A hobby store prices model train track using a proportional relationship between the length of track (in inches) and the cost in dollars.

If 6.4
6
.
4
inches of track costs $16
$
16
, what is the constant of proportionality?

Answer:

Total time taken by train = 8 hour 32 minutes

Step-by-step explanation:

Given:

Time train leave Zurich = 22:40 min

Time train arrives in Vienna = 07:32

Find:

Total time taken by train

Computation:

Total time taken by train = [23:60 - 22:40] + 7:32

Total time taken by train = 1:20 + 7:32

Total time taken by train = 8:52

Total time taken by train = 8 hour 32 minutes

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:

i dont see anything

Step-by-step explanation:

Answer:

100%_$40.80

? × _$38.76

Step-by-step explanation:

100%×$38.76÷$40.80=95%

Answer:

40.80

Step-by-step explanation:

Answer:

Amy is right

Step-by-step explanation:

4.32-2.6 = 1.72

Answer:

Amy is correct

Step-by-step explanation:

4.32-2.6 = 1.72

Answer:

3293/72

Step-by-step explanation:

change to improper fraction to times.

Answer:

70 x 47x = 3290

.

. . . . . . . . . . ........

Answer: 6x^3-35x^2+47x-12

Step-by-step explanation:

(2x-3)(x-4)(3x-1)

=(2x^2-11x+12)(3x-1)

=6x^3-35x^2+47x-12

Answer:

190%

Step-by-step explanation:

$1.56 is close to nearly 2x the value of $0.87

You can start by multiplying $0.87 by 2 to get $1.74

Now put $1.56 / $1.74

This gets you 0.89655172

By rounding this, you can get to 0.90

Move the decimal places two spots over to get a percentage = 90%

Since the eggs didn't decrease in value, you can add the 100% from the beginning of the problem.

100+90=190%

Answer:

Step-by-step explanation:

For this, we kind of have to test points to solve it. First, we can test theh interval x<= -2. Plug in  -2 and we get a negative value which works. Next, let's try -2<x<0. Plug in -1 and get a positive value which doesn't work.

Next try 0<=x<=7. Plug in any number like 4 and get a negative value which works.

Finally, try x>7. Plug in 8 for example and you would get a positive value. So the solution is

x <= -2 OR 0 <= x <= 7

Answer:

20% of 10% of 1000 = 20

Step-by-step explanation:

Now we have to,

→ find the 20% of 10% of 1000.

Let's find 10% of 1000,

→ (10/100) × 1000

→ 0.1 × 1000

→ 100

Then 20% of 10% of 1000 is,

→ (20/100) × 100

→ 0.2 × 100

→ 20

Hence, the answer is 20.

Answer:

5.7

Step-by-step explanation:

First find the coordinates of the points

A ( 2,2)

B ( -2,-2)

The distance is

d = sqrt(  (x2-x1)^2 + (y2-y1)^2)

  = sqrt(  (-2-2)^2 + (-2-2)^2 )

   = sqrt( (-4)^2 + (-4) ^2)

   = sqrt( 16+16)

  = sqrt( 32)

  =5.656854249

To the nearest tenth

5.7

Answer:

5.65

Step-by-step explanation:

(2,2) (-2,-2)

√(x2 - x1)² + (y2 - y1)²

√(-2 - 2)² + (-2 - 2)²

√(-4)² + (-4)²

√(16) + (16)

√32

= 5.65

Answer:

Option (A)

Step-by-step explanation:

From the picture attached,

ΔABC and ΔDEF are the similar triangles.

Therefore, by the property of similar triangles, their corresponding sides will be proportional.

[tex]\frac{AB}{DE}= \frac{BC}{EF}= \frac{AC}{DF}[/tex]

[tex]\frac{5.75}{18}=\frac{BC}{12}[/tex]

BC = [tex]\frac{12\times 5.75}{18}[/tex]

BC = 3.83 ft

Option (A) will be the correct option.

