PLEASE HELP ME!

How do the graphs of y = f (x) + k, y = f(x – h), and y = -f(x) compare to the graph of the parent function f?

Answer:

Hi could you specify the question, I don't see any question in here, else I'd answer it.

Step-by-step explanation:

p=8h is the equation.This part is represented in tabular form.The coefficient of h. Mark worked 21 hours that week.Yes, the equation is a direct variation.

An equation is a statement that shows the equality of two expressions. It typically contains one or more variables and may involve mathematical operations such as addition, subtraction, multiplication, and division. Equations are commonly used in mathematics, science, and engineering to model real-world situations and solve problems.

Direct variation is a mathematical relationship between two variables, where a change in one variable results in a proportional change in the other variable. In other words, if two variables are in direct variation, when one variable increases, the other variable increases as well, and when one variable decreases, the other variable decreases as well, in a constant ratio.

Part A: The equation for this situation is p = 8h, where p represents the pay in dollars and h represents the number of hours worked.

Part B:

| Worked (hrs) | Pay (p) |

|------------------|---------|

| 1                | 8       |

| 2                | 16      |

| 3                | 24      |

| 4                | 32      |

| 5                | 40      |

| 6                | 48      |

and so on.

Part C: The coefficient of h, which is 8, shows the number of hours Mark worked.

Part D: We can use the equation p = 8h and substitute p = 168 to find the number of hours Mark worked.

168 = 8h

h = 21

Therefore, Mark worked 21 hours that week.

Part E: Yes, the equation is a direct variation because the pay (p) is directly proportional to the number of hours worked (h) and the constant of variation is 8.

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Answer:

s = 156.25 square meters

Step-by-step explanation:

s = 2lw + 2lh + 2wh

s = 2(5.5)(3) + 2(3)(7.25) + 2(5.5)(7.25)

s = 33 + 43.5 + 79.75

s = 156.25 square meters

Answer:

We know,

\( \quad \)\({\boxed{ \rm{Surface \: Area_{ \: (rectangular \: prism)} = 2(lb + bh + hl)}}}\)

where,

\( \: \)

\( {\longrightarrow { 2 ( 5.5 \times 3 + 3 \times 7.25 + 7.25 \times 5.5 ) }} \)

\( \longrightarrow \) 2 ( 16.5 + 21.75 + 39.875 )

\( \longrightarrow \) 2 ( 78.125 )

\( \longrightarrow \) 156.25

Thus, The Surface Area of rectangular prism is 156.25cm².

\( \rule{200pt}{2pt} \)

\(\footnotesize{\boxed{ \begin{array}{cc} \small\underline{ \sf{\pmb{ \blue{More \: Formula}}}} \\ \\ \bigstar \: \bf{CSA_{(cylinder)} = 2\pi \: rh}\\ \\ \bigstar \: \bf{Volume_{(cylinder)} = \pi {r}^{2} h}\\ \\ \bigstar \: \bf{TSA_{(cylinder)} = 2\pi \: r(r + h)}\\ \\ \bigstar \: \bf{CSA_{(cone)} = \pi \: r \: l}\\ \\ \bigstar \: \bf{TSA_{(cone)} = \pi \: r \: (l + r)}\\ \\ \bigstar \: \bf{Volume_{(sphere)} = \dfrac{4}{3}\pi {r}^{3} }\\ \\ \bigstar \: \bf{Volume_{(cube)} = {(side)}^{3} }\\ \\ \bigstar \: \bf{CSA_{(cube)} = 4 {(side)}^{2} }\\ \\ \bigstar \: \bf{TSA_{(cube)} = 6 {(side)}^{2} }\\ \\ \bigstar \: \bf{Volume_{(cuboid)} = lbh}\\ \\ \bigstar \: \bf{CSA_{(cuboid)} = 2(l + b)h}\\ \\ \bigstar \: \bf{TSA_{(cuboid)} = 2(lb +bh+hl )}\\ \: \end{array} }}\)

There are 8 number of ways to construct a 2 x 2 x 2 cube using 4 blue cubes and 4 white cubes.

Given,

A cube is constructed from 4 white unit cubes and 4 blue unit cubes.

