The measure of angle CDE is
degrees.

The sum of the partial fraction is [tex]\frac{2x + 4}{x(x + 2)(x -4)} = -\frac 12 + \frac{1}{2(x -4)}[/tex]

The expression is given as:

[tex]\frac{2x + 4}{x(x + 2)(x -4)}[/tex]

As a partial fraction, we have:

[tex]\frac{2x + 4}{x(x + 2)(x -4)} = \frac Ax + \frac{B}{x + 2} + \frac{C}{x -4}[/tex]

Take the LCM

[tex]\frac{2x + 4}{x(x + 2)(x -4)} = \frac {A(x + 2)(x -4) +Bx(x -4) + Cx(x + 2)}{x(x + 2)(x -4)}[/tex]

This gives

2x + 4 = A(x + 2)(x -4) +Bx(x -4) + Cx(x + 2)

Expand

[tex]2x + 4 = A(x^2 - 2x - 8) + B(x^2 - 4x) + C(x^2 + 2x)[/tex]

Further expand

[tex]2x + 4 = Ax^2 - 2Ax - 8A + Bx^2 - 4Bx + Cx^2 + 2Cx[/tex]

Collect like terms

[tex]2x + 4 = Ax^2 + Bx^2 + Cx^2 - 2Ax - 4Bx + 2Cx - 8A[/tex]

By comparing the coefficients, we have:

A + B + C = 0

-2A - 4B + 2C = 2

-8A = 4

Divide both sides of -8A = 4 by -8

[tex]A = -\frac 12[/tex]

Substitute [tex]A = -\frac 12[/tex] in the other equations

[tex]-\frac 12 + B + C = 0[/tex]

[tex]B + C = \frac 12[/tex]

[tex]C = \frac 12 - B[/tex]

[tex]-2*- \frac 12 - 4B + 2C = 2[/tex]

1 - 4B + 2C = 2

- 4B + 2C = 1

Substitute [tex]C = \frac 12 - B[/tex] in - 4B + 2C = 1

[tex]- 4B + 2*\frac12 = 1[/tex]

- 4B + 1 = 1

Subtract 1 from both sides

-4B = 0

This gives

B = 0

Substitute B = 0 in [tex]C = \frac 12 - B[/tex]

[tex]C = \frac 12 - 0[/tex]

[tex]C = \frac 12[/tex]

So, we have:

[tex]A = -\frac 12[/tex], B = 0 and [tex]C = \frac 12[/tex]

The equation [tex]\frac{2x + 4}{x(x + 2)(x -4)} = \frac Ax + \frac{B}{x + 2} + \frac{C}{x -4}[/tex] becomes

[tex]\frac{2x + 4}{x(x + 2)(x -4)} = -\frac 12 + \frac{0}{x + 2} + \frac{1}{2(x -4)}[/tex]

Evaluate

[tex]\frac{2x + 4}{x(x + 2)(x -4)} = -\frac 12 + \frac{1}{2(x -4)}[/tex]

Hence, the sum of the partial fraction is [tex]\frac{2x + 4}{x(x + 2)(x -4)} = -\frac 12 + \frac{1}{2(x -4)}[/tex]

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Answer:

120 = L+2W

LW =area.

to maximize area with given fencing that would make Width = 30 feet and length = 60

A= LW = (120-2W)W = 120W -2W^2

A' = 120-4W =0

W = 30

L=120-2(30) = 60 feet

W by L is 30 by 60 feet for max area

Answer:

h(4)=17

Step-by-step explanation:

h(g(x)), h(x)= 2x+9; g(x)=4

2(4)+9= 8+9=17

Answer:

(x-7)

Step-by-step explanation:

(1/6)*(x-7)= (1/6)x-(7/6)

Explanation:

Given Inequalities:

(i) 3x + 8y ≤ 480

(ii) y - x ≤ 20

For first inequality:

(a) y intercept: (0, 60)

(b) x intercept: (160, 0)

For second inequality:

(a) y intercept: (0, 20)

(b) x intercept: (-20, 0)

The point (40, 40) falls between these two inequalities.

Using the permutation formula, it is found that Emily can make 120 arrangements with 1 plant in each spot.

