The sequences below are either arithmetic sequences or geometric sequences. For each sequence, determine whether it is arithmetic or geometric, and write the
formula for the
The
n’th term of that sequence.

8,16,32,…
4,11,17,….

9514 1404 393

Answer:

  y = 5x² -30x +39

Step-by-step explanation:

Multiply it out and collect terms.

  y = 5(x -3)² -6

  y = 5(x² -6x +9) -6 . . . . . expand the square

  y = 5x² -30x +45 -6 . . . . use the distributive property

  y = 5x² -30x +39 . . . . . . collect terms

_____

The expansion of a binomial square is ...

  (a +b)² = a² + 2ab + b²

In this problem, we have a=x, b=-3.

Answer:

y = 5x² -30x +39

the answer above me explains it better go look at it

Answer:

  (x +7)² +(y +2)² = 64

Step-by-step explanation:

You want the standard form equation of the circle described by ...

  3x² +42x +3y² +12y = 33

The standard form equation of a circle is ...

  (x -h)² +(y -k)² = r² . . . . . . . . circle centered at (h, k) with radius r

We can make the leading coefficient 1 by dividing the given equation by 3.

  x² +14x +y² +4y = 11

Completing the squares, we have ...

  (x² +14x +49) +(y² +4y +4) = 11 +49 +4

  (x +7)² +(y +2)² = 64

<95141404393>

Answer:

the answer is

x +5x – 14 = (x− 2 )(x + 7)

Answer:

The equation has zero solutions because the equation 2 = 3 is never true.

Hope it helps :)

The supplementary angles in the diagram is ∠6 and ∠3 .

Two angles are said to be supplementary angles if they add up to 180°. When line segment intersect each other, angle relationships are formed such as complementary angles, supplementary angles, vertically opposite angles etc.

Therefore, let's find the angle relationships in the line intersections.

Hence,

∠6 and ∠3 are supplementary angles because they add up to 180 degrees.

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a formula an for the -n- th term of the following sequence. assume the series begins can be represented by the formula an = (-1)^(n+1)(8 + 3n).



To find the formula for the -n- th term of the sequence, we need to observe the pattern in the given sequence. We can see that the sequence is alternating between positive and negative numbers, and the difference between the consecutive terms is increasing by 5.

Starting from the first term, 11, we can write the sequence as:

11 - 14 + 19 - 24 + ...

To find the pattern, we can write the terms in terms of their positions:

a1 = 11
a2 = -14
a3 = 19
a4 = -24

We can see that the sign of each term is alternating. To represent this in the formula, we can use (-1)^(n+1), which will give -1 for odd values of n and 1 for even values of n.

The other part of the formula should represent the increasing difference between the consecutive terms. We can see that the difference between the first two terms is 25, between the second and third terms is 33, and between the third and fourth terms is 43. We can observe that the difference between the consecutive terms is increasing by 8, which is 5 times the position of the term.

Therefore, the formula for the -n- th term of the sequence is:

an = (-1)^(n+1)(8 + 3n)


The formula for the -n- th term of the given sequence is an = (-1)^(n+1)(8 + 3n).

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The mean of a distribution is 35 and the standard deviation is 8. The mean, often represented as μ, is the average value of a set of numbers, while the standard deviation, represented as σ, is a measure of the amount of variation or dispersion within the dataset.

To calculate the mean, follow these steps:
1. Add up all the values in the dataset.
2. Divide the sum by the number of values in the dataset.

In this case, the mean is already given as 35.

To calculate the standard deviation, follow these steps:

1. Find the mean of the dataset (which is already provided as 35).
2. Subtract the mean from each value in the dataset and square the result.
3. Find the average of these squared differences.
4. Take the square root of the average to get the standard deviation.

In this case, the standard deviation is already given as 8.

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The lengths of the two pieces of a wire will be 19,19.

A square is a closed, two-dimensional object with four equal sides and four vertices. On either side, it has parallel sides.

