What is the difference between the sum of the measures of the interior angles of a regular hexagon and the sum of the measures of the exterior angles of a regular pentagon

The correct answer is OD. 8x + 1.

To divide 8x³ + x² - 32x - 4 by x² - 4, we can use polynomial long division.

The dividend is 8x³ + x² - 32x - 4, and the divisor is x² - 4.

We start by dividing the highest degree term, which is 8x³, by x². This gives us 8x.

Next, we multiply the divisor x² - 4 by the quotient 8x. The result is 8x³ - 32x.

Subtracting 8x³ - 32x from the dividend, we get x² - 32x.

Now, we divide x² - 32x by x² - 4. This gives us 1.

Multiplying the divisor x² - 4 by the quotient 1, we get x² - 4.

Subtracting x² - 4 from the remaining dividend, which is -32x, we get -32x + 4.

Since we can no longer divide, the final result is the quotient we obtained: 8x + 1.

Therefore, the correct answer is:

OD. 8x + 1.

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Answer:

4.2 units

Step-by-step explanation:

Assuming 1 grid box = 1 units, the coordinates of the two points are (-1, -1) and (2, 2).

Apply distance formula \( d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \) to find the distance between (-1, -1) and (2, 2).

Let,

\( (-1, -1) = (x_1, y_1) \)

\( (2, 2) = (x_2, y_2) \)

Plug in the values

\( d = \sqrt{(2 - (-1))^2 + (2 - (-1))^2} \)

\( d = \sqrt{(3)^2 + (3)^2} \)

\( d = \sqrt{9 + 9} \)

\( d = \sqrt{18} \)

\( d = 4.2 \) (to the nearest tenth)

The expression in simplified form is 4(2x - 3y).

Given that, an expression, 9x+(-x)+2y+(-14y), we need to simplify it,

9x+(-x)+2y+(-14y)

Opening the brackets,

= 9x - x + 2y - 14y

combining the like terms,

= 8x - 12y

Take 4 common,

= 4(2x - 3y)

Hence the expression in simplified form is 4(2x - 3y).

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Based on the given information, we know that x must be 2 since it is the only even prime number. We also know that y must be either 11, 13, 17, or 19 since those are the only prime numbers between 10 and 20.

So, the sum of x and y can be 2 + 11 = 13, 2 + 13 = 15, 2 + 17 = 19, or 2 + 19 = 21.

Out of these four possible sums, only 13, 17, and 19 are prime numbers. Therefore, we can say that the sum of x and y may or may not be a prime number, depending on the specific values of x and y.

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The function f(t) is defined as e raised to the power 5t plus 4t plus the natural logarithm of the quantity t squared plus 3 times the constant c, raised to the power of 7, plus t times e raised to the power of -1 plus 5 times e raised to the power of 6.

Given a function:

f(t)=e5t+4t+7ln(t2+3c)+te-1+5e6

where c is a constant.

The solution to the question is shown below.

Step 1: We have given a function:

f(t)=e5t+4t+7ln(t2+3c)+te-1+5e6

We have to find the number of words we have to write to express this function in words.

Step 2: Solution

f(t) = et5+4t + ln(t²+3c)⁷ +te-1+5e⁶

Where,

et5+4t = exponential function

ln(t²+3c)⁷ = natural logarithmic function

te-1 = linear function

e⁶ = exponential function

Therefore, f(t) can be expressed in words as:

The function f(t) is defined as e raised to the power 5t plus 4t plus the natural logarithm of the quantity t squared plus 3 times the constant c, raised to the power of 7, plus t times e raised to the power of -1 plus 5 times e raised to the power of 6.

Step 3: Conclusion

Hence, the function f(t) can be expressed in words with:The function f(t) is defined as e raised to the power 5t plus 4t plus the natural logarithm of the quantity t squared plus 3 times the constant c, raised to the power of 7, plus t times e raised to the power of -1 plus 5 times e raised to the power of 6.

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Answer:

The question is y/4= -7

So we will have to criss-cross it, so that x could be alone

When we criss-cross it we multiply

So,

y=4×-7

y=-28

Step-by-step explanation:

I explained my best, please give me brainliest

Answer:

The slope of the line represented by the table value is -8/5

On a graph, the absolute value of a number is always non-negative.

The absolute value of a number is defined as the distance of that number from zero on the number line. Since the distance can never be negative, the absolute value of a number is always non-negative.

This is reflected in the graph of an absolute value function. The graph of an absolute value function, |x| is a V-shape that opens upward, with the vertex of the V being the point where the absolute value function equals zero. The two arms of the V extend out from this point, going in opposite directions along the number line. The coordinates of the vertex (0,0) and the graph is always non-negative.

