The number has 2022 digits 7 when divided by 15, what is the decimal part of the quotient?

Given:

The expression is:

[tex]\dfrac{4x^3+3x^2}{(x+1)^2(x^2+7)}[/tex]

To find:

The correct form of the partial fraction decomposition for the given expression.

Solution:

We have,

[tex]\dfrac{4x^3+3x^2}{(x+1)^2(x^2+7)}[/tex]

By partial fraction decomposition, it can be written as:

[tex]\dfrac{4x^3+3x^2}{(x+1)^2(x^2+7)}=\dfrac{A}{x+1}+\dfrac{B}{(x+1)^2}+\dfrac{Cx+D}{x^2+7}[/tex]           ...(i)

[tex]\dfrac{4x^3+3x^2}{(x+1)^2(x^2+7)}=\dfrac{(x+1)^2(Cx+D)+(x+1)(x^2+7)A+(x^2+7)B}{(x+1)^2(x^2+7)}[/tex]

[tex]4x^3+3x^2=(x+1)^2(Cx+D)+(x+1)(x^2+7)A+(x^2+7)B[/tex]

[tex]4x^3+3x^2=x^3A+x^3C+x^2A+x^2B+2x^2C+x^2D+7xA+xC+2xD+7A+7B+D[/tex]

[tex]4x^3+3x^2=x^3(A+C)+x^2(A+B+2C+D)+x(7A+C+2D)+7A+7B+D[/tex]

On comparing both sides, we get

[tex]A+C=4[/tex]

[tex]A+B+2C+D=3[/tex]

[tex]7A+C+2D=0[/tex]

[tex]7A+7B+D=0[/tex]

On solving these equations, we get

[tex]A=\dfrac{23}{32},B=-\dfrac{1}{8},C=\dfrac{105}{32},D=-\dfrac{133}{32}[/tex]

Substituting these values in (i), we get

[tex]\dfrac{4x^3+3x^2}{(x+1)^2(x^2+7)}=\dfrac{\dfrac{23}{32}}{x+1}+\dfrac{-\dfrac{1}{8}}{(x+1)^2}+\dfrac{\dfrac{105}{32}x-\dfrac{133}{32}}{x^2+7}[/tex]

Therefore, the required partial fraction decomposition is:

[tex]\dfrac{4x^3+3x^2}{(x+1)^2(x^2+7)}=\dfrac{\dfrac{23}{32}}{x+1}+\dfrac{-\dfrac{1}{8}}{(x+1)^2}+\dfrac{\dfrac{105}{32}x-\dfrac{133}{32}}{x^2+7}[/tex]

Answer:

A on Edg

Step-by-step explanation:

got it right

Answer:

(0,-9)

Step-by-step explanation:

To find the y-intercept, substitute x=0

y=(0)^2+4(0)-9

=-9

Here's a tip to help you find the y-intercept faster, it is usually the constant of the graph equation

Answer:

see explanation

Step-by-step explanation:

Given a parabola in standard form

y = ax² + bx + c ( a ≠ 0 )

The equation of the axis of symmetry which is also the x- coordinate of the vertex is

x = - [tex]\frac{b}{2a}[/tex]

y = x² + 4x - 9 ← is in standard form

with a = 1, b = 4 , then

x = - [tex]\frac{4}{2}[/tex] = - 2

x = - 2 is the equation of the axis of symmetry

Substitute x = - 2 into the equation for corresponding y- coordinate of vertex

y = (- 2)² + 4(- 2) - 9 = 4 - 8 - 9 = - 13

vertex = (- 2, - 13 )

To find the y- intercept let x = 0 and solve for y

y = 0² + 4(0) - 9 = 0 + 0 - 9 = - 9

y- intercept = (0, - 9)

From the standard form of the parabola

• If a > 0 then vertex is a minimum

• If a < 0 then vertex is a maximum

Here a = 1 , that is > 0

vertex (- 2, - 13 ) is a minimum

Answer:

4 > [tex]-\frac{n}{4}[/tex]

-16 > n

Step-by-step explanation:

Greater than would mean that the "arrow" is not facing the number. It would mean it is larger than the other number. Also, you have to construct the other part of the inequality which would be [tex]-\frac{n}{4}[/tex].

4×4 > [tex]-\frac{n}{4}[/tex]×4

16 > -n

-16 > n

Answer:

H0 : The mean difference in strikes between pre and post strike is equal to 0

H1 : The mean difference in strikes between pre and post strike is not equal to 0

Step-by-step explanation:

The scenario described abibe meets the condition for a paired (dependent) sample t test as the same subject is involved in both the pre and post strike data. Therefore measurement from the strike(pre) must be paired with measurement from the strike(post) data.