Answer:

6 ft

Step-by-step explanation:

Draw a plane, showing the three (non-linear) points that define it.[tex]\boxed{\large{\bold{\blue{ANSWER~:) }}}}[/tex]

See this attachment

Answer:

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

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

Answer:

15

Step-by-step explanation:

32-19 = 13 that have both

70-57= 13 that have both again from that sample

total number of people that have both : 13 + 13 = 26

11 kids don't have either one, so :

26-11 = 15

Answer:

Answer A: g(x) = (x + 4)² - 3(x + 4) - 2

Step-by-step explanation:

f(x) + n - shift the graph n units up

f(x) - n - shift the graph n units down

f(x + n) - shift the graph n units left

f(x - n) - shift the graph n units right

f(x) = x² - 3x - 2.

shift 4 units left, f(x + 4) = (x + 4)² - 3(x + 4) - 2

Answer A: g(x) = (x + 4)² - 3(x + 4) - 2

Recall that the tangent function is defined by

tan(x) = sin(x)/cos(x)

Also recall the double angle identity for sine,

sin(2x) = 2 sin(x) cos(x)

Then the equation is the same as

3 sin(x)/cos(x) = 4 sin(x) cos(x)

Move everything to one side to prepare to factorize:

3 sin(x)/cos(x) - 4 sin(x) cos(x) = 0

sin(x)/cos(x) (3 - 4 cos²(x)) = 0

As long as cos(x) ≠ 0, we can omit the term in the denominator, so we're left with

sin(x) (3 - 4 cos²(x)) = 0

and so

sin(x) = 0   or   3 - 4 cos²(x) = 0

sin(x) = 0   or   cos²(x) = 3/4

sin(x) = 0   or   cos(x) = ±√3/2

On the interval [0, 2π),

• sin(x) = 0 for x = 0 and x = π

• cos(x) = √3/2 for x = π/6 and x = 11π/6

• cos(x) = -√3/2 for x = 5π/6 and x = 7π/6

(None of these x make cos(x) = 0, so we don't have to omit any extraneous solutions.)

Answer:

3/5

Step-by-step explanation:

cos A = adjacent side / hypotenuse in a right triangle

cos A = 24/40

Cos A = 6/10

cos A = 3/5

Answer:

5x-6

Step-by-step explanation:

f(x) = 2x + 3

g(x) = 3x - 9

f(x) + g(x) = 2x + 3  + 3x-9

               = 5x-6

Answer:

158.5

Step-by-step explanation:

= 52 - 6 × 1 + 75 × 3 / 2

= 52 - 6 + 75 × 3 ÷ 2

= 52 - 6 + 112.5

= 46 + 112.5

= 158.5

Answer:

The solution is 158,5

Step-by-step explanation:

52-6×1+75×3÷2

= 52-6+75×3÷2

= 46+225÷2

= 46+112,5

= 46+112,5

= 158,5

Answer:

[tex]3uq \\ 3 \times 2 \times 6 \\ = 36[/tex]

Answer:

[tex]36[/tex]

Step-by-step explanation:

[tex]3uq \\ = 3(2)(6) \\ = 36[/tex]

Answer:

9/10 or 90 %

Step-by-step explanation:

There are 54+27+5+4 total people = 90

The people with diploma is 54+27 = 81

P (diploma) = number with diploma / total

                  = 81/90

                  =9/10

                   90%

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:

Second option

Step-by-step explanation:

Let's assume that x is 1 and y is 3

a) [tex]\frac{1}{2}[/tex] < [tex]\frac{3}{2}[/tex] = true

b) -1 < -3 = false

c) 1+2 < 3+2 = true

d) 2 x 1 < 2 x 3 = true

Answer:

Step-by-step explanation:

The function [tex]f(x)=x^2+4[/tex] is a positive upwards opening parabola with the vertex at (0, 4), whereas

the function [tex]g(y)=y^2+4[/tex] is a positive rightwards opening parabola (sideways parabola) with the vertex at (4, 0). This means that answer to this is that g(y) is reflected over the x axis whereas f(x) is reflected over the y axis.