Write the form of the partial fraction decomposition of the rational expression.
11x - 10/ (x-6)(x+7)

Answers

Answer 1

Answer:

x+7x2+3x+2=6x+1+−5x+2

Step-by-step explanation:

Simplify the expression: x+7x2+3x+2=x+7(x+1)(x+2)

The form of the partial fraction decomposition is

x+7(x+1)(x+2)=Ax+1+Bx+2

Write the right-hand side as a single fraction:

x+7(x+1)(x+2)=(x+1)B+(x+2)A(x+1)(x+2)

The denominators are equal, so we require the equality of the numerators:

x+7=(x+1)B+(x+2)A

Expand the right-hand side:

x+7=xA+xB+2A+B

Collect up the like terms:

x+7=x(A+B)+2A+B

The coefficients near the like terms should be equal, so the following system is obtained:

{A+B=12A+B=7

Solving it (for steps, see system of equations calculator), we get that A=6, B=−5

Therefore,

x+7(x+1)(x+2)=6x+1+−5x+2

Answer: x+7x2+3x+2=6x+1+−5x+2


Related Questions

Solve each of the following equations. Show its solution set on a number line. 5− p+6 =−8

Answers

5-|p+6|=-8

5-distance=-8= distance of them= 13

|p+6|=13

distance between/from p and -6

= -19 or 7,

So

Please Make me the brainliest pls

Pls Help!
Aimee wants to order some DVDs from Amazon. Each DVD costs $8.49 and shipping for the entire order is $5. She has only $70 to spend. How many DVDs can she order?

Answers

Answer:

she can buy 13

please brainliest or hear

Answer:

She can order 7 DVDS

Step-by-step explanation:

8.49 x 7 = 59.43

59.43 + 5 = 64.43.

Solve

(Perimeter)

Rectangle

Side- 10

Side- 5

Answers

the perimeter is 30

10*2=20
5*2=10
20+10=30

Help me please sjsjdjs it’s due in a few minutes

Answers

Answer:

The answer is the 3rd dot.

Step-by-step explanation:

hope this helps

Answer:

The one right below 8

Step-by-step explanation:

find the median of the list of data. 12, 18, 21, 25, 30, 43

Answers

Median is the middle number
=21 and 25
(21+25)/2
=23

Find the ratio of the areas.

Answers

9514 1404 393

Answer:

  3 -2√2

Step-by-step explanation:

For a regular octagon of side length s, the "flat-to-flat" dimension across the center is s(1+√2). The flat-to-flat dimension of the shaded center octagon is simply s. The ratio of areas is the square of the ratio of linear dimensions, so we have ...

  small area / large area = (1/(1+√2))^2 = 1/(3+2√2)

  small area/large area = 3 -2√2

_____

The attachment shows octagons after the fashion described here. The side length of the larger one is 2 units. The numbers inside are the areas. They have the ratio shown above.

HELP ME ASAP!!!! I’m very confused and I need help!! Thanks!

Answers

Answer:

Reason 2)The transitive property of congruence

Step-by-step explanation:

There are several sort of "obvious" properties of equality/congruence. Keeping them sorted out can be a bit of a trick.

  A = A . . . . reflexive property

  A = B ⇔ B = A . . . . symmetric property (erroneously cited in the proof)

  A = B, B = C ⇒ A = C . . . . transitive property (the one needed in the proof)

__

Not to confuse the issue, but there is also the "substitution property of equality" that says if X = Y, then X can be substituted for Y or vice versa. In the end, the transitive property is an application of this, where we're substituting for B in the second equation, or for A in the first equation.

The A=B=C form of Statement 1) in the proof is what gives you the clue it is the transitive property that is wanted here.

What is the volume of the rectangular prism? A.6/9 B.8/9 C.8/27 D. 6/27

Answers

Answer:

the corrct answer is C

Step-by-step explanation:

got it correct

Determine if the ratios are equivalent: 12:16 and 72:96 *
10 points
Equivalent
Not Equivalent

Answers

Answer:

Step-by-step explanation:

12 : 16

Both have 4 in common

3 : 4

72 : 96

Both have 12 in common

6 : 8

Both have 2 in common

3 : 4

So both the ratios are equivalent

The base of a solid is the region in the first quadrant between the graph of y=x2 and the x -axis for 0≤x≤1 . For the solid, each cross section perpendicular to the x -axis is a semicircle. What is the volume of the solid?