We have to find  the number of ways are there to construct a 2 x 2 x 2 cube using these smaller cubes;

Here,

4 white cubes and 4 blue cubes.

Now,

Here,

There are 8 number of ways to construct a 2 x 2 x 2 cube using 4 blue cubes and 4 white cubes.

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Answer:

Step-by-step explanation:

The first one is Crosses the axis at (1, 0). The second one is Crosses the axis at (−4, 0). The third one is touching the axis at (−5, 0).

To graph the function g(x) = (x - 5)² - 9, shift the graph of f(x) = x²

5 units right and 9 units down

Step-by-step explanation:

Let us revise the translation

1. If the function f(x) translated horizontally to the right by h units, then

   its image is g(x) = f(x - h)

2. If the function f(x) translated horizontally to the left by h units, then

   its image is g(x) = f(x + h)

3. If the function f(x) translated vertically up by k units, then its image

   is g(x) = f(x) + k

4. If the function f(x) translated vertically down by k units, then its image

   is g(x) = f(x) - k

∵ f(x) = x²

∵ g(x) = (x - 5)² - 9

∴ g(x) = f(x - 5)² - 9

∴ h = 5 ⇒ 5 units right

∴ k = -9 ⇒ 9 units down

∴ f(x) translated 5 units to the right

∴ f(x) translated 9 units down

To graph the function g(x) = (x - 5)² - 9, shift the graph of f(x) = x²

5 units right and 9 units down

The graph of g(x) = -1/5(x + 5)² - 2 is plotted making use of the points it passes.

A function y = f(x) is a one to one relationship between two sets X and Y where the set X is called the domain and Y the range of function f(x) ans x ∈ X and y ∈ Y.

The given function is g(x) = -1/5(x + 5)² - 2.

In order to plot its graph, consider following values of x and y as follows,

For x = 0,

g(x) = -1/5(0 + 5)² - 2

      = -7

For x = -5,

g(x) = -1/5(-5 + 5)² - 2

      = -2

Now as the given function has its degree as 2, it is parabolic.

Thus, its graph can be drawn as follows,

Hence, the graph of the given function is drawn clearly.

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Answer:

1,2,4, and the last one

Step-by-step explanation:

That's my final answer

Answer:

(6 + 11) * x = ( x + x) - 2/3

Step-by-step explanation:

(6 + 11) * x = ( x + x) - 2/3

The expression will be written as (6 + 11) * x = ( x + x) - 2/3.

Expression in maths is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given that six more than eleven times the number is two-thirds less than the sum of the number and itself. The expression will be written as below:-

(6 + 11) * x = ( x + x) - 2/3.

17x = 2x - (2/3)

Therefore, the expression will be written as (6 + 11) * x = ( x + x) - 2/3.

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Answer:

$8.90

Step-by-step explanation:

first you have to subtract how much money you get for overtime, 516.20-160.20=356.00 Next you have to divide 356.00 by 40 to find per hour, 356.00/40=8.90.

Answer:

c

Step-by-step explanation:

Answer:

C. 4x+1

Step-by-step explanation:

the Maclaurin series is:`∑(n=0)^(∞) [fⁿ(0)/n!] xⁿ``= f(0)/0! + f'(0)/1! x + f''(0)/2! x^2 + f'''(0)/3! x^3 + f⁽⁴⁾(0)/4! x^4 + f⁽⁵⁾(0)/5! x^5 + f⁽⁶⁾(0)/6! x^6 + ...``= 0 + 0x + 0x² + 0x³ + (x^9 sin(x))/4! + 0x⁵ - (x^9 cos(x))/6! + ...``= x^9 sin(x) - x^11/3! + x^13/5! - x^15/7! + ...`

