Answer: -4
Step-by-step explanation:
Once you graph it, the solutions are where the graph meets the x axis.
This is at -4 and 9.
Review the work showing the first few steps in writing a partial fraction decomposition.
StartFraction 4 x + 40 Over (x + 2) (x + 6) EndFraction = StartFraction A Over x + 2 EndFraction + StartFraction 16 Over x + 6 EndFraction
4x + 40 = A(x + 6) + B(x + 2)
4x + 40 = Ax + 6A + Bx + 2B
What is the partial fraction decomposition in terms of x?
Answer:
8/(x + 2) - 4/(x + 6)
Step-by-step explanation:
4x + 40 = Ax + 6A + Bx + 2B
Equating coefficients of x
4 = A + B (1)
Equating constant terms:
40 = 6A + 2B (2)
Multiply equation (1) by -2:
-8 = -2A - 2B .. (3)
Add (2) and (3):
32 = 4A
A = 32/4
A = 8.
4 = 8 + B
B = 4 - 8
B = -4.
The decomposition of the given partial fraction in terms of x is [tex]\frac{4x+40}{(x+2)(x+6)} =\frac{8}{(x+2)}-\frac{4}{(x+6)}[/tex].
What is partial fraction?The partial fraction is the result of writing a rational expression as the sum of two or more fractions.
According to the given question.
We have a partial fraction
[tex]\frac{4x+40}{(x+2)(x+6)} =\frac{A}{(x+2)} +\frac{B}{(x+6)}[/tex]
We have to decompose the above partial fraction in terms of x.
The above partial fraction can be written as
[tex]\frac{4x+40}{(x+2)(x+6)} =\frac{A(x+6)+B(x+2)}{(x+2)(x+6)}[/tex]
⇒[tex]4x+40 = A(x+6)+B(x+2)[/tex]
⇒[tex]4x + 40 = Ax + 6A + Bx + 2B[/tex]
⇒[tex]4x + 40 = x(A+B) +6A + 2B...(i)[/tex]
On comparing the coefficient of x and the constant terms.
[tex]A+B = 4..(ii)[/tex]
⇒[tex]A = 4 - B[/tex]
and, [tex]6A+2B = 40..(iii)[/tex]
⇒[tex]2(3A+B) = 40[/tex]
Substitute the value of A in (iii)
⇒[tex]2(3A+B) = 40[/tex]
⇒[tex]3A+B = 20[/tex]
⇒[tex]3(4-B)+B = 20[/tex]
⇒[tex]12 - 3B +B = 20[/tex]
⇒[tex]12 - 2B = 20[/tex]
⇒[tex]-2B = 8[/tex]
⇒[tex]B = -4[/tex]
So, [tex]A = 4-(-4) = 8[/tex]
Substitute the value of A and B in the given partial fraction.
⇒[tex]\frac{4x+40}{(x+2)(x+6)} =\frac{8}{(x+2)}-\frac{4}{(x+6)}[/tex]
Hence, the decomposition of the given partial fraction in terms of x is [tex]\frac{4x+40}{(x+2)(x+6)} =\frac{8}{(x+2)}-\frac{4}{(x+6)}[/tex].
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fA= 2.3, B = 8.7 and C = 2.2, find the percentage error in evaluating A+B/C
Answer:
8.8
Step-by-step explanation:
You need to at A and B so 2.3+8.7=11. Then you take your 11 and - by C 2.2.
Hope this helps.
What is the solution of (4 x minus 16) superscript one-half baseline = 36? x = 5 x = 13 x = 20 x = 328
Answer:
328
Step-by-step explanation:
(4x − 16)^½ = 36
Square both sides:
4x − 16 = 36²
4x − 16 = 1296
Solve for x:
4x = 1312
x = 328
Answer X=328
Step-by-step explanation:
can you solve please -8(0.09) (-0.5)=?
-8(0.09) (-0.5) = 0.36
-8(0.09) (-0.5)
(-0.72) (-0.5)
0.36
Answer:
[tex]\boxed{\sf{0.36}}[/tex]Step-by-step explanation:
This problem can be solved by multiplying left to right by a decimal.
-8(0.09)(-0.5)
First, you have to do is remove these parenthesis.
