Which of the graphs below represents a sketch of:

The area of R is ln(4) - ln(√2) and the value of k is √2.

a) To find the area of the region R, we need to find its definite integral with respect to x. Using substitution, we can write the integral as follows:

Let u = [tex]x^{2}[/tex] + 2, du/dx = 2x, dx = du/2x

Area of R = ∫[0,√6] x/([tex]x^{2}[/tex] + 2) dx = ∫[2,8] (1/2) du/u = (1/2) ln(u) evaluated from 2 to 8 = (1/2) ln(8) - (1/2) ln(2) = ln(4) - ln(√2)

b) The line x = k divides the region R into two regions of equal area if the definite integral of R with respect to x from 0 to k is equal to the definite integral of R with respect to x from k to √6.

Letting k = x in the definite integral, we have:

∫[0,k] x/( [tex]x^{2}[/tex]  + 2) dx = ∫[k,√6] x/( [tex]x^{2}[/tex]  + 2) dx

(1/2) ln([tex]k^{2}[/tex] + 2) - (1/2) ln(2) = (1/2) ln(6 - [tex]k^{2}[/tex] ) - (1/2) ln(2)

Solving for k, we get:

ln( [tex]k^{2}[/tex]  + 2) = ln(6 - [tex]k^{2}[/tex] )

[tex]k^{2}[/tex] + 2 = 6 - [tex]k^{2}[/tex]

2 [tex]k^{2}[/tex]  = 4

k = ±√2

Since k must be in the first quadrant, k = √2.

So, the line x = √2 divides the region R into two regions of equal area.

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The time that the ferries will leave together next, given the time they leave the jetty would be 12 : 15 pm

The ferries leave at intervals of 8 minutes, 12minutes, and 15 minutes. To find  the time when they will all leave at the same time again, you need to find the lowest common multiple of 8, 12 and 15 as this would show the next time the ferries would be lined up together again.

The lowest common multiple of 8, 12 and 15 is 120 which in minutes is 2 hours.

The next time both ferries would leave together is:

= 10 : 15 + 2 hours

= 12 : 15 pm

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Answer:

The width of the base is 120ft. The length of the base is 60ft less than three times the width [1][2], so the length of the base is 180ft. Therefore, the dimensions of the base are 120ft x 180ft.

The solution to the system of equations is: D. (-4, -7).

To solve the system of equations, y = (3/2)x - 1 and y = 3x + 5, you can set the two equations equal to each other and solve for one of the variables. For example, setting the two equations equal to each other:

(3/2)x - 1 = 3x + 5

Then you can solve for x by isolating it on one side of the equation:

(3/2)x - 3x = 5 + 1

-5x/2 = 6

x = -4

Now that you know the value of x, you can substitute it back into one of the equations to find the value of y:

y = (3/2)(-4) - 1 = -6 - 1 = -7

So the solution to the system of equations is x = -4, y = -7.

The solution is: (-4, -7).

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Answer:

2. 5/4

Step-by-step explanation:

The constant of proportionality in this proportional relationship is the ratio of y to x for any given pair of values. To find it, we can divide the y value by the x value for one of the pairs. For example, using the first pair (x = 2, y = 5/2), we can divide 5/2 by 2 to get the constant of proportionality:

(5/2) / 2 = 5/4

Answer:

240000000

Step-by-step explanation:

2.4x100000000=240000000

The missing entries for f(x) are 20, 30, and 40, and the missing entries for g(x) are 40, 80, and 160.

The missing entries for f(x) can be found by knowing that f is a linear function and using the values given. A linear function has the form f(x) = ax + b, where a is the slope and b is the y-intercept. Since f(0) = 10 and f(1) = 20, we can use these two points to find a and b.

Putting x = 0 in the equation, we get:

f(0) = 10 = a(0) + b

Putting x = 1 in the equation, we get:

f(1) = 20 = a(1) + b

Solving these two equations simultaneously, we find:

a = 10

b = 0

So, the equation for f is:

f(x) = 10x + 0 = 10x

Using this equation, we can find the missing entries for f(x) in the table:

f(2) = 10x = 10(2) = 20

f(3) = 10x = 10(3) = 30

f(4) = 10x = 10(4) = 40

So the missing entries for f(x) are 20, 30, and 40.