The square of a square's side determines its area.

Given data -

Length of a wire = 38 m

As the wire is divided into two pieces,

Let the length of two pieces of wire be x and y m respectively.

As per given data, x + y = 38

Therefore, y = 38 - x    

As each piece is bent into a square, area of squares will be

\((x/4)^{2}\)  and  \((y/4)^{2}\)

Therefore, the sum of areas of two squares will be A = \((x/4)^{2}\) +      \((y/4)^{2}\)

A = \(x^{2}\)/16 + \(y^{2}\)/16

A = \(x^{2}\)/16 + \((38-x)^{2}\)/16

By differentiating, we will get

A' = \(\frac{2x}{16}\) - \(\frac{2(38-x)}{16}\)

In order to minimize the the sum of the areas of the two squares, we will take A' = 0

0 = x - (38 - x)

2x = 38

x = 19

Therefore y = 19

The length of two pieces of a wire should be 19 m each.

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Answer:

not true

Step-by-step explanation:

The actual answer is 8/9.

Therefore, the percentage of values that lie below 21 is approximately 68%.

The empirical rule, also known as the 68-95-99.7 rule, provides a rough estimate of the percentage of values within a certain number of standard deviations from the mean in a normal distribution. According to this rule:

Approximately 68% of values lie within one standard deviation of the mean.

Approximately 95% of values lie within two standard deviations of the mean.

Approximately 99.7% of values lie within three standard deviations of the mean.

In this case, we have a normal distribution with a mean of 19 and a standard deviation of 2. To find the percentage of values that lie below 21, we need to determine how many standard deviations away 21 is from the mean.

The distance from the mean to 21 is (21 - 19) = 2. Since the standard deviation is 2, 21 is one standard deviation above the mean.

According to the empirical rule, approximately 68% of values lie within one standard deviation of the mean. In this case, it means that approximately 68% of the values lie below 21.

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The area of the part cleaned by the windshield is 8.4 inches

A sector is said to be a part of a circle made of the arc of the circle along with its two radii.

The area of a sector is expressed as ;

A = πr² × tetha/360

where r is the radius of the circle

The radius here is the length of the windshield = 4 in. And it rotates at an angle of 60°

Therefore;

A = 3.14 × 4² × 60/360

A = 3.14 × 4² × 1/6

A = 50.24 /6

A = 8.4 inches²

Therefore the area of the part cleaned by the windshield is 8.4 inches²

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Answer:

x=-6

Step-by-step explanation:

First you have to add 4 to both sides

3x - 4 + 4 = 2x - 10 + 4

Then you simplify it

3x + 2x - 6

Subtract 2x from both sides

3x - 2x = 2x - 6 - 2x

Simplify

x = -6

Answer:D.x=-6

Step-by-step explanation: Subtract 2x from both sides.(3x-4-2x=2x-10-2x)-->x-4=-10. 2nd step Add 4 to both sides then it would be(x-4+4=-10+4)--> -10+4=x=-6

Answer:

99.5

Step-by-step explanation:

Answer: 4/12

Step-by-step explanation: Simplified into 1/4                                         :)

Answer:

4/12 chance of getting striped card

Step-by-step explanation:

There are 4 striped cards, out of 12 cards, so that would be 4/12

∫(1,2,3)(3,2,4)​ydx+(1/z−x/y^2)dy−y/z^2dz = f(3, 2, 4) - f(1, 2, 3).

The potential function for the given vector field can be found by integrating each component of the vector field with respect to the corresponding variable. Let's find the potential function step by step:

For the first component, integrating 1/y with respect to x gives us ln|y| + g(y, z), where g(y, z) is a function that depends only on y and z.

For the second component, integrating (z - y^2x) with respect to y gives us zy - y^3x/3 + h(x, z), where h(x, z) is a function that depends only on x and z.

For the third component, integrating (-y/z^2) with respect to z gives us y/z + k(x, y), where k(x, y) is a function that depends only on x and y.