[tex]\sf{8*0.09*0.5}[/tex]
Then, you solve.
Multiply.
[tex]\sf{8*0.09*0.5=\boxed{\sf{0.36}}}[/tex]
=0.36
Therefore, the final answer is 0.36.I hope this helps you! Let me know if my answer is wrong or not.
Can someone help me please
Answer:
The Area of the shaded region :
(x²)(4x-1) - (5x)(x+7) =
4x³ - x² - 5x² - 35x =
4x³ - 6x² - 35x
Complete the state symbol in the equation. CuCO3+H2SO4(aq)+H2O+CO2
Answer:
H2O = liquid (l)
CO2 = gas (g)
CuCO3 = solid (s)
Step-by-step explanation:
H2O is water
CO2 is carbon dioxide
CuCO3 is copper carbonate
The price of general admission Twins tickets increased from $7 to $18 when they moved to Target Field. What is the percent increase in the ticket price? Explain how you know
Answer:
257 1/7%
Step-by-step explanation:
[tex] \frac{18}{7} = 2.57142857[/tex]
2.57142857 = 257 1/7 %
assume that
show work
Answer:
Assume what? And show work for what?
Which is the solution to the inequality?
y + 15 less-than 3
Hey there!
"less than" is "<"
y+15<3
Solve it:
y<3-15
y<-12
Hope everything is clear.
Let me know if you have any questions!
Always remember: Knowledge is power!
Answer:
y < -12
Step-by-step explanation:
Edge
MATH
NATION
Question 1 of 10
NEXT QUESTION
Suppose h(t) = -0.2t2 + 2t models the height, in feet, of a ball that is kicked into the air where t is
given as time, in seconds.
After how many seconds does the ball reach its maximum?
Step-by-step explanation:
the point of extreme value we get a the zero dilution of the first derivative of the function.
h(t) = -0.2t² + 2t
h'(t) = -0.4t + 2
so,
-0.4t + 2 = 0
2 = 0.4t
t = 2/0.4 = 5 seconds
so, after 5 seconds the ball reaches its maximum height.
FYI : that height is then h(5).
-0.2×5² + 2×5 = -5 + 10 = 5 ft
so, all in all, a very weak kick in very low gravity ...
Answer number 8 please. Thank you.
Answer:
The answer is C. A triangle has a total angle of 180°, therefore C. is more than 180°
100 point to the first correct answer
Given the discrete random variable X: What is the probability distribution of X if X ~B(2, 5/17)?
Answer:
X ~ B(n, p)
Given: X ~ B(2, 5/17)
⇒ n = 2
⇒ p = 5/17
Binomial distribution formula:
[tex]\sf P(X = x) = nC_x (1-p)^{(n-x)}p^x[/tex]
As n = 2, calculate P(X = 0), P(X = 1) and P(X = 2):
[tex]\sf P(X = 0) = 2C0 (\frac{12}{17})^{(2-0)}(\frac{5}{17})^0=\dfrac{144}{289}}[/tex]
[tex]\sf P(X = 1) = 2C1 (\frac{12}{17})^{(2-1)}(\frac{5}{17})^1=\dfrac{120}{289}}[/tex]
[tex]\sf P(X = 2) = 2C2 (\frac{12}{17})^{(2-2)}(\frac{5}{17})^2=\dfrac{25}{289}}[/tex]
**Probability Distribution Table attached**
Which equation can be used to solve for m∠1? m∠1 = one-half(a – b) m∠1 = one-half(a b) m∠1 = one-half(c – d) m∠1 = one-half(c d)
The equation will be:
[tex]m\angle 1=\dfrac{1}{2}(arc\ a-arc\ b)[/tex]
What is arc of circle?The arc of the circle is the curved line on the circle formed by the angle and the radius of the circle.
In the attached picture of the question, we can see that
The measure of the interior angle is the semi-sum of the arches that comprise it and its opposite.
So the equation will be
[tex]m\angle 1=\dfrac{1}{2}(arc\ a-arc\ b)[/tex]
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Answer: a
Step-by-step explanation:
If two triangles are congruent, which of the following statements must be
true? Check all that apply.
