find the equation of a line that is parallel to y=3x+6 and passes through A
) (0,-2) B. (2,5) C.(4,1)

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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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:

The median of 38, 42, 77, 47, 74, 51, 48, 41, 82, 72, 74, and 129 is 61.5.

Step-by-step explanation:

First, rearrange the data set in order.

38, 42, 77, 47, 74, 51, 48, 41, 82, 72, 74, 129

38, 41, 42, 47, 48, 51, 72, 74, 74, 77, 82, 129

Identify how many numbers are in the set. This will make it easier to infer the median.

Counting will show that this is a 12 number data set.

To find the median:

If there are an ODD amount of numbers in a data set, take the middle number. That is your median.

If there are an EVEN amount of numbers in a data set, take the middle two numbers, add them, then divide that by 2. That is your median.

Knowing this, take your middle two numbers, 51 and 72, and add them and divide by 2.

51 + 72 = 123

123/2 = 61.5

The median of this data set is 61.5.

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).

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.

Answer:

x = -2

Step-by-step explanation:

Since this is a vertical line, the equation of the line will not be in y = mx+b form. The slope of the line is undefined. So, the equation will be x =.

To figure out what x equals, look at all the x values in the coordinates or look to see where it crosses the x axis, which is at -2.

The equation is x = -2.

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:

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]

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:

h(4)=17

Step-by-step explanation:

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

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

Answer:

9 units

Step-by-step explanation:

Reflections do not change the size of a shape, only dilations do. The side length will stay 9 units.

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 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 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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Answer:

(x-7)

Step-by-step explanation:

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

Mark me the Brainliest!

Answer:

The point will be plotted on Y axis

Answer:

function

Step-by-step explanation:

no repeated domain means its a function

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 %

The lines that best represent perpendicular lines are: D. FI and JH.

Perpendicular lines are lines that meet at a right angle, that is, the point of their intersection forms a right angle.

From the image given, lines FI and JH intersect at point I, and also appears to form a right angle.

Therefore, the lines that are perpendicular in the image are: D. FI and JH.

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Answer: 5.2

The apothem angle is 360/10, which is 36.

Therefore, we have tangent 36  = 3.8/a

And solving for a, we find that it is 5.2

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>24

Step-by-step explanation:

multiply both sides by 3 to get ride of the denominator:

h>24

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:

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.)

Given : f(x) = 6x - 2 and g(x) = 2x + 4 .

Need To Find : Functions : (I). (f+g)(x) &, (II). (f-g)(x) .

ㅤ(I) (f+g)(x)

[tex]\sf\quad\dashrightarrow \:\: \big(\:f\:+\:g\: \big)\:x\: \:\\\sf\quad\dashrightarrow \:f \big(x \big)\:+\:g \big(x \big)\:\:\\\sf\quad\dashrightarrow \: \big(6x-2 \big)\:+\: \big(2x+4 \big)\:\:\\\sf\quad\dashrightarrow \:6x-2\:+\:2x+4\:\:\\\pmb{\sf\quad\dashrightarrow \:8x \: +\: 2\:}\:\\[/tex]

ㅤ(I) (f-g)(x)

[tex]\sf\quad\dashrightarrow \:\: \big(\:f\:-\:g\:\big)\:x\: \:\\\sf\quad\dashrightarrow \:f\big(x\big)\:-\:g\big(x\big)\:\:\\\sf\quad\dashrightarrow \:\big(6x-2\big)\:-\:\big(2x+4\big)\:\:\\\sf\quad\dashrightarrow \:6x-2\:-\:2x-4\:\:\\\pmb{\sf\quad\dashrightarrow \:4x \: -\: 6\:}\:\\[/tex]

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:

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]

Answer:

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

#6

Sum of exterior angles of any polygon=360°

sides=6

Measure of one angle

Option D

#7

4ft=1cm

and

Dimensions are 8cm and 15cm

Option B

Answer:

6.  d.  m∠YXZ = 60°

7.  b.  8 cm x 15 cm

Step-by-step explanation:

Question 6

∠YXZ is the exterior angle of a regular polygon

Exterior angle of a regular polygon = 360° ÷ number of sides

⇒ ∠YXZ = 360° ÷ 6

⇒ ∠YXZ = 60°

Question 7

Scale  1 cm : 4 ft

Therefore, to convert actual dimensions in feet to sketch dimensions in centimeters, divide dimensions in feet by 4:

⇒ width = 32 ft

⇒ width = 32 ÷ 4 = 8 cm

⇒ length = 60 ft

⇒ length = 60 ÷ 4 = 15 cm

Therefore, the dimensions of the sketch are 8 cm x 15 cm