Now, let's find a potential function for the entire vector field by combining the above results. We have f(x, y, z) = ln|y| + g(y, z) + zy - y^3x/3 + h(x, z) + y/z + k(x, y).

To evaluate the line integral, we need to find the potential function at the endpoints of the curve and subtract the values. The endpoints of the curve are (1, 2, 3) and (3, 2, 4).

Substituting the coordinates of the first endpoint into the potential function, we have f(1, 2, 3) = ln|2| + g(2, 3) + 3(2) - (2^3)(1)/3 + h(1, 3) + 2/3 + k(1, 2).

Similarly, substituting the coordinates of the second endpoint into the potential function, we have f(3, 2, 4) = ln|2| + g(2, 4) + 4(2) - (2^3)(3)/3 + h(3, 4) + 2/4 + k(3, 2).

Finally, the value of the line integral is obtained by subtracting the potential function at the first endpoint from the potential function at the second endpoint:

∫(1,2,3)(3,2,4)​ydx+(1/z−x/y^2)dy−y/z^2dz = f(3, 2, 4) - f(1, 2, 3).

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Answer:

x + 2

Step-by-step explanation:

im sure its the right answe

Answer:

Step-by-step explanation:

44

The correct answer is 3p² + 8mp + 3, which is different from Chen's answer of 3p² + 6m + 5.

What is a polynomial?

In mathematics, a polynomial is an expression consisting of variables (also known as indeterminates) and coefficients, which involves only the operations of addition, subtraction, and multiplication. Polynomials can have one or more terms, and each term can have one or more variables with non-negative integer exponents.

Chen's error is in the second line where they added the terms -(-2p²-mp+1) without distributing the negative sign to each term inside the bracket. The correct way to subtract a polynomial is to change the sign of each term inside the bracket and then add them to the other polynomial. So, the correct simplification would be:

P²+7mp+4-(-2p²-mp+1)

= P²+7mp+4+2p²+mp-1 (Distributing the negative sign)

= 3p²+8mp+3

Therefore, the correct answer is 3p² + 8mp + 3, which is different from Chen's answer of 3p² + 6m + 5.

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Answer:

Step-by-step explanation:

a. 1/2x = 10  x = 20

b. 1/4s = 8    s = 32

c. 1/3t = 6     t = 18

d. 1/5 y = 20    y = 100

4. Division

a. 4x = 32    x = 8

b. 13x = 39     x = 3

c. 5x = 25    x = 5

d. 10x = 100    x = 10

5. Mixed Practice

a. x + 4 = 7     x = 3

b. 33 - y = 44       y = -11

c. s + 18 = 26      s = 8

d. m - 40 = 20     m = 60

e. z + 100 = 100    z = 0

f. x + 22 = 23      x = 1

g. s - 4 = 96     s = 100

h. 1/4x = 4       x = 16

i. 24x = 3 x = 1/8

j. 1/5x = 50 x = 250

k. 1/3y = 33 x = 99

l. t + 12 = 16 t = 4

m. t - 12 = 16 t = 28

n. 1/2q = 8 q = 16

o. 12t = 24       t = 2

Answer:

12.5 m

Step-by-step explanation:

recall that 1 km = 1000 m

hence 90 km/h is equivalent to 90 km/h x 1000 m/km = 90,000 m/hr

also recall that 1 hour = 60 x 60 = 3600 s

hence 90,000 m/hr is equivalent to 90,000 m/hr x (1/3600) hr/s = 25 m/s.

given that is eyes were closed for 0.5 s.

in 0.5s, he travelled :

0.5s x 25 m/s = 12.5 m

The sculpture's base length = 9 cm and the height of sculpture is found as 6 cm.

Explain about the pyramid:

The base and apex are joined to form a pyramid. To identify them from the base, the triangular sides are also also referred to as lateral faces. In a pyramid, the apex, which creates the triangle face, is connected to each base edge.

volume of a pyramid = V=1/3 a²h

Given volume V = 162 cm³

Let 'x' be the side length.