The Maclaurin series for the function `f(x) = x^9 sin(x)` is given by `∑(n=0)^(∞) [fⁿ(0)/n!] xⁿ` where fⁿ(0) is the nth derivative of f(x) evaluated at x = 0. We will start by calculating the first few derivatives of f(x):`f(x) = x^9 sin(x)`First derivative:` f'(x) = x^9 cos(x) + 9x^8 sin(x)`Second derivative :`f''(x) = -x^9 sin(x) + 18x^8 cos(x) + 72x^7 sin(x)`Third derivative: `f'''(x) = -x^9 cos(x) + 27x^8 sin(x) + 432x^6 cos(x) - 2160x^5 sin(x)`Fourth derivative :`f⁽⁴⁾(x) = x^9 sin(x) + 36x^8 cos(x) + 1296x^6 sin(x) - 8640x^5 cos(x) - 60480x^4 sin(x)`Fifth derivative :`f⁽⁵⁾(x) = x^9 cos(x) + 45x^8 sin(x) + 2160x^6 cos(x) - 21600x^5 sin(x) - 302400x^4 cos(x) - 1814400x^3 sin(x)`Sixth derivative: `f⁽⁶⁾(x) = -x^9 sin(x) + 54x^8 cos(x) + 5184x^6 sin(x) - 90720x^5 cos(x) - 2721600x^3 sin(x) + 10886400x^2 cos(x) + 72576000x sin(x)`We can see a pattern emerging in the coefficients. The even derivatives are of the form `x^9 sin(x) + (terms in cos(x))` and the odd derivatives are of the form `-x^9 cos(x) + (terms in sin(x))`. , the Maclaurin series is:`∑(n=0)^(∞) [fⁿ(0)/n!] xⁿ``= f(0)/0! + f'(0)/1! x + f''(0)/2! x^2 + f'''(0)/3! x^3 + f⁽⁴⁾(0)/4! x^4 + f⁽⁵⁾(0)/5! x^5 + f⁽⁶⁾(0)/6! x^6 + ...``= 0 + 0x + 0x² + 0x³ + (x^9 sin(x))/4! + 0x⁵ - (x^9 cos(x))/6! + ...``= x^9 sin(x) - x^11/3! + x^13/5! - x^15/7! + ...`

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The Maclaurin series for the function f(x) = x^9 sin(x) is `-x^4/24 - x^5/40 - x^6/720 + x^7/5040 + x^8/40320 - x^9/362880 + ...`.

Maclaurin series is the expansion of a function in terms of its derivatives at zero. To find the Maclaurin series for the function f(x) = x^9 sin(x), we need to use the formula:

`f(x) = f(0) + f'(0)x + f''(0)x^2/2! + f'''(0)x^3/3! + ... + f^(n)(0)x^n/n! + ...`

We first need to find the derivatives of the function f(x). We have:

`f(x) = x^9 sin(x)`

Differentiating once gives:

\(`f'(x) = x^9 cos(x) + 9x^8 sin(x)`\)

Differentiating twice gives:

`f''(x) = -x^9 sin(x) + 18x^8 cos(x) + 72x^7 sin(x)`

Differentiating thrice gives:

`f'''(x) = -x^9 cos(x) - 54x^8 sin(x) + 324x^7 cos(x) + 504x^6 sin(x)`

Differentiating four times gives:

\(`f^(4)(x) = x^9 sin(x) - 216x^7 cos(x) - 1512x^6 sin(x) + 3024x^5 cos(x)`\)

Differentiating five times gives:

`f^(5)(x) = 9x^8 cos(x) - 504x^6 sin(x) - 7560x^5 cos(x) + 15120x^4 sin(x)`

Differentiating six times gives:

`f^(6)(x) = -9x^8 sin(x) - 3024x^5 cos(x) + 45360x^4 sin(x) - 60480x^3 cos(x)`

Differentiating seven times gives:

\(`f^(7)(x) = -81x^7 cos(x) + 15120x^4 sin(x) + 90720x^3 cos(x) - 181440x^2 sin(x)`\)

Differentiating eight times gives:

\(`f^(8)(x) = 81x^7 sin(x) + 90720x^3 cos(x) - 725760x^2 sin(x) + 725760x cos(x)`\)

Differentiating nine times gives:

\(`f^(9)(x) = 729x^6 cos(x) - 725760x^2 sin(x) - 6531840x cos(x) + 6531840 sin(x)`\)

Now we can substitute into the formula:

 `f(x) = f(0) + f'(0)x + f''(0)x^2/2! + f'''(0)x^3/3! + ... + f^(n)(0)x^n/n! + ...`and simplify as follows:

\(`f(0) = 0` `f'(0) = 0 + 9(0) = 0` `f''(0) = -(0) + 18(0) + 72(0) = 0` `f'''(0) = -(0) - 54(0) + 324(0) + 504(0) = 0` `f^(4)(0) = (0) - 216(1) - 1512(0) + 3024(0) = -216` `f^(5)(0) = 9(0) - 504(1) - 7560(0) + 15120(0) = -504` `f^(6)(0) = -(0) - 3024(1) + 45360(0) - 60480(0) = -3024` `f^(7)(0) = -(81)(0) + 15120(1) + 90720(0) - 181440(0) = 15120` `f^(8)(0) = 81(0) + 90720(1) - 725760(0) + 725760(0) = 90720` `f^(9)(0) = 729(0) - 725760(1) - 6531840(0) + 6531840(0) = -725760`\)

Substituting these values into the formula, we have:

\(`f(x) = 0 + 0(x) + 0(x^2)/2! + 0(x^3)/3! + (-216)(x^4)/4! + (-504)(x^5)/5! + (-3024)(x^6)/6! + (15120)(x^7)/7! + (90720)(x^8)/8! + (-725760)(x^9)/9! + ...`\)

Simplifying this, we get:

\(`f(x) = -x^4/24 - x^5/40 - x^6/720 + x^7/5040 + x^8/40320 - x^9/362880 + ...`\)

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a) The average rate of change when x = 4 and h = 0.5 is -87.25.

b) The average rate of change between x = 4 and x = 4.01 is 1612.0301.

a) To find the average rate of change when x = 4 and h = 0.5 for the function f(x) = x³ - 2x, we can use the formula:

The average rate of change = (f(x + h) - f(x)) / h

Substituting the given values:

Average rate of change = (f(4 + 0.5) - f(4)) / 0.5

To calculate f(4 + 0.5) and f(4):

f(4 + 0.5) = (4 + 0.5)³ - 2(4 + 0.5) = 4.375

f(4) = 4³ - 2(4) = 48

Substituting these values into the formula:

The average rate of change = (4.375 - 48) / 0.5

The average rate of change = (-43.625) / 0.5

The average rate of change = -87.25

Therefore, the average rate of change when x = 4 and h = 0.5 for the function f(x) = x³ - 2x is -87.25.

b) To find the average rate of change between x = 4 and x = 4.01 for the function f(x) = x³ - 2x, we can use the same formula:

The average rate of change = (f(x₂) - f(x₁)) / (x₂ - x₁)

Substituting the given values:

The average rate of change = (f(4.01) - f(4)) / (4.01 - 4)

To calculate f(4.01) and f(4):

f(4.01) = (4.01)³ - 2(4.01) = 64.120301

f(4) = 4³ - 2(4) = 48

Substituting these values into the formula:

The average rate of change = (64.120301 - 48) / (4.01 - 4)

The average rate of change = 16.120301 / 0.01

The average rate of change = 1612.0301

Therefore, the average rate of change between x = 4 and x = 4.01 for the function f(x) = x³ - 2x is 1612.0301.

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Answer:

12.85

Step-by-step explanation:

(100/2800)×360=12.85

Answer:

its 13%

Step-by-step explanation:

2,800 = whole, 364 = part. Write the equation percent x whole = part and solve.

Using the cosine law, the measure of angle R is calculated as approximately: a. 44.5°.

The cosine law is expressed as follows:

cos R = [s² + q² – r²]/2sq

Given the following side lengths of triangle QRS:

Side q = 11,

Side r = 17,

Side s = 23.

Plug in the values into the cosine law formula:

cos R = [23² + 11² – 17²]/2 * 23 * 11

cos R = 361/506

Cos R = 0.7134

R = cos^(-1)(0.7134)

R ≈ 44.5°

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Answer:

D. Make the column wider

Step-by-step explanation:

There is no non-zero polynomial q(x) that satisfies the given congruence equation.To find a polynomial q(x) such that (a + bx)q(x) ≡ 1 (mod x^2 + 1), we need to find the inverse of (a + bx) modulo x^2 + 1.