A. The triangles have the same size, but not the same shape.
B. The corresponding sides of the triangles are congruent.
I c. The corresponding angles of the triangles are congruent.
D. The triangles have the same size and shape.
B. The corresponding sides of the triangles are congruent.
I c. The corresponding angles of the triangles are congruent.
D. The triangles have the same size and shape.
Step-by-step explanation:
.
While pushing a shovel into the ground with a force of 555 newtons ant an angle of 44 ∘ 44 ∘ to the ground. Find the magnitudes of the horizontal and vertical components of the force to the nearest whole newton.
The Horizontal component is 554.889N and the vertical component is
9.8235 Newton
Resolution of ForcesGiven Data
Force = 555 NewtonAngle of Applied force = 44°Fx = Horizontal component of the applied forceFy = the vertical component of the applied forceResolving the vertical force
Fy = 555 sin44°
Fy = 555 *0.01770
Fy = 9.8235 Newton
Resolving the horizontal force
Fx = 555 cos 44°
Fx = 555 *0.9998
Fx = 554.889 Newton
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I bought a keychain for $6.75 and a T-shirt that cost X dollars each altogether the items cost $31.50 complete the type diagram
Answer:
24.75
Step-by-step explanation:
keychain=$6.75
t.shirt=X
according to question
X+6.75=31.50
X=24.75
Pls help me! 19 and 20.
Answer:
See below ↓
Step-by-step explanation:
19.
[tex]\frac{x-1}{2} - \frac{x-3}{5} - \frac{x-7}{10} + \frac{x-2}{5}[/tex][tex]\frac{5(x-1)-2(x-3)-(x-7)+2(x-2)}{10}[/tex][tex]\frac{5x-5-2x+6-x+7+2x-4}{10}[/tex][tex]\frac{4x+4}{10}[/tex][tex]\frac{2x+2}{5}[/tex]20.
[tex]\frac{2x+3}{2x} + \frac{x+3}{4x} - \frac{18x+6}{8x^{2} }[/tex][tex]\frac{4x(2x+3)+2x(x+3)-(18x+6)}{8x^{2} }[/tex][tex]\frac{8x^{2} +12x+2x^{2} +6x-18x-6}{8x^{2} }[/tex][tex]\frac{10x^{2}-6}{8x^{2} }[/tex][tex]\frac{5x^{2}-3}{4x^{2} }[/tex]20 points!!!Solid metal support poles in the form of right
cylinders are made out of metal with a density of 5.2
g/cm². This metal can be purchased for $0.35 per
kilogram. Calculate the cost of a utility pole with a
radius of 19 cm and a height of 620 cm. Round your
answer to the nearest cent. (Note: the diagram is not
drawn to scale)
Density is mass per unit volume. The cost of the metals from the calculations performed is $1280.
What is density?Density is defined as the ratio of the mass of an object to its volume. We have the following information;
Mass of the metal = ?
Density of the metal = 5.2 g/cm3
height of the metal = 620 cm
radius of the metal = 19 cm
Volume of a cylinder = πr^2h = 3.142 * (19)^2 * 620 cm = 703242cm^3
Mass = density * volume = 5.2 g/cm3 * 703242cm^3
= 3657 Kg
If the cost is $0.35 per kilogram, then 3657 Kg costs; 3657 Kg * $0.35
= $1280
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PLEASE HELP I HAVE A TEST TOMORROW
Answer:
a = 12
Step-by-step explanation:
Pythagorean Theorem: A^2 + B^2 = c^2
9^2 + b^2 = 15^2
81 + b^2 = 225
225 - 81 = 144
[tex]\sqrt{144}[/tex] = 12
Have an amazing day!!
Good luck on your test!!
Please rate and mark brainliest!!
Step-by-step explanation:
use the picture as reference and solve accordingly
best of luck for your test
Find the value of x that makes m || n
x=
F(x)=x^2
G(x)=x^2-8x+16
In which direction and by how many units should f(x) be shifted to match g(x)?
