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f(x) = 12(x - 1)/[(x + 2)(x - 3)] is the equation of the function graphed as in the figure. This can be obtained using the formula of f(x) = P(X)/Q(X) by vertical asymptotes and factors of the polynomial.

Let  where P(X) and Q(X) are polynomial function.

The function has the following:

This means that, -3 and 2 are roots of the denominator. Thus, the equation of the denominator is:

⇒ Q(X) = (x + 2)(x - 3)

Let a be the leading coefficient of P(X)

⇒ P(X) = a(x - 1)

Now for finding the value of a we can rewrite the equation as,

⇒ f(x) = P(X)/Q(X)

⇒ f(x) = a(x - 1)/[(x + 2)(x - 3)]

⇒ f(0) = a(0 - 1)/[(0 + 2)(0 - 3)]

Since from the graph we can say that the y-intercept is (0, - 2), this means that when x = 0, y = -2, f(0) = - 2

⇒ - 2 = -a/[(2)(- 3)]

⇒ a = - 2 × 2 × 3

⇒ a = - 12

By putting a = -12 in f(x) we get,

⇒ f(x) = 12(x - 1)/[(x + 2)(x - 3)]

Hence f(x) = 12(x - 1)/[(x + 2)(x - 3)] is the equation of the function graphed as in the figure.

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Hello and Good Morning/Afternoon:

Let's take this problem step-by-step:

What does the problem want us to find:

 [tex]\hookrightarrow \text {Slope-intercept form}[/tex]

What is the slope-intercept form:

 [tex]\hookrightarrow \text {it is when the function has the y-variable isolated by itself to one side}\\\hookrightarrow \text{and everything else to the other side}[/tex]

Let's apply our knowledge:

  [tex]2x =3y-5\\-3y=-5-2x\\y=\frac{2}{3} x+\frac{5}{3}[/tex]

Answer:[tex]y=\frac{2}{3} x+\frac{5}{3}[/tex]

Hope that helps!

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Answer:

124.5°

Step-by-step explanation:

Let the smallest angle be x. Then, the sum of the angles is an arithmetic sequence with first term x, common difference 7, and 8 terms.

Using the sum of an arithmetic series formula,

[tex]\frac{8}{2}(2x+(8-1)(7))=1080 \\ \\ 4(2x+49)=1080 \\ \\ 2x+49=270 \\ \\ 2x=221 \\ \\ x=110.5[/tex]

So, the third angle is 110.5+14=124.5

Answer:

Area under the graph = 6 sq.units

I've shown the complete calculation over the attached page

Answer:

0.524

Step-by-step explanation:

That is the answer not really sure tho

Using the relation between velocity, distance and time, it is found that her jogging rate was of 6 mph.

Velocity is distance divided by time, hence:

[tex]v = \frac{d}{t}[/tex]

Jogging, her velocity was of v, while the time was of t, for a distance of 12 miles, hence:

[tex]v = \frac{12}{t}[/tex]

Biking, her velocity was of v + 6, while the time was of 3 - t, for a distance of 12 miles, hence:

[tex]v + 6 = \frac{12}{3 - t}[/tex]

[tex]v = \frac{12}{3 - t} - 6[/tex]

Then:

[tex]\frac{12}{t} = \frac{12}{3 - t} - 6[/tex]

[tex]\frac{12}{3 - t} - \frac{12}{t} = 6[/tex]

[tex]\frac{12t - 36 + 12t}{t(3 - t)} = 6[/tex]

18t - 6t² = 24t - 36

6t² + 6t - 36 = 0

t² + t - 6 = 0

(t + 3)(t - 2) = 0. -> t = 2 hours.

Hence her jogging rate in mph is given as follows:

[tex]v = \frac{12}{2} = 6[/tex]

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The volume of a container shows the amount of space that it has inside of it.

The use of bento boxes that has edges that are a foot long and the use of a rectangular-shaped container to ship it would have been more useful if the dimensions were provided.

Provided that the dimensions are provided, the formula that can be used to find the volume of a container is:

V = L × W × H

Where:

L= Length

W= Width

H= Height

It is worthy to note that your question is incomplete as you did not include the answer choices for how the manager found the volume of the container and other questions so a general overview was given.

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The manager can find the volume of the container using the formula lwh. The employee correctly determines that the container can be filled with 3 layers of 21 bento boxes. He can find the volume of the container by multiplying the number of bento boxes that fill the container by the volume of one bento box. The volume found by using the formula is equal to the volume of the total number​of bento boxes in the container.

The number of tickets sold are:

From the question, we have the following parameters:

Number of tickets = 63

Total amount = 444 Birr

Adult ticket = 8 Birr per adult

Children ticket = 6 Birr per adult

Represent the children tickets with x and adults ticket with y.