We are working with an arrangement, which means that the order in which the plants are inserted is important, hence the permutation formula is used to solve this question.

The number of possible permutations of x elements from a set of n elements is given by:

[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]

In this problem, 3 plants are selected from a set of 6, hence the number of arrangements is given by:

[tex]P_{(6,3)} = \frac{6!}{3!} = 120[/tex]

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Answer:

11.94 %

Step-by-step explanation:

Compound interest formula     FV = PV e^(it)    i = decimal interest per year  

                                                                             t = time   FV = future value

2600 = 1000e^(i * 8)

  solve for i = 11.94 %

Answer:

a<-12

Step-by-step explanation:

The ratio of a : b : c in its simplest form is 5 : 12 : 30 respectively

So,

a / b = 1/6

b/c = 2/5

1/6 + 2/5

=(5 + 12) /30

a : b and b : c

= 5/30 and 12/30

Therefore,

a : b : c = 5 : 12 : 30

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Mark me the Brainliest!

Answer:

The point will be plotted on Y axis

The length of the other leg of the right triangle will be 13.86 cm.

The complete question is given below.

The triangle BCD ​ is a right triangle. The length of the hypotenuse is 19 centimeters. The length of one of the legs is 13 centimeters.

What is the length of the other leg?

The Pythagoras theorem states that the sum of two squares equals the squared of the longest side.

The Pythagoras theorem formula is given as

H² = P² + B²

Let the unknown sides be x. Then we have,

19² = 13² + x²

361 = 169 + x²

 x² = 361 – 169

 x² = 192

  x = 13.856 ≈ 13.86 cm

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Answer:

function

Step-by-step explanation:

no repeated domain means its a function

By identifying the intersection between the graphs, we conclude that the solution is (-3, 4).

To graphically solve a system of equations, we need to graph the equations of the system in the same coordinate axis, and then find the intersection points between the graphs.

Here we already have the equations graphed, so we only should find the points of intersection.

We can see two red lines, we can see that the lines intersect at the point (-3, 4). This means that the solution of the system of equations is the point (-3, 4).

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Answer: 78.09

Step-by-step explanation:

Seventy-eight is the whole number, so it goes to the left of the decimal point 78.09

Nine-hundredths is decimal, it goes two places to the right of the decimal point because it's hundredths 78.09

because the x values are identical the radius would be found by subtracting the y values.

6-2 = 4

the radius is 4

Answer: 81.

Step-by-step explanation: It is given that the side lengths are all 9 feet. Since the bathroom is a square, all the sides of the bathroom are 9 feet. You can use the formula (area = s^2). 9 x 9 is 81.

Answer:

(4,-3)

Step-by-step explanation:

The scale factor is 1/3. So, multiply the numbers by 1/3.

12*1/3 is 4.

-9*1/3 is -3.

The new coordinates are (4,-3).

By finding the scale factor of the model, we will see that the area is 561,600 square feet.

On the model, the length is 13 inches, and the actual length is 780 ft, then the scale factor is:

k = (780ft)/(13 in) = 60 ft/in

This means that each inch in the model is equal to 60ft in the actual plot of land.

Then the width is:

W = (12in)*( 60 ft/in) =  720 ft

And the area is the product between length and width, so we have:

A = (780ft)*(720ft) = 561,600 ft²

Then the correct option is D.

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Answer:

Hold its nose

Step-by-step explanation:

You can actually de-scent a skunk if it is the powerful defensive odor you are referring to. When you have a skunk de-scented, they are no longer able to spray, and at this point they are now similar to having a pet cat or dog; lovable and highly desire affection and attention from their owners.

Answer:

B. The graph of p is less steep than the graph of q.

Step-by-step explanation:

We can start by looking at each equation's y-intercepts, which are both -3/11, eliminating option A.

Next, we take a look at each equation's slope to see which is larger.

5/8 is 0.625 in decimal form. 8/5 is 1.6 in decimal form.

Therefore, q(x) has the larger slope, meaning the graph of p is less steep than the graph of q. (B.)

Answer:

x=7 ................................

