2. Identify the Formula for finding the nth term of an Arithmetic Sequence, where A(n) is the nth term of an Arithmetic Sequence, is the first term, n is the term number and d is the common
difference

A(n) = 2 - 1 + (n - 1)d

A(n) = a + (n - 1)d

A(n) = a + (n)(d - 1)

O A(n) = a + (n + 1)d

Step-by-step explanation:

Simple, she found the sum of the interior angles not exterior angles.

The exterior angles of any polygon add up to 360 degrees.

What Cindy did was found the total interior angle measure of a hexagon which is 720

Step-by-step explanation:

Can you tell us how many word search magazines there are? Thank you,

Answer:

loyalty...........................

Angle that the tent pole makes with the sides of the tent is 39.6°.

Trigonometric functions are defined as the real functions which are simply the functions of an angle of a triangle. They are basically the periodic functions which relate an angle in a right angled triangle to the ratios of the length of two sides.

Given that,

A conical circus tent has a 20 ft central pole that supports it. The slant height of the tent is 26 ft long.

The central pole forms a right triangle with the floor of the tent.

We need the angle tent pole makes with the sides of the tent.

We have the hypotenuse as the slant height and the central pole is the adjacent side of the angle.

The cos of the missing angle is the ratio of the length of the central pole to the length of the side of the tent.

cos x = 20 / 26 = 0.7692 ≈ 0.77

Applying arccosine,

x = cos⁻¹ (1.3) = 39.6°

Hence the required angle is 39.6°.

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Answer:

x = ±sqrt(14)

Step-by-step explanation:

x^2 = 14

Take the square root of each side

sqrt(x^2) = ±sqrt(14)

x = ±sqrt(14)

Answer:

x =7 cus 2(7) is 14

Step-by-step explanation:

i.  The position vector of X is 2b - a.

ii.  The position vector of Y is (3b + c)/4.

iii.  The ratio XY : Y Z is \(|(2b - a) - ((3b + c)/4)|/|((3b + c)/4) - (a + c)/2|\). Simplifying this expression will give us the final ratio.

i. To find the position vector x of point X, we can use the concept of vector addition. Since AB : BX = 2 : 1, we can express AB as a vector from A to B, which is given by (b - a). To find BX, we can use the fact that BX is twice as long as AB, so BX = 2 * (b - a). Adding this to the vector AB will give us the position vector of X: x = a + 2 * (b - a) = 2b - a.

ii. Similar to the previous part, we can express BC as a vector from B to C, which is given by (c - b). Since BY : YC = 1 : 3, we can find BY by dividing the vector BC into four equal parts and taking one part, so BY = (1/4) * (c - b). Adding this to the vector BY will give us the position vector of Y: y = b + (1/4) * (c - b) = (3b + c)/4.

iii. Z is the midpoint of AC, so we can find Z by taking the average of the vectors a and c: z = (a + c)/2. The ratio XY : YZ can be calculated by finding the lengths of the vectors XY and YZ and taking their ratio. Since XY = |x - y| and YZ = |y - z|, we have XY : YZ = |x - y|/|y - z|. Plugging in the values of x, y, and z we found earlier, we get XY : YZ =\(|(2b - a) - ((3b + c)/4)|/|((3b + c)/4) - (a + c)/2|\).

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Answer: 275,400

Step-by-step explanation:

- First we do 18 multiplied by 20 which would get us the answer of 360

- Next we do 45 multiplied by 17 which would get us the answer of 765

- Now we multiply both 360 and 765 and get the answer of 275,400

1 cm = 10 mm. Length of book : 28 cm. Length of book = 280 mm. This shows that measurements in mm are the same but look to have a higher number .

The conversion factor provided states that 1 cm is equal to 10 mm, which means that 1 cm is made up of 10 individual millimeters.

The length of my book in when measured in millimeters is 280 mm.

In centimeters, this is therefore:

= 280 mm / 10 cm /mm

= 28 cm

Although the numerical value appears higher when expressed in millimeters, it is important to note that the actual length of the book remains the same.

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a) The drawing of all data points on a 2D plane is illustrated below.

b) The angle in between the five other points is 27

c) The matrix outer product for X is R = XXT.

d) The matrix outer product can also be calculated via R is (2,27)

The data matrix X is a 2-by-7 matrix, where each column represents a data point with two components. We can visualize each data point as a vector in a two-dimensional plane, where the horizontal axis represents the first component and the vertical axis represents the second component.

To draw all data points on a 2D plane, we can plot each column of X as a vector starting from the origin. Proper labeling of the two axes and providing important tick values will facilitate a precise graphical description of the data.

Next, we can use the inner product formula to calculate the angle between the first data point (2, 27) and the other five data points, respectively.

The inner product, also known as the dot product, is a way to measure the similarity between two vectors by multiplying their corresponding components and summing the products.

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Answer:

1) 38

2) 3

Step-by-step explanation:

f(x)=36+2

f(x)=38

29=9x+2

27=9x

x=3

Question: What is the value of the function at x=−2?

