Answer this please !

The function that gives the value of tn for the geometric series is presented as follows;

[tex]t_n = 2 \times 3^{(n - 1)} [/tex]

The given geometric series is presented as follows;

2 + 6 + 18 + 54 +...

From the above series, we have;

The nth term of the geometric series is therefore;

[tex]t_n = a \cdot r^{(n - 1)} [/tex]

Which gives;

[tex]t_n = 2 \times 3^{(n - 1)} [/tex]

Where, tn is the nth term

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The function with the greatest rate of change over the interval [0, 2] is: D. a.

In Mathematics, the rate of change of a function over a given interval can be determined by calculating the slope of the straight line which connect its end points.

Mathematically, the slope of any straight line can be calculated by using this formula;

[tex]Slope = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}[/tex]

For line a, we have:

Points (x, y) = (0, 1) and (2, 4)

Slope = (4 - 1)/(2 - 0)

Slope = 3/2 or 1.5.

For line b, we have:

Points (x, y) = (0, 0) and (2, 2)

Slope = (2 - 0)/(2 - 0)

Slope = 2/2 or 1.0.

For line c, we have:

Points (x, y) = (0, -1) and (2, 0)

Slope = (0 + 1)/(2 - 0)

Slope = 1/2 or 0.5.

For line d, we have:

Points (x, y) = (0, 0.5) and (2, 2.5)

Slope = (2.5 - 0.5)/(2 - 0)

Slope = 2/2 or 1.

In conclusion, we can logically deduce that "function a" has the greatest rate of change over the interval [0, 2].

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Answer:

Below in bold.

Step-by-step explanation:

f(x) = 2x^2 - 12x + 24

Convert to vertex form:

f(x) = 2(x^2 - 6x) + 24

     = 2[(x - 3)^2 - 9] + 24

     = 2(x - 3)^2 - 18 + 24

     = 2(x - 3)^2 + 6

So the vertex is at (3, 6) and the axis of symmetry is x = 3.

The value of X is 1/3 and Y is 1/2 and Z is 1/4.

According to the statement we have given the equations which are

X + Y = 5XY  -(1)

Y + Z = 6YZ  -(2)

Z  + X = 7XZ  -(3)

and we have to find the value of X,Y,Z.

So, solve the equations for the X,Y,Z

From (1) equation

Y = X / (5X-1)  -(4)

From (3) equation

Z = X / (7X-1)  -(5)

Put (4) and (5) in (2) then

X / (5X-1)  + X / (7X-1)  = 6{[X / (5X-1)][X / (7X-1)]}

X(7X-1)  + X(5X-1) =  6{[X / (5X-1)][X / (7X-1)]} /  {[1 / (5X-1)][1 / (7X-1)]}

Then after solving

12(X)^2 -2X = 6(X)^2

6(X)^2 -2X = 0

X (6X-2) = 0

X = 0, X = 1/3

Here X = 0 is neglected.

So, X=1/3  -(6)

Put (6) in (4) and (5) then

From 4

Y = X / (5X-1)

Y = (1/3) / (5(1/3)-1)

Y = (1/3) / (2/3)

Y = 1/2.

From (5) equation

Z = X / (7X-1)

Z = (1/3) / (7(1/3)-1)

Z = (1/3) / (4/3)

Z = 1/4.

So, The value of X is 1/3 and Y is 1/2 and Z is 1/4.

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Answer:

Step-by-step explanation:

All pyramids have a volume as one-third of a prism with the same base area and the same height.

This will make the formula for the volume [tex]\frac{1}{3}(base*height)[/tex]. We already know the height of the pyramid is 10, but the area of the base for this rectangle would be its length and its width. Let's calculate this:

[tex]7*2.3=16.1\hspace{0.1cm}in^2[/tex]

Let's put these values back into the formula:

[tex]V=\frac{1}{3}(16.1*10)\\ V=\frac{1}{3}(161)\\ V= 53.7\hspace{0.1cm}in^3[/tex]

In Wagnerian music drama, a basic recurring theme representing a person, object, event, or emotion is known as Leitmotif.

What is serious opera called?

What is Wagnerian leitmotif?

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The possible outcomes are WH, BH, BH, BH, RH, RH, WL, BL, BL, BL, RL, RL

The given parameters are:

Coin = Head (H) and Tail (T)

Marble = W, B, B, B, R, R

See attachment for the tree diagram

From the tree diagram, we have the following possible outcomes

WH, BH, BH, BH, RH, RH, WL, BL, BL, BL, RL, RL

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Answer:

3. 6 5. 3

Step-by-step explanation:

PEMDAS

3. 0.5 x (24) / 3 + 2

12/3 +2

4 + 2

6

5. (4 + 6/3) x 0.5

(4 + 2) x 0.5

6 x 0.5

3

Answer: number 3. is 6 and number 5. is 3

hope it helped

Answer:

C

Step-by-step explanation:

y=mx+b where m is the slope or weekly payments and b is the y-intercept or initial fee.

300 = 30w + 60 fits this

Answer:

Rotation, Reflection, Dilation.