Answers

Answer:

The volume of the solid is π/40 cubic units.

Step-by-step explanation:

Please refer to the graph below.

Recall that the area of a semi-circle is given by:

[tex]\displaystyle A=\frac{1}{2}\pi r^2[/tex]

The volume of the solid will be the integral from x = 0 to x = 1 of area A. Since the diameter is given by y, then the radius is y/2. Hence, the volume of the solid is:

[tex]\displaystyle V=\int_0^1\frac{1}{2}\pi \left(\frac{y}{2}\right)^2\, dx[/tex]

Substitute:

[tex]\displaystyle V=\frac{1}{2}\pi\int_0^1\left(\frac{x^2}{2}\right)^2\, dx[/tex]

Simplify:

[tex]\displaystyle V=\frac{1}{2}\pi \int_0^1\frac{x^4}{4}\, dx[/tex]

Integrate:

[tex]\displaystyle V=\frac{1}{2}\pi \left[\frac{x^5}{20}\Big|_0^1\right][/tex]

Evaluate:

[tex]\displaystyle V=\frac{\pi}{40}\left((1)^5-\left(0\right)^5\right)=\frac{\pi}{40}\text{ units}^3[/tex]

The volume of the solid is π/40 cubic units.

Volume of a solid is the measure of the 3 dimensional space it occupies. The volume of the considered solid is obtained as [tex]\dfrac{\pi}{40} \: \rm unit^3[/tex]

How to find the volume of a three dimensional region bounded by curves?

For that, we can try to find infinitesimally small 3-d region's volume, and then integrate that region over the dimensions available to get the total volume of the specified region.

We can also use the fact that continuous curves are almost linear and non-changing in infinitely zoomed region.

The given solid has base bounded by x-axis, [tex]y=x^2[/tex] and 0≤x≤1

Its three dimensional region is along the z axis, for each x, there is a semicircle perpendicular with radius being 'y'.

If we take [tex]dx[/tex]x-axis, then the curve  [tex]y=x^2[/tex]cylinder(split from height because of semicircle)) with diameter y, and height [tex]dx[/tex]volume is : [tex]V_{dx} = \dfrac{1}{2} \times \pi (\dfrac{y}{2})^2 \times dx = \dfrac{\pi (x^2)^2}{8}dx = \dfrac{\pi x^4}{8} dx[/tex]

Integrating this for 0≤x≤1, we will get the volume of the three dimensional region needed as:

[tex]V = \int_0^4V_{dx} = \int_0^1 \dfrac{\pi x^4}{8} dx = \dfrac{\pi}{8} [\dfrac{x^5}{5}]^1_0 = \dfrac{\pi 1^4}{40} = \dfrac{\pi}{40}[/tex] (in cubic units).

Thus, the volume of the considered solid is obtained as [tex]\dfrac{\pi}{40} \: \rm unit^3[/tex]

Learn more about volume of three dimensional region here:

https://brainly.com/question/338504

What is the volume of a sphere with a surface area of 16pi ft^2?

Answers

Answer:

B

Step-by-step explanation:

Sphere Surface Area = 4 • π • r²

For it to equal 16 PI, then radius must equal 2

4*PI*2*2 = 16 PI

Sphere Volume = 4/3 • π • r³

Sphere Volume = 4/3 • π • 2^3

Sphere Volume = 4/3 *PI * 8

Sphere Volume = 32 / 3 PI

Sphere Volume = 10.666 PI cubic feet AND I think that is answer B

which SHOULD read 10 (2/3) PI ft^3

Determine if each set of coordinates form a horizontal or vertical line.
a. (-3, 6) & (-3, 2)
b. (8, 4) & (-3, 4)
c. (11, -5) & (-9, -5)
d. (9, -3) & (9, -12)

Answers

Answer:

a. vertical

b. horizontal

c. horizontal

d. vertical

Step-by-step explanation:

if the x coordinate changes it's horizontal and if the y coordinate changes it's vertical

Same-side interior angles always add
up to 180°. If <4 and 46 are same-side
interior angles, what is the measure of «6?
t
44=123°
46 = [?]
o
46

Answers

Answer:

Solution given;