Answer: y=2

Step-by-step explanation: I took the test.

*THIS IS THE CORRECT ANSWER. PLEASE DON'T ANSWER 3. IT IS WRONG!*

By algebra properties, the expression for the discrete function is f(n) = - (n + 1) / (n² - n).

In this question we find a relationship between f(n) and the variable n and we are asked to derive the expression of f(n) in terms of the variable n. This can be done by means of algebra properties. First, write the entire expression:

(2 · n) / n - (2 · n) / (n - 1) = [f(n) · 2 · n] / (n + 1)

Second, clear f(n) by algebra properties:

2 - (2 · n) / (n - 1) = [f(n) · 2 · n] / (n + 1)

2 · (n + 1) - [2 · n · (n + 1)] / (n - 1) = f(n) · 2 · n

(n + 1) / n - (n + 1) / (n - 1) = f(n)

Third, simplify the resulting expression to find the final form of the discrete function:

f(n) = (n + 1) · [1 / n - 1 / (n - 1)]

f(n) = (n + 1) · [(n - 1) - n] / [n · (n - 1)]

f(n) = (n + 1) · [- 1 / (n² - n)]

f(n) = - (n + 1) / (n² - n)

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a. $456 would be the amount a customer could save during the first year by switching from Cable Zone to Super Vision.

b. Super Vision raises the rates 23% after a new customer's first year,  a customer who switched from Super Vision save $180 in the second year.

c. Super Vision raises the rates 18% for the third year compared to the second year, for the third year, Cable Zone would be cheaper.

a. To calculate how much a customer could save during the first year by switching from Cable Zone to Super Vision, we need to compare the costs of the two providers.

Cable Zone charges $46 for monthly home phone service, $36 for monthly Internet service, and $56 for monthly cable television. Therefore, the total cost per month with Cable Zone is:

$46 (home phone) + $36 (Internet) + $56 (cable television) = $138

Super Vision, on the other hand, offers all three services for a flat $100 monthly fee. So, the customer would save:

$138 (Cable Zone cost) - $100 (Super Vision cost) = $38 per month

Therefore, during the first year, the customer could save:

$38 (monthly savings) * 12 (number of months) = $456

b. After the first year, Super Vision raises the rates by 23%. The new monthly fee would be:

$100 (original fee) + 23% (rate increase) * $100 (original fee) = $123

To calculate the savings in the second year, we need to compare the new Super Vision fee to the cost with Cable Zone:

$138 (Cable Zone cost) - $123 (Super Vision cost) = $15 per month

Therefore, in the second year, the customer would save:

$15 (monthly savings) * 12 (number of months) = $180

c. If Super Vision raises the rates by 18% for the third year compared to the second year, we need to calculate the new monthly fee. The new Super Vision fee would be:

$123 (second-year fee) + 18% (rate increase) * $123 (second-year fee) = $145.14

To determine which company is cheaper for the third year, we compare the new Super Vision fee to the cost with Cable Zone:

$138 (Cable Zone cost) - $145.14 (Super Vision cost) = -$7.14

In this case, the Super Vision cost is higher than the Cable Zone cost by $7.14 per month. Therefore, for the third year, Cable Zone would be cheaper.

Overall, during the three-year period, the customer would save a total of $456 (first year) + $180 (second year) = $636 by switching to Super Vision.

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Answer: To calculate the tip amount, we need to multiply the bill amount by the percentage tip as a decimal:

Tip amount = 0.20 x $76 = $15.20

To find the total amount to pay, we add the bill amount and the tip amount:

Total amount = $76 + $15.20 = $91.20

Rounding this to the nearest dollar gives:

Total amount = $91

Therefore, you need to pay $91 in total if you leave a 20% tip on a $76 bill.

Step-by-step explanation:

Answer:

Kevin would have to save for 12 weeks.

Step-by-step explanation: The reason he would have to save for 12 weeks is that 8 times 12 is 96, and 96 + 42 is 138.

Answer:

Step-by-step explanation:

Find the height of a square pyramid that has a volume of 8 cubic feet and a base length of 2 feet

Volume v = 1/3*a²h

inverse formula

8 = 1/3 * 2² * h

8 = 4 h /3

divide both the sides by 4

h = 6 feet

Answer:

The answer is 8300.

Step-by-step explanation:

1) We round the number up to the nearest hundred, if the last two digits in the number are 50 or above.

2) We round the number down to the nearest 100 if the last two digits in the number are 49 or below.

3) If the last two digits are 00, then we do not have to do any rounding because it is already to the hundred.

Answer:

y-1= -1/3(x+3)

Step-by-step explanation:

y-y1=m(x-x1)

y-1=m(x+3)

the slope is rise over run

the slope is -1/3

Answer:

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

Step-by-step explanation:

To find the equation of a line parallel to the given line and passing through the point (-3, 1), we can use the point-slope form of a linear equation. The point-slope form is given by:

y - y₁ = m(x - x₁)

Where (x₁, y₁) is the given point and m is the slope of the line.