Step-by-step explanation:

Answer: Graph provided below.

Step-by-step explanation:

Draw the graph of y = -2x and then shade the region below it because y is less than and equal to -2x. To draw the graph of y = -2x, plug in x values into the equation and plot the corresponding coordinates. See this video on how to graph linear equations:

https://www.khanacademy.org/math/in-in-grade-9-ncert/xfd53e0255cd302f8:linear-equations-in-two-variables/xfd53e0255cd302f8:graph-of-a-linear-equation-in-two-variables/v/graphs-of-linear-equations

The statement that can be concluded from the triangle is A. RS/VU=ST/UT and ∠S≅∠U.

The Side-Angle-Side Similarity Theorem states that if two sides in one triangle are proportional to two sides in another triangle and the included angle in both are congruent, then the two triangles are similar.

In this problem the included angle is ∠S≅∠U, therefore side RS must be proportional to side VU  and side ST must be proportional to side UT

Hence, RS/VU=ST/UT.

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Answer:

No largest no could be 100

Step-by-step explanation:

Yes, the sum of the three numbers is 200, and the largest number can indeed be 75.

Let's assume the three numbers are:

Smallest number = 25

Middle number = x (unknown)

Largest number = 75

The sum of the three numbers is 200, so we can set up the equation:

25 + x + 75 = 200

Now, let's solve for x:

x = 200 - 25 - 75

x = 100

So, the middle number is 100.

Now, we can check if the largest number (75) is correct:

25 + 100 + 75 = 200

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the operation:

[tex]2*10^1 - 4*10^0 = 20 - 4 = 16[/tex]

Gives a square number.

A perfect square is the product of a number and itself.

As you can see in the example, 16 is a square number. Then let's try to get 16.

To get 16 we can use the difference:

20 - 4

So the first therm needs to be equal to 20, and the second equal to 4.

To write 20 in scientific notation we have:

[tex]2*10^1[/tex]

To write 4 in in scientific notation:

[tex]4*10^0[/tex]

Then the operation:

[tex]2*10^1 - 4*10^0 = 20 - 4 = 16[/tex]

Gives a square number.

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The five rational numbers are 1/1729, 1/2, 3/2, 2/1, 1729/1 and the numbers should be of form p/q where p or q should be a taxicab number.

According to the question,

To represent 5 rational numbers on line, the numbers should be of form p/q where p or q should be a taxicab number.

A taxicab number is a smallest integer can be expressed as a sum of two positive integer cube.

The most famous taxicab number is 1729. Thus,

1729 = 1³ + 12³

1729 = 9³+ 10³

Now, 2 = 1³ + 1³ so, 2 is the first taxicab number. Therefore, five rational numbers are  1/1729, 1/2, 3/2, 2/1, 1729/1.

In 1/1729 -> 1729 is taxicab number

In 1/2 -> 2 is taxicab number

In 3/2 -> 2 is taxicab number

In 1/1729 -> 2 is taxicab number

In 1729/1  -> 1729 is taxicab number

Hence, five rational numbers are 1/1729, 1/2, 3/2, 2/1, 1729/1 and the numbers should be of form p/q where p or q should be a taxicab number.

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The next step Javier needs to take in order to evaluate the expression is to simplify it to it's lowest term. Details below

From the question given, we were told that Javier submitted 2 for a

Thus, the new expression becomes

2 × 2³ - 1

Recall

Aⁿ × Aᵐ = Aⁿ⁺ᵐ

Thus,

2 × 2³ = 2¹⁺³ = 2⁴

Therefore,

2 × 2³ - 1 = 2⁴ - 1

But

2⁴ = 16

Thus,

2⁴ - 1 = 16 - 1

2⁴ - 1 = 15

Therefore,

2 × 2³ - 1 = 15

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By the definition of similar polygons, the lengths of corresponding sides are proportional.

The proportion for [tex]x=40[/tex].

As it is given in the definition, similar polygons have congruent angles and proportional sides.

Therefore, by the definition of similar polygons, the lengths of corresponding sides are proportional.

Cross multiply and solve the proportion  [tex]x[/tex] as follows:

The blank should be proportional.

[tex]\frac{12}{8} =\frac{20+x}{x}\\ 12x=160+8x\\4x=160\\x=40[/tex]

Therefore, the proportion for [tex]x=40[/tex].

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The extreme drop can be said to most likely represent: b. A reflection of the migratory nature of the birds at the lake.

Bird migration is a natural process which can be described as a the movement of different birds by flight across thousands of kilometers in search of ecological conditions and habitats that favors breeding, feeding, and raising of their young.

Migratory birds have well built physiology and morphology that make them better equip to fly fast and across long distances in search of the best ecological conditions, which is dependent on seasons.

Like in the graph given, like we see that at the beginning of January, number of birds were few in the lake until sudden increase occurred. It can be said that during those period of increase, the ecological conditions favored the survival of the bird until November and December. This extreme drop can be said to most likely represent: b. A reflection of the migratory nature of the birds at the lake.