<6+ 4=180[co interior angle]

<6=180-123

<6=57° is your answer

Hey everyone it is math pleased help me it is due today

Answers

Answer:

93 in²

Step-by-step explanation:

Given triangular prism with:

a = 1.5 in, b = 2 in, c = 2.5 in, l = 15 in

Total surface area is:

A = Pl + 2B, where P is the perimeter of base, B is area of base

Considering all given values we have:

A = (1.5 + 2 + 2.5)*15 + 2*(1/2*1.5*2) = 93 in²

what is the value of A when we rewrite (32/5)^-2x as A^x​

Answers

Answer:

[tex](\dfrac{25}{1024})^x[/tex]

Step-by-step explanation:

The given expression is :

[tex](\dfrac{32}{5})^{-2x}[/tex]

We need to rewrite it in the form of [tex]A^x[/tex].

We know that, [tex](\dfrac{1}{x})^{-a}=x^a[/tex]

So,

[tex](\dfrac{32}{5})^{-2x}=(\dfrac{5}{32})^{2x}\\\\=(\dfrac{5^2}{32^2})^x\\\\=(\dfrac{25}{1024})^x[/tex]

So, [tex]A=\dfrac{25}{1024}[/tex]. Hence, this is the required solution.

Answer: A = (32/5)^-2

Step-by-step explanation:

Using the order of operations, what are the steps for solving this expression? 40/8+3^2+(15-7)*2 Arrange the steps in the order in which they are performed.​

Answers

9514 1404 393

Answer:

simplify parenthesesevaluate the exponential termdivide 40/8multiply 8*2add 5+9add 14+16

Step-by-step explanation:

  40/8+3^2+(15-7)*2 . . . . given

The order of operations tells you to start by evaluating expressions in parentheses. Here, that is the subtraction of 7 from 15.

  40/8 +3^2 +8*2 . . . . (15-7) = 8

Then you evaluate exponential terms.

  40/8 +9 +8*2 . . . . . 3^2 = 9

Then perform multiplication and division, left to right. Here, division is first, then multiplication.

  5 +9 +8*2 . . . . . divide 40/8 = 5

  5 +9 +16 . . . . . . multiply 8*2 = 16

Finally, perform addition and subtraction, left to right.

  14 +16 . . . . add 5+9

  30 . . . . . . . add 14+16

Answer:

it is 8

Step-by-step explanation:

11. Saul's baseball bat has a mass of 1 kilogram His baseball has a mass
of 150 grams. What is the mass in grams of both items combined?
C. 1.150 grams
A. 1.15 grams
D. 115,000 grams
B. 115 grams

Answers

The mass of both combined would be 1150 grams or 1.150 kilograms

please answer fast :)

Will says you cannot use a graphing calculator to graph a line when the equation is in point slope form. Explain Will's reasoning. How could you modify an equation given in point-slope for so that you could graph the line on a graphing calculator? Use the equation y - 2 = -3(x + 5) as an example in your explanation.

Answers

Answer: y-2=3x-15 that’s wher my knowledge stops hopefully that helps a little. ‍♀️

A city has the population of 210,000 people. Suppose that each year the population grows by 7.5%. What will the population be after 13 years?

Answers

Answer:

6  5

Step-by-step explanation:

4 5  6 7

Graph this function.

F(x)= -1/3x + 8

I need help ASAP! The -1/3x is a fraction. Can anyone help?

Answers

Step-by-step explanation:

Rewrite the function as an equation.

[tex]y = - \frac{x}{3} + 8[/tex]

Rewrite in slope-intercept form.

[tex]y = - \frac{1}{3} x + 8[/tex]

Use the slope-intercept form to find the  slope  and  y-intercept.

Slope : - 1/3

y-intercept: (0,8)

Any line can be graphed using two points. Select two x values, and plug them into the equation to find the corresponding y values.

Graph the line using the slope and the y-intercept, or the points.