Answer:
4 units right
Step-by-step explanation:
The question of shifts or other transformations can be more easily answered when the transformed function is written in vertex form.
g(x) = (x -4)²
Compared to f(x) = x², this is g(x) = f(x-4). That change corresponds to a right-shift of 4 units.
f(x) should be shifted right 4 to match g(x)
_____
Additional comment
The square of a binomial is (a -b)² = a² -2ab +b². The form of G(x) can be seen to match this form, so we know G(x) can be written as the square shown above.
A ball is thrown into the air with an initial velocity of 64 feet per second from a height of 336 feet. After how many seconds will the ball return to the ground and have a height of zero again
Answer:
7 seconds
Step-by-step explanation:
Ballistic motion is usually modeled in the vertical direction in US customary units by the equation h(t) = -16t^2 +v0·t +h0, where v0 and h0 are the initial velocity and height, and h(t) is the height as a function of time in seconds. For the given initial conditions, the equation of vertical motion will be ...
h(t) = -16t^2 +64t +336
__
This question asks you for the value of t for which h(t) = 0. We can solve that equation by factoring.
0 = -16t^2 +64t +336
0 = t^2 -4t -21 . . . . . . . . divide by -16
0 = (t -7)(t +3) . . . . . . . factor the quadratic
t = 7 . . . . . . the positive value of t that makes the equation true
The ball will return to the ground after 7 seconds.
__
Additional comment
A graph of the function reveals the ball reaches a maximum height of 400 feet after 2 seconds.
In metric units, the equation is h(t) = -4.9t^2 +v0·t +h0, where distances are in meters instead of feet. Time is still in seconds.
Help Anyone please? >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
Which system represents the statements below?
The sum of two numbers is 10. One number is five times the other.
Answer:
the answer is c
Step-by-step explanation:
y = 5x
as it says x + y = 10
so one number which is represented as x is times 5 as the other which brimg to our answer y =5x
The height of a building in a drawing is 15 inches at the actual height of the building is 165 feet find the scale factor of the drawling
165 ft / 15 inches = 11
scale = 1 inch = 11 feet
which is written as 1:11
3x - 12y = 6
x - 4y = 2
solve by elimination
Answer:
the problem has an infinite number of solutionsExplanation:
3x - 12y = 6x - 4y = 2make the coefficient of x same by multiplying the entire following by 3
⇒ ( x - 4y = 2 ) * 3⇒ 3x - 12y = 6 __ equation 23x - 12y = 6 __ equation 1solving using elimination method:
3x - 12y = 6
3x - 12y = 6
===========
0
Please help! locks in 30 min!
Sofia buys 3.8 pounds of potatoes for $0.85 per pound. Flynn buys 4.2 pounds of potatoes for $0.75 per pound.
How much more does Sofia spend than Flynn?
pls pls pls pls pls pls pls
The inverse, converse and contrapositive of a statement are used to determine the true values of the statement
How to determine the inverse, converse and contrapositiveAs a general rule, we have:
If a conditional statement is: If p , then q .
Then:
Inverse -> If not p , then not q .Converse -> If q , then p .Contrapositive -> If not q , then not p .Using the above rule, we have:
Statement 1
Inverse: If a parallelogram does not have a right angle, then it is not a rectangle. Converse: If a parallelogram is a rectangle, then it has a right angle.Contrapositive: If a parallelogram is a not rectangle, then it does not have a right angle.All three statements above are true
Statement 2
Inverse: If two angles of one triangle are not congruent to two angles of another, then the third angles are not congruent. Converse: If the third angles of two triangle are congruent, then the two angles are congruent to two angles of anotherContrapositive: If the third angles of two triangle are not congruent, then the two angles are not congruent to two angles of anotherAll three statements above are also true
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Annabelle read 10 books in 2 months. What was her rate of reading, in books per month?
Answer:
5 books per month
Step-by-step explanation:
We are trying to find a rate.
To find books per month, we would take the number of books and divide it by the number of months.
This would give us 10 books/2 months.
10/2 simplifies to 5.
Therefore the answer would be 5 books per month.
Answer:
You need to divide it I don't have a calculator because my mom don't want me to calculate she let me to calculate it on my brain btw please brainless me
4/5 and -4/5 are same or not
Answer:
not
Step-by-step explanation:
Answer:
4/5 and -4/5 are not same because
4/5=