So, we have the following system of equations

x + y = 63

6x + 8y = 444

Express the equations as a matrix

x      y

1       1       63

6      8       444

Apply the following transformation

R2 = R2 - 6R1

This gives

x      y

1       1       63

0      2       66

Apply the following transformation

R2 = 1/2R2

x      y

1       1       63

0      1       33

From the above matrix, we have the following system of equations

x + y = 63

y = 33

Substitute y = 33 in x + y = 63

x + 33 = 63

Subtract 33 from both sides of the above equation

x = 30

Hence, 30 children tickets were sold and 33 adult tickets were sold

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Given the area and perimeter of the rectangular dining room, the dimensions of the dining room are 8m by 8m.

The area of rectangle is expressed as;

A = l × b

The perimeter of a rectangle is expressed as;

P = 2( l + b )

Given that;

We use the information given to form a system of equations.

A = l × b

64 = l × b

P = 2( l + b )

32 = 2( l + b )

Hence, we have;

64 = l × b --------- equ 1

32 = 2( l + b )-----equ 2

Lets make l the subject of the formula in equation 1

64 = l × b

l = 64/b -------------equ 3

Substitute equation 3 into equation 2

32 = 2( l + b )

32 = 2l + 2b

32 = 2(64/b) + 2b

32 = 128/b + 2b

Now, we solve for b.

32 = 128/b + 2b

32 - 2b = 128/b

32b - 2b² = 128

2b² - 32b + 128 = 0

We factor out 2

2( b² - 16b + 64) = 0

From perfect square rule

2( 8-b )² = 0

divide both side by 2 and take the square root of both side

( 8-b )² = 0

8-b = 0

b = 8

Substitute b=8 into equation 1

64 = l × b

64 = l × 8

l = 64/8

l = 8

Given the area and perimeter of the rectangular dining room, the dimensions of the dining room are 8m by 8m.

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Answer:

8

Step-by-step explanation:

let the number=x

8(x-2)=16(x-5)

divide by 8

x-2=2(x-5)

x-2=2x-10

2x-x=-2+10

x=8

Answer:

Step-by-step explanation:

The perimeter formula and the given relation between length and width can be used to write and solve an equation for the field dimensions.

Let w represent the width of the field. Then (3w-120) is the length of the field, and its perimeter is ...

  P = 2(L +W)

  1040 = 2((3w-120) +w)

Dividing by 2 and simplifying, we have ...

  520 = 4w -120

  130 = w -30 . . . . . . divide by 4

  160 = w . . . . . . . . . add 30

  3w-120 = 3(160) -120 = 360 . . . the field's length

The dimensions of the field are 160 feet long by 360 feet wide.

Based on the given diagram (see attachment), the statement which is missing in the proof is: D. m∠7 ≅ m∠5.

Parallel lines can be defined as two (2) lines that are always the same (equal) distance apart and never meet.

In Geometry, two (2) lines are considered to be parallel if their slopes are the same (equal) and they've different y-intercepts. This ultimately implies that, two (2) lines are parallel under the following conditions:

m₁ = m₂

Note: m is the slope.

From the given diagram (see attachment), we can logically deduce that line m is parallel to line n (m || n) and a transversal line intersects both of them.

Based on these reasons, we can prove the following statements:

In conclusion, we can logically deduce that the statement which is missing in the proof is m∠7 ≅ m∠5.

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Answer:

here you go

Step-by-step explanation:

The equation in the form of the given expression is (0)² + (1)² = 1

According to some of the trigonometry identity

sin 0 = 0

cos 0 1

Given the expression below

sin^2 0+cos^2 0=1

This can also be expressed as:

(sin0)² + (cos0)² = 1

Substitute

(0)² + (1)² = 1

Hence the equation in the form of the given expression is (0)² + (1)² = 1

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For circumference use C = 2πr because π is the ratio of Circumference to diameter and diameter is 2 x radius.

C = 2 x 3.142 x 9.5 cm ≈ 59.7 cm

Area of a circle is π x r² = 3.142 x (9.5 cm)² ≈ 283.6 cm²

The circumference of a circle with a radius of 9.5 centimeters is about 59.7 centimeters and the area of a circle with radius of 9,5 centimeters is about 283.6 centimeters.

The Average number of sheep grazed in per acre is 6 approx. in rancher’s herd.

According to the statement

We have given that the A rancher’s herd of 250 sheep grazes over a 40-acre pasture.

And we have to find the how many sheep are grazing on each acre.

So, For this purpose If we assume that the sheep are equally distributed, to see how many sheep there are in each acre we just divide the number of sheep by the number of acres. So,

we have to find the average of number of sheep in per acre.

We know that

The total area of the rancher’s herd = 40 acre

The number of sheep grazes in the land = 250 sheep

Now, we have to find the Average number

Average number of sheep grazed in per acre = 250/40

Average number of sheep grazed in per acre = 6 approx.