To find the missing entries for g(x), we need to know the form of the exponential function g. A common form for exponential functions is g(x) = ab^x, where a is the y-intercept and b is the growth factor. Since g(0) = 10 and g(1) = 20, we can use these two points to find a and b.

Putting x = 0 in the equation, we get:

g(0) = 10 = a(1)^0 = a

So, a = 10.

Putting x = 1 in the equation, we get:

g(1) = 20 = 10b

Solving for b, we find:

b = 2

So, the equation for g is:

g(x) = 10(2^x)

Using this equation, we can find the missing entries for g(x) in the table:

g(2) = 10(2^2) = 10(4) = 40

g(3) = 10(2^3) = 10(8) = 80

g(4) = 10(2^4) = 10(16) = 160

So the missing entries for g(x) are 40, 80, and 160.

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--The given question is incomplete; the complete question is

"The table below shows some values of a linear function f and an exponential function g. find exact values (not decimal approximations) for each of the missing entries.                                                                                    x      0  1  2  3 4                                                                                                                                             f(x)  10 _ 20 _ _                                                                                                                                 g(x) 10 _ 20 _ _"--

The length of the fabric which Brandon formed a rectangle, is 11 inches.

To find the length of the fabric, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.

In this case, the length of the fabric is one of the other two sides, and the diagonal cut is the hypotenuse. So, we can write the equation:

[tex]L^2 + 5^2 = 13^2[/tex]

where L is the length of the fabric.

Solving for L, we get:

[tex]L^2 = 144 - 25 = 119, and L =\sqrt{119} = 11.[/tex]

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The correct grouping of the trinomial "-10x² + 13x + 3" is option 4, (-10x² + 0x) + (13x + 3).

To find the correct grouping, we need to factor out the greatest common factor from the first two terms, -10x² + 13x.

The greatest common factor of -10x² and 13x is -x². So, we can factor out -x² and get:

-x² * (10 - 13/x) + 3 = (-x² * 10) + (13/x - x²) + 3 = (-10x² + 7x) + (6x + 3)

Therefore, choice 3 is the correct grouping of the trinomial -10x² + 13x + 3.

A trinomial is a mathematical expression consisting of three terms. It is a polynomial of degree three and has the general form ax³ + bx² + cx + d, where a, b, c, and d are constants and x is a variable.

Complete Question:

'which of the answer choices is a correct grouping of the following trinomial? −10x² 13x 3

1. (-10x² + 5x) - (6x + 3)

2.(-10x² + 2x) +(15x + 3)

3.(-10x² + 7x) +(20x + 3)

4.(-10x² + 0x) +(13x + 3)

5.(-10x² + 0x) - (x + 3)

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Step-by-step explanation:

0.3333333333.... = 1/3

0.2222222222... = 1/3 / 3 × 2 = 2/9

so, we now know all the involved fractions.

(1/3 - 1)² - sqrt(1 - 3/2/2) + 2/9

(-2/3)² - sqrt (1 - 3/4) + 2/9

4/9 - sqrt(1/4) + 2/9

6/9 - 1/2

2/3 - 1/2

to calculate that we need to bring both fractions to the same denominator (6).

2/2 × 2/3 - 3/3 × 1/2 = 4/6 - 3/6 = 1/6

so, the complete result is 1/6.

The arc length covered by the central angle equal to 72° is 12.56°

Arc length is the distance between two points along a section of a curve.

Given that, a circle with radius 10 units and a central angle equals 72°, we need to find the arc length covered by the central angle = 72°

We know that,

Arc length = 2π × radius × (θ / 360°), where θ is the central angle

Arc length = 2 × 3.14 × 10 × 72°/360°

= 12.56°

Hence, the arc length covered by the central angle equal 72° is 12.56°

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Max's next step after swinging arcs on either side of the segment is to place the compass on the other endpoint and swing another arc that intersects the previous arcs.