A design engineer wants to construct a sample mean chart for controlling the service life of a halogen headlamp his company produces. He knows from numerous previous samples that this service life is normally distributed with a mean of 500 hours and a standard deviation of 20 hours. On three recent production batches, he tested service life on random samples of four headlamps, with these results SampleService Life (hours) 1495500505500 2525515505515 3470480460470 If he uses upper and lower control limits of 520 and 480 hours, on what sample(s) (if any) does service life appear to be out of control

Answers

Answer:

Sample number 3

Step-by-step explanation:

From the given information:

Sample                   Service life(hours)                Total        Mean(X)

                     1               2            3           4

1                 495         500       505       500       2000        500

2                 525         515       505       515         2060        515

3                 470         480       460       470        1880          470

Total = [tex]\text{addition \ of \ numbers \ of \ observations}[/tex]

Mean = [tex]\dfrac{\text{addition \ of \ numbers \ of \ observations}}{4}[/tex]

Thus;

[tex]UCL = \mu+x = 500 + 20 = 520\\ \\ LCL= \mu -x = 500 -20 =480[/tex]

To plot on an X_Bar chart, we have:

Sample        Mean (X)     UCL        LCL

1                      500           520        480

5                     515            520        480

6                     470            520        480

The x-Bar chart is shown in the image attached below. From the image, we realize that the average service life for sample number 3 occurs to be out of the statistical control.

4. Which set is an example of like fractions?
O A. 10/10 and 5/5
O B.74 and 4
O C.2/1 and 23
OD.72 and 32
A

Answers

A, they both equal to 1 when simplified
Answer is A. 10/10=1 and 5/5=1
Also, when simplified by 2, 10/10 equals 5/5. 10:2/10:2=5/5

PLEASE HELP ASAP ITS DUE SOON!!!!

Answers

Answer:

A

Step-by-step explanation:

Look at the y axis and find the highest point.

Answer:

I believe it would be a: y=30; The maximum height...

Step-by-step explanation:

It's where the line would be, and describes exactly where the line of symmetry would be. Hope this helps :)

PLEASE HELP ASAP!!! WILL MAKE YOU THE BRAINLYIST!!!!
Assume this dance floor is 20 feet long and 30 feet wide. How many people will fit on this dance floor if you assume each person will dance in a space that is 2 feet wide and 2 feet long?

Answers

15 ppl would fit

Bc if you find the area of the dance floor which is 20 feet times 30 feet it equals 60 feet. Then multiply how much space someone takes which is 2 feet times 2 feet equals 4 feet. Then you divide the area of the dance floor by the number for F space one person takes up which is 60÷4. You would get 15 people

A rocket is launched from atop a 101 foot cliff with an initial velocity of 116 ft/s.
a) Substitute the values into the vertical motion formula h(t) = -16t2 + vt + h, where v represents the rocket’s initial velocity and h represents the rocket’s initial height.
t?

Answers

Answer:

ball-x2-y2-z2-r2--n-dimensions-represent-ball-hypersphere-s-q7037775 ... -feet-rectangular-field-divide-half-fence-middle-pa-q7037837 0.8 2015-06-26 ... -thrown-vertically-upward-initial-velocity-v-original-position-s-height-h-time-t- ...

Step-by-step explanation:

Alana has $80 in a savings account. The interest rate is 5% per year and is not compounded. How much interest will she earn in 1 year?

Answers

Answer:

Answer:

I = $ 1,937.50

Step-by-step explanation:

Equation:

I = Prt

Calculation:

First, converting R percent to r a decimal

r = R/100 = 3.875%/100 = 0.03875 per year,

then, solving our equation

I = 10000 × 0.03875 × 5 = 1937.5

I = $ 1,937.50

The simple interest accumulated

on a principal of $ 10,000.00

at a rate of 3.875% per year

for 5 years is $ 1,937.50.

I hope this is correct and hope it helps!

Find the range for the set of data: 22, 25, 25, 27, 32​

Answers

Answer: Range for set is 10

Hope this help!

Mina has 1/2 of a bag of popcorn. She eats half of her popcorn. How much popcorn does Mina have left?

b.1/8 of a bag

c.1 bag

c.1/4 of a bag

d.1/2 of a bag
no links k

Answers

Answer:

c.1/4 of a bag

cuz half of 1/2 is 1/4


subtract the fractions
7/39 1/42

Answers

Answer:

7/39-1/42= 85/546

Step-by-step explanation:

so its 85/546

Answer:

7/39 1/42

so it's 85/546

Please help will give brainliest

Answers

Answer:

One-third of the volume

Step-by-step explanation:

Volume of cylinder = πr²h

Volume of cone = (1/3)πr²h

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