For a paired test involving a single subject ; The mean difference in the two sample is 0 ; that is both are the same while the alternative negates the null by claiming that the mean difference is not equal to zero.

Answer:

A

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

because line FB divides triangle f v w into two equal halves therefore line WP is equal to line PV which is equal to 12

The required value of the PV is 12 in triangle DEF where p is the incenter.

Point P is the incenter of ΔDEF. Point P is the point of concurrency of the angle bisector. PV to be determined.

The incenter of a triangle is the intersection point of the internal angle bisectors of the triangle. In additional expressions, it can be clarified as the point where the internal angle bisectors of the triangle and perpendicular distance from this point to any of the sides of triangle is the same.

Since in triangle FGH, P is the incenter and PW, PV,PX is perpendicular distance to the sides HF, GF and GH respectively.
From image,
PW = 12
So by the property of incenter, perpendicular distance from this point to any of the sides of triangle is the same.

PW = PV
PV = 12

Thus, the required value of the PV is 12 in triangle DEF where p is the incenter.

Learn more about incenter here:
https://brainly.com/question/27868922
#SPJ2

Answer:

usual number of yellow eggs = 12

Usual maximum = 21

Usual minimum = 3

Step-by-step explanation:

To solve this, we will use the expected value of a binomial probability.

The formula is;

E(X) = np

Where;

n is sample size

p is probability of success.

We are given;

n = 58

p = 21%

Thus;

usual number of yellow eggs in samples = np = 58 × 21% = 12.18 ≈ 12

From USL(Upper specification limit) and LSL(Lower specification limit) formula, we can find the maximum usual number and minimum usual number of eggs respectively.

Thus;

USL = n(p + 3√(p(1 - p)/n)

USL = 58(0.21 + 3√(0.21(1 - 0.21)/58)

USL = 21.48 ≈ 21

LSL = n(p - 3√(p(1 - p)/n)

LSL = 58(0.21 - 3√(0.21(1 - 0.21)/58)

LSL = 2.87 ≈ 3

Answer:

157 miles

Step-by-step explanation:

total cost = flat fee + cost per mile * miles

133.17 = 16.99 + .74 * m

Subtract 16.99 from each side

116.18 = .74m

Divide each side by .74

116.18 / .74 = .74m/.74

157 = m

Last year He was 7 years old.

His father is 4 times the age 7 x 4 = 28

Last year his dad was 28, so this year he is 29.

Combined age this year = 29 + 8 = 37

51 - 37 = 14 years

14/ 2 people = 7 years

8 + 7 = 15

29 + 7 = 36

15 + 36 = 51

It will take 7 years.

Answer:

Let the inverse of f(x) be h(x):

[tex]{ \tt{h(x) = \frac{1}{4x} }}[/tex]

Answer:

The answer is C!

Step-by-step explanation:

Answer:

D

NOTE: the answer "C" is NOT correct... see the image the green is "C" the purple is "D"

Step-by-step explanation:

Answer:

70 degrees

Step-by-step explanation:

there are multiple ways, as all the trigonometric functions are related.

let's try it this way :

consider the missing side to be the radius of a circle.

then 41 would be the cos value of the angle (multiplied by that radius, of course).

so, let's calculate the missing side per Pythagoras

c² = a² + b² = 113² + 41² = 12769 + 1681 = 14450

c = 120.21

and now

41 = cos(?) × 120.21

cos(?) = 41/120.21 = 0.341...

? = 70.0576... ≈ 70 degrees

Answer:

70°

Step-by-step explanation:

tangent θ = (opposite side / adjacent side)

tangent θ = (113 / 41)

θ = arctan (113 / 41)

θ = 70.0576°

*Note: "arctan" is the same as "inverse tangent"

**Note: "soh-cah-toa" (and "cho-sha-cao" for sec, csc, & cot) is an easy mnemonic device to remember the trig functions (sin, cos, & tan) and their relations to the sides of a given angle.

Answer: No

Step-by-step explanation:

Add 2 sides together. If the sum of greater than the length of the 3rd side for all 3 options it can form a right triangle if it doesn’t than it can’t:

9 + 12 = 21 which is not greater than the 3rd side length of 21 so this cannot form a right triangle.

Answer:

Step-by-step explanation:

So, yearly $2100 is paid, plus the 1.73% interest, so 1.73% interest is $2136.33every year interest stacks on itself so youll take 1.73% of the year 1 total with interest.  