So, The Average number of sheep grazed in per acre is 6 approx. in rancher’s herd.

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Answer:

I think it's 120 dollars sorry if i get it wrong but I am sure it is right tell me when you get the right answer byeeee.

Answer:

x=10 and x=-4

Step-by-step explanation:

When the absolute value is all by itself on one side of the equation, the next step is to remove the absolute value bars. This will create TWO separate equations.

| x - 3 | = 7

x-3 = 7 This is one of the equations. Just straight up copied the equation but without the bars.

Here is the second equation:

x - 3 = -7

It is the left side copied, without the bars, but the right side has the opposite sign.

Solve these both separately to find the answers.

x-3=7 and x-3=-7

x=10 and x=-4

Answer:

40 meters a minute

Step-by-step explanation:

800m - 20 min

800/20

40m-1 min

The difference between the total number of wholesalers and those that supply on 30-day credit, gives the number that require cash on delivery as 2

The number of wholesalers Sue has sourced = 4

Terms of two suppliers = 30 days credit

Amount of stock Sue has = $15000

Amount of stock on credit = $10000

Operating cash reserve of the business = $20000

Required:

The number of wholesalers that require terms of cash on delivery

Solution:

Given that the number of wholesalers = 4

The number number of suppliers (wholesalers) that supply on 30-day credit = 2

Therefore;

The number of wholesalers that require terms of cash on delivery = 4 - 2 = 2

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Answer:

a

Step-by-step explanation:

[tex]\sqrt{9^2 + 12^2 + 5^2}=\sqrt{250}=5\sqrt{10}[/tex]

The value of diameter and radius of circle is 7 cm and 3.5cm.

According to the statement

we have given that the a figure of circle and we have to find the radius and the diameter of the circle.

So, We know that the

The radius of a circle runs from its center to its edge, the diameter runs from edge to edge and cuts through the center.

Here from the figure it is clear that the

Diameter of circle = 7cm

and the radius of circle we have to find

So,

Radius of circle = Diameter /2

Substitute the values in it then

Radius of circle = 7cm /2

Radius of circle = 3.5 cm.

So, The value of diameter and radius of circle is 7 cm and 3.5cm.

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Answer: 8  units

Step-by-step explanation:

Answer:

2.8 metres each

Step-by-step explanation:

14/5

2.8

Solving for y:

6y - 2x = 20

6y = 2x + 20

y = [tex]\frac{2x + 20}{6}[/tex]

y = [tex]\frac{2x}{6} + \frac{20}{6}[/tex]

y = [tex]\frac{1x}{3} + \frac{10}{3}[/tex]

Hope it helps!

Answer:

Step-by-step explanation:

6y - 2x = 20

     -6      -6

-2x = 20 - 6y

divide both sides by -2

[tex]\frac{-2x}{-2}[/tex] = [tex]\frac{20 - 6y}{-2}[/tex]

Dividing by -2 undoes the multiplication by -2.

[tex]x = \frac{20 - 6y}{ -2}[/tex]

Divide 20 -6 by -2

x = 3y - 10

Or

y = [tex]\frac{10}{3}[/tex]x +[tex]\frac{x}{3}[/tex]

Perimeter → 25cm

Area → 25.5cm²

[tex]perimeter = > 2.5 \times 2 + 5.5 + 3.5 + 6 + 3 + 2 = 5 + 9 + 9 + 2 = 25[/tex]

[tex]area = > 3 \times \frac{1}{2} \times 2 + 3 \times 3.5 + 6 \times 2 = 3 + 12 + 10.5 = 25.5[/tex]

Answer:

5

Step-by-step explanation:

The midpoint of segment AB is (1, 1).

Substituting these coordinates into the equation of the line,

[tex]2(1)+3(1)-k=0 \\ \\ 5-k=0 \\ \\ k=5[/tex]

Answer:

350

Step-by-step explanation:

Let the number of adult tickets be x, then the number of student tickets sold would be (x–54).

We now have

x+(x–54)=646

2x=700

x=350

Therefore, 350 adult tickets were sold.

Answer:

Y=mx+b

Step-by-step explanation:

The answer is y = -4/5x + 4.

We know the general form for slope intercept form is :

y = mx + c

The given equation is in standard form.

4x + 5y = 20

Bring 4x to the other side by subtracting 4x on both sides.

4x + 5y - 4x = 20 - 4x

5y = -4x + 20

Divide 5 on both sides to isolate the variable y.

5y x 1/5 = 1/5 x (-4x + 20)

y = -4/5x + 4

Answer:

-4

Step-by-step explanation:

7x^3 + 5x^2 - 2
= 7*-1 + 5*1 - 2

= -7 + 5 - 2

= -4