After swinging arcs on either side of the segment, Max's next step is to place the compass on the other endpoint of the segment.

He needs to make sure the compass width remains the same as before.

Then, he swings another arc that intersects the previous arcs.

The point where the new arc intersects the segment is the midpoint of the segment.

By connecting this point with the endpoints of the segment, Max will have successfully bisected the segment.

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Answer:

(x-4)2=16

Step-by-step explanation:

The equation of the line perpendicular to the line 2x + 5y + 5 = 0 is 5x - 2y + 1 = 0.

As per the given data the given equation is 2x + 5y + 5 = 0

Here we have to determine the equation of the line perpendicular to the line 2x + 5y + 5 = 0

Firstly write the equation in y = mx + c format.

2x + 5y + 5 = 0

5y = -2x - 5

y = [tex]$\frac{-2}{5}[/tex]x - 1

[tex]m_{1}=\frac{-2}{5}[/tex]

Condition for two perpendicular lines.

[tex]m_{1} \times m_{2}[/tex] = -1

[tex]$\frac{-2}{5} m_{2} = -1[/tex]

[tex]$m_{2} = \frac{5}{2}[/tex]

Now substitute the slope value in the equation y = mx + c

We get:

y = [tex]$(\frac{5}{2} )[/tex]x + c

2y = 5x + 2c

2y - 5x = 2c

Since the line passes through (-1, -2)

Hence:

2(-2) - 5(-1) = 2c

-4 + 5 = 2c

2c = 1

c = [tex]$\frac{1}{2}[/tex]

Now substitute the value of c in 2y - 5x = 2c

2y - 5x = 2[tex]$(\frac{1}{2} )[/tex]

2y - 5x = 1

(0r)

5x - 2y + 1 = 0

Therefore the equation is 5x - 2y + 1 = 0.

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Answer:

0.6 divided by 78 is 0.00769230769

or if you meant

78 divided by 0.6 it is 360

Step-by-step explanation:

Answer:

reason 1: Given

reason 2: Property of Cross Multiplication

reason 3: Vertical Angles are Congruent.

reason 4: SAS

The expression after multiplying the factors in the form is -573.21.

The provided expression is (-√36)(-√22)(-√415).

We have to multiply the factor and express in the radical form.

Let us solve this step by step and one by one,

(-√36) = -6

Now, for -√22,

-√22 = -4.69

Now, for -√415,

-√415 = -20.37

Now, we have to simply multiply these three values and that will be the radical form,

So,

(-√36)(-√22)(-√415) = -6 x -4.69 x -20.37

(-√36)(-√22)(-√415) = -573.21

So, the expression after simplification is -573.21.

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Answer:

x = 6

Step-by-step explanation:

6x-9=51-4x

10x - 9 = 51

10x = 60

x = 6

Let's check

6(6) -9 = 51 -4(6)

36 - 9 = 51 - 24

27 = 27

So, x = 6 is the correct answer.

Based on the information we can infer that 25 km is equivalent to 7.5 cm on the map.

To find the relationship between centimeters and kilometers on the map we must take into account the following information:

3cm = 10km

According to the above, we must make a rule of three to find the equivalence of kilometers. Below is the procedure:

According to the above, 7.5 centimeters would represent the 25 kilometers distance on the map.

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The surface area of the pyramid is A = 386.24 inches²

The total surface area is the summation of the areas of the base and the three other sides. A = B + ( 1/2 ) ( P x h ), where B is the area of the base of the pyramid, P is the perimeter of the base, and h is the slant height of the pyramid

Surface Area of Pyramid = B + ( 1/2 ) ( P x h )

Given data ,

Let the surface area of hexagonal pyramid be represented as A

Surface area of hexagonal pyramid = Area of base + area of lateral surface

Area of the base = 166.3 inches²

Now , the Area of the lateral surface = 3a √ ( h² + ( 3a²/4 ) )

where a = 8 inches

h = 6 inches

Substituting the values in the equation , we get

Area of the lateral surface = ( 3 x 8 ) √ ( 36 + ( 3 x 64 / 4 ) )

On simplifying the equation , we get

Area of the lateral surface = 219.96 inches²

So , Surface area of hexagonal pyramid = Area of base + area of lateral surface

Surface area of hexagonal pyramid A = 166.3 inches² + 219.96 inches²

Surface area of hexagonal pyramid A = 386.24 inches²

Hence , the surface area of hexagonal pyramid is 386.24 inches²

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Alright, so they want you to find the probability of landing on 4 or 2.