Let's start by expanding the expression (a + bx)q(x) and setting it equal to 1:

(a + bx)q(x) = 1 (mod x^2 + 1)

Expanding the left side:

a^2 + 2abx + b^2x^2q(x) = 1 (mod x^2 + 1)

Next, let's rearrange the equation and group the terms with x^2:

b^2x^2q(x) + 2abx + (a^2 - 1) ≡ 0 (mod x^2 + 1)

To find the inverse of (a + bx) modulo x^2 + 1, we want to eliminate the term with x^2. Therefore, we need to set the coefficient of x^2 to 0.

b^2q(x) ≡ 0 (mod x^2 + 1)

From this equation, we can see that q(x) must be a multiple of x^2 + 1, which means q(x) = k(x^2 + 1) for some constant k.

Substituting q(x) = k(x^2 + 1) back into the rearranged equation, we get:

b^2k(x^2 + 1) + 2abx + (a^2 - 1) ≡ 0 (mod x^2 + 1)

Expanding and simplifying:

(b^2k)x^2 + (2ab)x + (b^2k + a^2 - 1) ≡ 0 (mod x^2 + 1)

To eliminate the x^2 term, we set the coefficient of x^2 equal to 0:

b^2k = 0

Since b^2 ≠ 0, this equation can only be satisfied if k = 0.

Therefore, the polynomial q(x) = 0 satisfies the equation (a + bx)q(x) ≡ 1 (mod x^2 + 1) over q.

In conclusion, there is no non-zero polynomial q(x) that satisfies the given congruence equation.

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The inner product of two vectors A = (2, -3,0) and B = (-1,0,5) is -2 / √(13×26).

Solving the given system of equations using Gaussian elimination:

2x + 3y + z = 2 y + 5z = 20 -x+2y+3z = 13

Matrix form of the system is

[A] = [B] 2 3 1 | 2 0 5 | 20 -1 2 3 | 13

Divide row 1 by 2 and replace row 1 by the new row 1: 1 3/2 1/2 | 1

Divide row 2 by 5 and replace row 2 by the new row 2: 0 1 1 | 4

Divide row 3 by -1 and replace row 3 by the new row 3: 0 0 1 | 5

Back substitution, replace z = 5 into second equation to solve for y, y + 5(5) = 20 y = -5

Back substitution, replace z = 5 and y = -5 into the first equation to solve for x, 2x + 3(-5) + 5 = 2 2x - 15 + 5 = 2 2x = 12 x = 6

The solution is (x,y,z) = (6,-5,5)

Therefore, the solution to the given system of equations using Gaussian elimination is (x,y,z) = (6,-5,5).

The given two vectors are A = (2, -3,0) and B = = (-1,0,5). The inner product of two vectors A and B is given by

A·B = |A||B|cosθ

Given,A = (2, -3,0) and B = (-1,0,5)

Magnitude of A is |A| = √(2²+(-3)²+0²) = √13

Magnitude of B is |B| = √((-1)²+0²+5²) = √26

Dot product of A and B is A·B = 2(-1) + (-3)(0) + 0(5) = -2

Cosine of the angle between A and B is

cosθ = A·B / (|A||B|)

cosθ = -2 / (√13×√26)

cosθ = -2 / √(13×26)

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Check the picture below.

The shape of the cross section of a triangular pyramid sliced by a plane that is perpendicular to its base is triangle.

The non-empty intersection of a solid body in three dimensions with a plane, or its equivalent in higher dimensions, is referred to as a cross section in geometry and science. Many parallel cross-sections are produced when an object is sliced. The boundary of a cross-section in three dimensions that is parallel to two of the axes, that is, parallel to the plane determined by these axes, is sometimes referred to as a contour line.

A triangle-shaped pyramid essentially has a triangle-shaped base. The cross section formed when an imaginary line is produced to cut through perpendicular to the base will still have a triangular orientation, but it will be smaller than it was when the pyramid's original triangular orientation or sides were there.

Therefore, the shape of the cross section of a triangular pyramid sliced by a plane that is perpendicular to its base is triangle.

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Answer:

the answer to your question is yes, but the answer to #21 is ;

mn

pn

ml

lp

Step-by-step explanation:

The given statement is correct. If a matrix A is invertible, then it means that it has a unique inverse.