Year 1 total: $2136.33

Year 2 total:$2173.29

Year 3 total:$2210.89

Year 4 total:$2249.14

Year 5 total:$2288.05

Total Paid After 5 years:$11057.70

Year 1 total interest:$36.33

Year 2 total interest:$36.96Year 3 total interest:$37.60Year 4 total interest:$38.25Year 5 total interest:$38.91

Total Interest paid after 5 years:$188.05

Answer:

32 cars

Step-by-step explanation:

we know that 14 and 30 lie on opposite sides of the ferris wheel, so we need to calculate how many cars are inbetween car number 14 and carn number 30. since each car is numbered starting from 1, we know that the cars do not skip any numbers. after counting, we know that there are 16 cars inbetween car number 14 and car number 30. since there are 2 sides of a circle we have to double our number by 2. so 16×2 is 32

Math step-by-step:

30-14=16

16×2=32

Answer:

D

Step-by-step explanation:

Pythagorean

[tex]x^{2} + 9^{2} = 15^{2}[/tex] (x>0)

=> [tex]x=\sqrt{15^{2}-9^{2} }[/tex] [tex]=12[/tex]

Answer:

83 spins

Step-by-step explanation:

Number of red spins = n

Number of orange spins = 8n

Number of yellow spins = 3n

Total number of trials = 240

Total number of spins :

(n + 8n + 3n) = 240

12n = 240

n = 240 / 12

n = 20

Number of red spins = 20

(1000/240) * n

4.1666666 * 20

= 83.333

= 83 spins

Answer:

[tex]2x + 3 = 13 \\ 2 \times 5 + 3 = 15 \\ 10 + 13 = 15 \\ 23 = 15 \\ 23 - 15 = 8 \\ \\ 3x + 2 = 13 \\ 3 \times 5 + 2 = 13 \\ 15 + 2 = 13 \\ 17 - 13 \\ = 4 \\ \\ x - 5 = 0 \\ 5 - 5 = 0 \\ 0 = 0 \\ \\ 4x - 9 = 21 \\ 4 \times 5 - 9 = 21 \\ 20 - 9 = 21 \\ 21 - 11 \\ = 10[/tex]

Answer:

A) 6 square inches.

Step-by-step explanation:

A(Triangle) = 1/2bh

b = base length

h = height length

A(Triangle) = 1/2(4)(3) = 6

Therefore, the area of the triangle is 6 in².

Answer:

Step-by-step explanation:

7) PQ // RS,  RQ is transversal

x = 38 {Alternate interior angles are congruent}

In ΔPQR ,

x + y + ∠P  = 180   {Angle sum property of triangle}

38 + 90 + y = 180

  128 + y =  180

           y = 180 - 128

y = 52

9) Construct XY // AB

XY // AB  & AC is transversal

∠1 = ∠4     ---------(I)      {alternate interior angles are equal}

XY // AB  & BC is transversal

∠3 = ∠5     ---------(II)      {alternate interior angles are equal}

∠1 + ∠2 + ∠3 = 180   {straight line angles}

∠4 + ∠2 + ∠5 = 180    {From (I) & (II) }

Sum of three angles of triangle is 180.Hence proved.

Answer:

in neighbourhood q the total number of people in the nine families I higher than that in neighbourhood s because of we add up the number of people in the families in neighbourhood q we get a total of 35 yet we have a total of only 27 people in the nine families in neighbourhood s

hope that helps ❤

Answer:

C. 2x

Step-by-step explanation:

Let

B's age = x years

A's age = 2 times older than B

= 2 * x

= 2x years

A's age = 2x years

For instance, if B's age is 17 years

Then,

A's age = 2x

= 2(17)

= 34 years old

Answer:

Options (1) and (4)

Step-by-step explanation:

Given equation for the deposit in the saving account is,

y = 20x + 50

Here, y = Amount of money in the account

20 = money added in the account every month

50 = Initial deposit

By comparing this equation with the slope-intercept form of the equation of a line,

y = mx + b

Here, slope m = money added in the account every month

And b = y-intercept

Therefore, Options (1) and (4) will be the answer.

Answer:

100%_$40.80

? × _$38.76

Step-by-step explanation:

100%×$38.76÷$40.80=95%

Answer:

40.80

Step-by-step explanation:

Answer: 4 Shirts

Step-by-step explanation:

Given

Person has [tex]\$80[/tex]

Pant costs [tex]\$29[/tex] and shirt costs [tex]\$12[/tex]

Suppose [tex]x\ \text{and}\ y[/tex] as number of pant and shirts

Spent money must be equal or less than the total money. The inequality becomes

[tex]\Rightarrow 80\geq29x+12y[/tex]

For 1 pair of pants that is, 1 pants

[tex]\Rightarrow 80\geq 29+12y\\\Rightarrow 51\geq 12y\\\Rightarrow 4.25\geq y[/tex]

That is maximum number of shirts that can be bought are 4.