First, let's calculate the slope of the given line using the two points (-2, -4) and (2, 2):

slope = (y₂ - y₁) / (x₂ - x₁)

= (2 - (-4)) / (2 - (-2))

= 6 / 4

= 3/2

Since the line we want to find is parallel to the given line, it will have the same slope. Therefore, the slope (m) of the new line is also 3/2.

Now we can substitute the values into the point-slope form using the point (-3, 1):

y - 1 = (3/2)(x - (-3))

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

The equation in point-slope form of the line parallel to the given line and passing through the point (-3, 1) is:

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

The total weight of the contents is 141.33 pounds.

What is a rectangular prism?

A three-dimensional solid form with six faces, including rectangular bases, is called a rectangular prism. A rectangular prism also refers to a cuboid. A cuboid and a rectangular prism have the same cross-section.

Here, we have

Given: A container built for transatlantic shipping is constructed in the shape of a right rectangular prism. Its dimensions are 5 ft by 14.5 ft by 6.5 ft. The container is entirely full and, on average, its contents weigh 0.3 pounds per cubic foot.

The volume of the container is calculated as:

5 ft× 14.5 ft× 6.5 ft= 471.125 ft³

Then, the total weight of the contents is calculated as:

471.125 ft³×  0.3 pounds per cubic foot= 141.3375 pounds≅ 141.33 pounds

Hence, the total weight of the contents is 141.33 pounds.

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Answer:

Part A:  8x + 24

Part B:  Expressions M and N are not equivalent for any value of x because if you do 8x + 24 = 8x + 10, the 8x will cancel out from both sides and you are left with 24 = 10, which is not true, and therefore has no solution.

Step-by-step explanation:

For Part A, to apply the Distributive Property, you multiple the 4 with both terms in the parentheses. So, you do 4(2x) + 4(6). This expression is equal to 8x + 24.

Hope this helped! :)

Answer: 48 more monthly payments

Step-by-step explanation:

The equation that represents the condition is m° + 66° + m° = 120°. Then the value of m is 27°.

When two lines intersect, then their opposite angles are equal. Then the equation is given as,

m° + 66° + m° = 120°

Simplify the equation for m, then the value of 'm' is calculated as,

m° + 66° + m° = 120°

2m° = 120° - 66°

2m° = 54°

m° = 27°

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Answer:

I think it's 27

because length is 3 times its width

Answer:

108 inches²

Step-by-step explanation:

Rectangular prism = cuboid

To find how much paper is required to cover the box, we need to find the TSA of the cuboid.

TSA of cuboid = 2 [LB + LH + HB] = 2 [ (3×4) + (3×6) + (4×6) ] = 2 [ 12+18+24 ] = 2 × 54 = 108 inches²

Answer:

health class

Step-by-step explanation:

when the mean absolute deviation (M.A.D) is lower, that means the data is closer together. When it is higher that means the data is more spread out.

Answer: Hope this helps you understand!

Step-by-step explanation:

Let's simplify step-by-step.

−5r2−6rs+6s2−(6r2+9rs−10s2)

Distribute the Negative Sign:

=−5r2−6rs+6s2+−1(6r2+9rs−10s2)

=−5r2+−6rs+6s2+−1(6r2)+−1(9rs)+−1(−10s2)

=−5r2+−6rs+6s2+−6r2+−9rs+10s2

Combine Like Terms:

=−5r2+−6rs+6s2+−6r2+−9rs+10s2

=(−5r2+−6r2)+(−6rs+−9rs)+(6s2+10s2)

ANSWER:

=−11r2+−15rs+16s2

Answer:

11r^2+15rs−16s^2

Step-by-step explanation:

Use the distributive property.

(6r^2+9rs−10s^2)−(−5r^2−6rs+6s^2)

6r^2+9rs−10s^2+5r^2+6rs−6s^2

Use the commutative property to combine like terms, then simplify.

6r^2+9rs−10s^2+5r^2+6rs−6s^2

6r^2+5r^2+9rs+6rs−10s^2−6s^2

11r^2+15rs−16s^2

Answer:

Step-by-step explanation:

Set equations as follows

20 years ago

Mike was four times as old as John:

Four years from now

Mike will be twice as old as John:

Simplify each equation

Solve for y by substitution

Find the value of x

I hope you can convert the above equations into required format. Let me know if not.

Answer:

E

Step-by-step explanation:

Answer:

53 is the average value.

Step-by-step explanation:

To find the average, or mean of multiple values you first add them all up:

38+48+58+68=212

Then you count how many different numbers there are, (there are 4 numbers here, if there are 2 of the same numbers you still count them both, just so you understand).

Then you need to divide the total you got, 212, by the total amount of numbers, 4, to get the average amount, 53.

I hope that my answer has helped you, have a great day, ask any questions you have below.