Then , (x - 3)  be the height of sculpture.

Put the values and find the length.

162 = 1/3 (x)² (x-3)

162 * (3) =  (x)² (x-3)

486 = x²(x-3)

486 = x³ - 3x²

x³ - 3x² - 486 = 0

(use a graphing tool or calculator equation mode).

x = 9

Thus,

side length of sculpture = 9 cm

height of sculpture = 9 - 3   = 6cm

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Correct question:

Nathan has a sculpture in the shape of a pyramid. The height of the sculpture is 3 centimeters less than the side length,x,of its square base. Nathan uses the formula for the volume of a pyramid to determine the dimesnsioms of the sculpture.

V=1/3 a^2h

Here, a is the side length of the pyramids square base and h is it’s height.

If 162 cubic centimeters of clay were used to make the sculpture, the equation x^3 + _x^2+ _ =0 can be used to find that the length of the sculptures.  base is _ centimeters.

Answer: -32

Step-by-step explanation: You can start by first changing the equation to (-2)^5. Then you just multiply -2 by itself 4 times to get -32.

Unfortunately, I am unable to directly interpret or visualize figures or images. However, I can provide you with a general explanation. In a discretized reservoir using block-centered grids, the standard ordering refers to the arrangement of grid cells or blocks in a particular pattern.

This pattern is often used to establish the connectivity and adjacency relationships between the cells in the reservoir model. Typically, the standard ordering arranges the grid cells in a sequential manner, starting from the top-left corner and moving row by row. Each grid cell represents a discrete volume or unit in the reservoir. The non-zero elements, indicated by the "x" positions in the coefficient matrix, would correspond to the active or connected cells within the reservoir model. These active cells are the ones that contribute to fluid flow and other reservoir properties. To visualize the discretized reservoir using the standard ordering, you would need to refer to the coefficient matrix and determine the dimensions of the reservoir model, such as the number of rows and columns. Then, starting from the top-left corner, you can represent each active cell or block using a graphical representation, such as a square or rectangle, in a sequential manner based on the standard ordering. This way, you can construct a visual representation of the discretized reservoir model.

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Answer:

w = 64

Step-by-step explanation:

-3/4w = -48

Divide both sides by -3/4 to get w alone

-3/4w/-3/4 = -48 / -3/4

w = 64

Hope this helps, have a great day:)

Answer:

2y-4y=2+2.

-2y=4.

y= -2.

Answer:

y=−2

Step-by-step explanation:

Step 1: Subtract 4y from both sides.

−2y−2=2

Step 2: Add 2 to both sides.

−2y=4

Step 3: Divide both sides by -2

y=−2

The inverse of the function f(x) = (1/2)x is f^(-1)(x) = 2x.

To find the inverse of a function, we need to switch the roles of x and y and solve for y. Let's follow the steps to find the inverse of the function f(x) = (1/2)x:

Step 1: Replace f(x) with y: y = (1/2)x.

Step 2: Swap x and y: x = (1/2)y.

Step 3: Solve for y: Multiply both sides of the equation by 2 to isolate y: 2x = y.

Step 4: Replace y with f^(-1)(x): f^(-1)(x) = 2x.

Therefore, the inverse of the function f(x) = (1/2)x is f^(-1)(x) = 2x.

We can verify this by composing the function and its inverse. If we apply f(x) followed by f^(-1)(x), we should get the original value of x. Let's check:

f(f^(-1)(x)) = f(2x) = (1/2)(2x) = x.

As expected, the composition of the function and its inverse gives us the original value of x, indicating that we have found the correct inverse.

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Answer:

A≈19.31

Step-by-step explanation:

Formula to find area of Octagon: A=2(1+√2)a^2

Divide 16/8 since there are 8 sides.

Answer:

19.31

Step-by-step explanation:

Formula:

\(A=2(1+\sqrt{x} 2)a^2\)

Hope this helps :)

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