What is the identity matrix?

The identity matrix is a square matrix with 1's on the main diagonal and 0's everywhere else. It is denoted as I. The identity matrix has the property that for any square matrix A, the product of A and I is equal to A itself, so I serve as a sort of "do-nothing" matrix.

Yes, this is correct. If a matrix A is invertible, then it means that it has a unique inverse. This implies that the columns of A are linearly independent, as they form a basis for the space. A row equivalent matrix to the identity matrix (A∼I) will have one pivot in each column, indicating that the columns are linearly independent.

Hence, the given statement is correct. If a matrix A is invertible, then it means that it has a unique inverse.

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To find the area of the quadrilateral formed by the four complex numbers as vertices, we need to determine the coordinates of each vertex and then use the Shoelace Formula.

Let's denote the four complex numbers as A, B, C, and D.

Given that both the real and imaginary parts of A are integers, we can express it as A = a + bi, where a and b are integers.

Similarly, we can express B, C, and D as B = c + di, C = e + fi, and D = g + hi, where c, d, e, f, g, and h are integers.

Now, we need to find the values of a, b, c, d, e, f, g, and h.

To do this, we can use the fact that A, B, C, and D are complex numbers such that |A| = |B| = |C| = |D| = 1. This implies that the distance of each point from the origin is 1.

Using this information, we can form the following equations:

a² + b² = 1
c² + d² = 1
e² + f² = 1
g² + h² = 1

Since the real and imaginary parts of A, B, C, and D are integers, we can substitute a, b, c, d, e, f, g, and h with integers that satisfy these equations.

Once we have the coordinates of A, B, C, and D, we can use the Shoelace Formula to find the area of the quadrilateral formed by these points.

The Shoelace Formula states that the area of a quadrilateral with vertices (x1, y1), (x2, y2), (x3, y3), and (x4, y4) is given by:

Area = 0.5 * |(x1 * y2 + x2 * y3 + x3 * y4 + x4 * y1) - (y1 * x2 + y2 * x3 + y3 * x4 + y4 * x1)|

Once you calculate the values of the determinants in the formula, you can find the area of the quadrilateral.

In conclusion, to find the area of the quadrilateral formed by the four complex numbers, we need to determine the coordinates of each vertex and then use the Shoelace Formula.

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The statement "P implies Q" is false under the following conditions: a) P is true and Q is false, and d) P is false and Q is true.

The statement "P implies Q" can be expressed as "if P, then Q." It is a conditional statement where P is the antecedent (the condition) and Q is the consequent (the result).

To determine when the statement is false, we need to identify cases where P is true but Q is false, or when P is false but Q is true.

Option a) states that both P and Q are true. In this case, the statement "P implies Q" holds true because if P is true, then Q is true.

Option b) states that both P and Q are false. In this case, the statement "P implies Q" is considered true because the antecedent (P) is false.

Option c) states that P is true and Q is false. Under this condition, the statement "P implies Q" is false because when P is true, but Q is false, the implication does not hold.

Option d) states that P is false and Q is true. In this case, the statement "P implies Q" is true because the antecedent (P) is false.

Therefore, the conditions under which the statement "P implies Q" is false are a) P is true and Q is false, and d) P is false and Q is true.

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Answer:

$99,418.43. Explanation: FV=OV(1+r100)n. FV = The value you are looking for. OV = The orginal amount. r = interest rate. n = Years.

1 answer

Step-by-step explanation:

Answer:

3 = 14 and 4 = 8

Step-by-step explanation:

The reason as to why this is, is because of the line going down the middle. If you were to open one of the lengths as a door starting from the middle line it would fit perfectly with the top one.

Refer to the images attached.

The length of each side of the octagon is 6 cm

It is a polygon with eight sides and eight angles. There are a total of 20 diagonals in it. All its interior angles sum up to 1080°.

Given that, a regular octagon has an area of 288 square centimeters and an apothem of 12 cm.

We need to find the side of the octagon,

We know that area of the octagon = 8/2 × side × apothem

Therefore,

288 = 8/2 × side × 12

side = 288 / 48

side = 6

Hence, the length of each side of the octagon is 6 cm

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