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Answer:

B) 16

Step-by-step explanation:

12/3 = x/4

48 = 3x  Divide both sides by 3

16 = x

Answer:

B) 7/9

Step-by-step explanation:

          LCM of 3 and 9 is 9.

          [tex]\sf \dfrac{1}{3}=\dfrac{1*3}{3*3}\\\\[/tex]

              [tex]\sf =\dfrac{3}{9}[/tex]

      [tex]\sf \dfrac{4}{9}+\dfrac{1}{3}=\dfrac{4}{9}+\dfrac{3}{9}\\\\[/tex]

                 [tex]\sf =\dfrac{7}{9}[/tex]

The ordered pairs (5 , -2) , (3 , 1) , (4 , 2) are in the set of the solution (Option C)

An ordered pair is a composite of the x coordinate (abscissa) and the y coordinate (ordinate), with two values expressed between parenthesis in a predetermined order.

It aids visual comprehension by locating a point on the Cartesian plane.

The first line has negative slope and passing through points (0 , 0) and (4 , -2)

That is y > (-1/2)x

The second line has positive slope and passing through points (-2 , 0) and (2 , 2)

That is: y < (1/2)x + 1.

- Refer to the accompanying diagram to discover the common component of the solutions.

- The inequity is shown by the red shading.

- The inequity is shown by the blue shading.

- The two-colored shaded area reflects the common solutions to the two inequalities.

- Let's discover the ordered pairs in the system of linear inequalities' solution set.

- Points (-4, 2), (-3, 1), (4, -3) define the common shaded area.

- Points (5, -2), (3, 1), (3, -1) (4 , 2)

As a result, Point (5, -2) is in the darkened region.

As a result, Point (3, 1) is in the darkened area.

As a result, Point (4, 2) is in the darkened area.

As a result, the ordered pairings (5, -2), (3, 1), (4, 2) are in the solution set.

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The angle subtended at the centre of the circle by a 2.9 centimeter arc is  equal to 15° 38.46'/15° 38' 27.6''.

In this problem we have to determine the measure of a central angle of a circular section in DMS (Degrees - Minutes - Seconds) system, in which a degree is equal to 60 minutes and a minute to 60 seconds. First, we must calculate the radius of the circle by the area formula:

r = √ (A / π)     (1)

r = √ (354 / π)

r ≈ 10.615 cm

Then, the measure of the central angle in radians is found by the equation of circular arc:

θ = s/r

θ = 2.9 cm / 10.615 cm

θ = 0.273 radians

Finally, we convert the angle into DMS system:

θ = 0.273 rad × 180°/π

θ = 15.641°

Degrees: 15°

Minutes and seconds: 0.641° (38.46')

Minutes: 38'

Seconds: (0.46' = 27.6'')

The angle subtended at the centre of the circle by a 2.9 centimeter arc is  equal to 15° 38.46'/15° 38' 27.6''.

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The value of 'k' in the quadratic Equation    [tex]4x^{2}+kx+4=0[/tex] having one rational solution is k is 8.

Here, the given equation is  [tex]4x^{2}+kx+4=0[/tex]

By comparing the given equation with the standard form of the quadratic equation we get,

a = 4

b = k

c = 4

The given quadratic is having one rational solution, which means [tex]b^{2} -4ac=0[/tex]

Therefore,

[tex]k^{2} -4 \times 4\times4=0\\k^{2} -64=0\\k^{2} =64\\k=\sqrt{64} \\k=8[/tex]

Therefore, the value of k is 8.

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Answer:

84

Step-by-step explanation:

Total students he surveyed: 27

Amount that found it something OTHER than easy: 14 (11 moderate + 3 difficult)

This means that [tex]\frac{14}{27}[/tex] found it something other than easy

Multiply that by 162 to find the proportion for the larger population:

162 * (14/27), and we get 84.

The woman's shadow is moving away from the pole at the speed of 4 feet/sec.

The height of a pole-mounted street light = 18 ft

The height of a lady = 6 ft

The woman is moving quickly and directly away from the pole. Her speed = 4ft/sec.

The woman's distance from the pole at the precise moment question want to know the speed of the woman's shadow's leading edge = 45ft

A woman standing 6 feet tall moves away from the pole in a straight route at a pace of 4 feet per second. If we assume that t is the passing time in seconds and that x is the distance in feet between the pole and the lady, we are informed that dx/dt=4 ft/sec.

Therefore, it is concluded that the final answer is 4 ft/sec.

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The missing letter is p. The correct option is B. p

From the question, we are to determine the missing letter in the given pattern

The given pattern is

t, s, r, q, _, o, n, m,...

Consider the English alphabet

a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y, z.

If we study the pattern, we will realize that the alphabets are in the reverse order.

Hence, the missing letter is p. The correct option is B. p

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Answer: Y-intercept: (0,5) X-intercept: (3,0)

Step-by-step explanation: Set x and y equal to 0.

SOLUTION :

c² = 5² + 5²

c² = 25 + 25

c² = 50

c = √50 ft

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