Answer:

6

Step-by-step explanation:

[tex]f(a)=a^4-2a^3 -10a^2 -7a \\\\f(-2) = (-2)^4-2(-2)^3 -10(-2)^2 -7(-2)\\\\~~~~~~~~~=16-2(-8)-10(4)+14\\\\~~~~~~~~~=30+16-40\\\\~~~~~~~~~=46-40\\\\~~~~~~~~~=6[/tex]

The height of the pile is 150.7 mm, and the volume is V = 6,830,477.5 mm³.

We know that each paper is 0.55mm thick, then if we pile 274 of these, the height of the pile will be:

H = 0.55mm*274 = 150.7mm

Now we want to get the volume of the pile of paper. Remember that for a rectangular prism of height H, width W, and length L, the volume is:

V = H*W*L

In this case, we have:

Then the volume is:

V = (150.7mm)*(185 mm)*(245 mm) = 6,830,477.5 mm³

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Three selected options are as follows:

Distance is a numerical measurement of how far apart objects or points are. In Physics or everyday usage, distance may refer to a physical length or an estimation based on other criteria.

Here, put the values in option substitute  in given equation D(t)

Option 1: At t = 0 hour,

              D (0) = 300 X 0 + 125 = 125 ≠ 300    Option Incorrect

Option 2 : At t = 2 hours,

                D(2) = 300 X 2 + 125 = 725  Option Correct.

Option 3: At t = 2.5 hours,

               D(2.5) = 875  Option Incorrect

Option 4: At t = 3 hours,

               D(3) = 875 Option Correct

Option 5: At t = 6 hours,

                D(6) = 75 X 6 + 612.5 = 450 + 612.5

                        = 1062.5 miles  Option Correct

Thus, Option two, four and five are correct.

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Answer:

D) 39

Step-by-step explanation:

[tex]||\text{c}\bold{u}||=||3\langle5,12\rangle||=||\langle3*5,3*12\rangle||=||\langle15,36\rangle||=\sqrt{15^2+36^2}=\sqrt{225+1296}=\sqrt{1521}=39[/tex]

The expression E(p) represents the elasticity at point p and by putting the known data we can find the value of elasticity.

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

We have a demand function:

q=0. 6(3800-p²)

Differentiate with respect to p:

[tex]\rm \dfrac{dq}{dp} = -1.2p[/tex]

We know the elasticity:

[tex]\rm E(p) = \dfrac{dq}{dp}\times\dfrac{p}{q}[/tex]

[tex]\rm E(p) =-1.2p \times\dfrac{p}{0.6(3800-p^2)}[/tex]

[tex]\rm E(p) = -\dfrac{2p^2}{(3800-p^2)}[/tex]

Here the data for p and q are not given, but we can find any value using the above expression by putting the known data.

Thus, the expression E(p) represents the elasticity at point p and by putting the known data we can find the value of elasticity.

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The value of the car after three years is £6936

The initial value of the car is given as:

Value =  £12000

When the value depreciates by 20% after the first year, the new value of the car is:

New =  £12000 * (1 - 20%)

Evaluate

New =  £9600

When the value depreciates by 15% after the second year, the new value of the car is:

New =  £9600* (1 - 15%)

Evaluate

New =  £8160

When the value depreciates by 15% after the third year, the new value of the car is:

New =  £8160 * (1 - 15%)

Evaluate

New =  £6936

Hence, the value of the car after three years is £6936

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The probability that the lunch combo will have an ham sandwich is 3 / 7.

Probability simply means possibility. It describes how likely an event will occur or happen.

Mathematically,

probability = number of favourable outcome to A / total number of possible outcome

Therefore,

probability that a lunch combo will include a ham sandwich = 6 / 14 = 3 / 7

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The area of the Triangle PQR which is in the circle,  is given as 784.25. See the computation below.

Mathematically speaking, a circle is a 2-dimensional shape whose boundaries are round and are equidistant from a fixed center.

The area of ΔPQR is given as ((√3)/4) x QR²

= (√3)/4) x (6√2 - 2√6)²

= 0.43301270189 x  (8.48528137424 x 4.89897948557)²

=  0.43301270189 x 1728

Area of ΔPQR = 784.25

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