There are 8 numbers total so that will be our denominator x/8

There are two outcomes we are finding the probability, that gives us 2/8

We must simplify the fraction into its lowest form.

2/8=1/4

Your answer would be 1/4

Answer:  the answer is $442.80

Answer:

442.80

Step-by-step explanation:

You would first multiply 15 by 36 to get a product of 540. Then you would subtract $540 by $37.80 and $59.40 to get a difference of 442.80

15x36 =540
540 - 37.80 - 59.40 = $442.80

After solving, the height of the cylinder is 6 meters.

The surface area of a cylinder is 24π m².

The distance around the base of the cylinder is 3π meter.

The diameter of a base of the cylinder is 4 meter.

Now the radius of the cylinder = diameter/2

The radius of the cylinder = 4/2

The radius of the cylinder = 2 meter.

The formula of surface area of cylinder:

S = 2πrh

From the question:

2πrh = 24π

Now putting the value of r

2π × 2 × h = 24π

4πh = 24π

Divide by 4π on both side, we get

h = 6

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The complete question is:

The surface area of a cylinder is 24π m². The distance around the base of the cylinder is 3π meter and the diameter of a base of the cylinder is 4 meter. What is the height of the cylinder? Enter your answer, in a simplified fraction, in the box.

Volume of solid is 343 cubic yards.

Volume is defined as the amount of space occupied by an object within the boundaries in the three dimensional space.

A base of a solid whose height is 7 yards is shown.

Let us consider the solid as cube.

Volume of cube = [tex]a^{3}[/tex] cubic units.

Here side, a =7 yards.

Volume ,V= [tex]7^{3}[/tex] = 343 cubic yards.

Hence, Volume of solid is 343 cubic yards.

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The number of blocks needed to make the 9th figure in the pattern is 24.

An equation is the statement of two expressions located on two sides connected with an equal to sign. The two sides of an equation is usually called as left hand side and right hand side.

Given that,

Dionne builds a pattern that is represented by the equation b = 2f + 6, where f is the figure number of the pattern and b is the number of blocks in each figure.

For the first figure, number of blocks = (2 × 1) + 6 = 8

For the 2nd figure, number of blocks = (2 × 2) + 6 = 10

This will go on.

For the 9th figure, number of blocks =  (2 × 9) + 6 = 24

Hence there will be 24 blocks in the 9th figure.

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Answer:

x = 2

Step-by-step explanation:

3x + 5 = 11

Let x = 1. Let's substitute the value of x into the equation to check if it's correct.

3(1) + 5 = 3 + 5

            = 8

8 ≠ 11

x is not 1.

---

Let x = 3. Let's substitute the value of x into the equation to check if it's correct.

3(3) + 5 = 9 + 5

            = 14

14 ≠ 11

x is not 3.

---

Let x = 2. Let's substitute the value of x into the equation to check if it's correct.

3(2) + 5 = 6 + 5

            = 11

11 = 11 so you can see that the value of 2 for x satisfies the equation!

x = 2.

---

THE ANSWER IS 33$ BECAUSE YOU JUST ADD THE BEADS PLUS PENDANT PLUS CHAIN

The scale factor of K = 10/3 represents enlargement.

Given is the scale factor of K = 10/3.

For the scale factor of {K} > 1, the dilation is enlargement and for the scale factor of {K} < 1, the dilation is reduction.

Now -

10/3 > 1

So, it represents the enlargement.

Therefore, the scale factor of K = 10/3 represents enlargement.

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When solving an equation, it is important to check for extraneous solutions.

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