8x2y2 – 4x2y – 12xy
4(8x2y2 – x – 12xy)
4(2xy – 4x2y – 12xy)
4x2y2(2xy – xy –3)
4xy(2xy – x – 3)
Answer:
4xy[2xy - x - 3]
Step-by-step explanation:
When finding the Greatest Common Factor [GCF], along with the coefficient, you have to factor out the least degree term possible, which in this case is 4xy. This is because although all terms have y and x, their degrees are not all similar, so we have to go with 4xy.
Which shows the correct values for proma’s friends who prefer orange juice ?
Answer:
Girls: 9; Boys: 11
Step-by-step explanation:
16-7=9
14-3=11
10 points i need help i need to finish in 1 hour
how much does it cost to buy 3 drinks
Answer:
4.50
Step-by-step explanation:
3 divided by 2 is 1.5, which is equivalent to $1.50. So each drink cost 1.50. 1.50 x 3 = 4.50.
What is the slope of a line that is perpendicular to the line represented by the equation x – y = 8?
Answer:
-1
Step-by-step explanation:
Given equation of line is:
x - y = 8
In order to find the slope of other line we have to convert the given equation in standard form
So,
-y = -x + 8
Multiplying the equation with -1
y = x - 8
The co-efficient of x is the slope of the line.
Here the co-efficient is 1 so the slop of line is 1.
We know that the producct of slopes of perpendicular lines is -1.
Let m2 be the slope of the other line then
1 * m2 = -1
m2 = -1
So the slope of line perpendicular to line x-y = 8 will be: -1 ..