It's important to note that although the absolute value is always non-negative on a graph, the input value (x) can be both positive and negative. The output of the absolute value function (|x|) will always be positive.

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Answer:

A

Step-by-step explanation:

12-4/6-2=8/4=2/1

Answer:

0.0000000000783

Step-by-step explanation:

Since the exponent is negative you will move the decimal point 11 places to the left, including the number 7.

Answer:

Step-by-step explanation:

If one angle of a parallelogram is a right angle, then it is a rectangle.

The required answer is  y(t) =  | 4t(2t + 8t^2 + 2t^3) | .

Explanation:-

To solve the differential equation y' = Ay, where A is the given matrix and y(1) = [1], use the matrix exponential method. The solution can be written as y(t) = e^(At) * y(0), where e^(At) represents the matrix exponential and y(0) is the initial condition vector.

First,  to find the matrix exponential e^(At). To calculate this,  use the power series expansion of the exponential function:

e^(At) = I + At + (At)^2/2! + (At)^3/3! + ...

To obtain e^(At),to calculate the powers of A multiplied by t.  start by calculating A^2:

A^2 = A * A =

|-6 24 | |-6 24 | | -12 48 |

| 1 -8 | * | 4 2 | = | -4 -2 |

| 4 2 | | -12 -6 | | 16 4 |

Next,  calculate A^3:

A^3 = A * A^2 =

|-6 24 | |-6 24 | | 48 240 |

| 1 -8 | * | -4 -2 | = | 0 -16 |

| 4 2 | | 16 4 | | 8 32 |

Now calculate e^(At) using the power series expansion:

e^(At) ≈ I + At + (At)^2/2! + (At)^3/3! + ...

I is the identity matrix of the same size as A. In this case, it is a 3x3 matrix with ones on the diagonal and zeros elsewhere:

I =

| 1 0 0 |

| 0 1 0 |

| 0 0 1 |

Now  substitute the values of A, A^2, and A^3 into the power series expansion:

e^(At) ≈ I + At + (At)^2/2! + (At)^3/3!

e^(At) ≈

| 1 0 0 | + t |-6 24 | + t^2 | -12 48 | /2! + t^3 | 48 240 | /3!

| 0 1 0 | | 1 -8 | | -4 -2 | | 0 -16 |

| 0 0 1 | | 4 2 | | 16 4 | | 8 32 |

calculate the matrix exponential:

e^(At) ≈| 1 - 6t + 6t^2 - 2t^3 24t - 48t^2 + 24t^3 |

         =| t 1 - 8t + 4t^2 |

         =| 4t 2t + 8t^2 + 2t^3 |

Now  find the solution y(t) by multiplying e^(At) with the initial condition y(0):

y(t) = e^(At) * y(0) =

| 1 - 6t + 6t^2 - 2t^3 24t - 48t^2 + 24t^3 | * | 1 |

| t 1 - 8t + 4t^2 | | 0 |

| 4t 2t + 8t^2 + 2t^3 | | 1 |

Simplifying the multiplication, we get:

y(t) =| 1 - 6t + 6t^2 - 2t^3 + 24t - 48t^2 + 24t^3 |

     = | t(1 - 8t + 4t^2) |

      = | 4t(2t + 8t^2 + 2t^3) |

Now substitute t = 1 to find the particular solution that satisfies the initial condition y(1) = [1]:

y(1) =| 1 - 6(1) + 6(1)^2 - 2(1)^3 + 24(1) - 48(1)^2 + 24(1)^3 |

     =| 1(1 - 8(1) + 4(1)^2) |

     =4(1)(2(1) + 8(1)^2 + 2(1)^3) |

Simplifying further,

y(1) =| 1 - 6 + 6 - 2 + 24 - 48 + 24 |

     =| 1 - 8 + 4 |

     =| 8 + 16 |

y(1) =| -1 |

     =| -3 |

     =| 24 |

Therefore, the solution to the differential equation y' = Ay with the initial condition y(1) = [1] is:

y(t) = | 1 - 6t + 6t^2 - 2t^3 + 24t - 48t^2 + 24t^3 |

y(t) = | t(1 - 8t + 4t^2) |

 y(t) =  | 4t(2t + 8t^2 + 2t^3) |

Substituting t = 1, we have:

y(1) =| -1 |

     =| -3 |

      =| 24 |.

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The equation that relates the graph is a) y= - 1/2(x-3)²+2

Here Let put x=7

y= -1/2(x-3)²+2

= -1/2(7-3)²+2

= -1/2(4)²+2

= -1/2(16)+2

= - 8+2

= - 4

Hence (7,-4) is marked.

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The range is the most convenient measure of dispersion because it is simple to calculate and understand. The range is the most imprecise measure of variability because can be greatly affected by outliers or extreme values and may not accurately reflect the true variability of the data.

The range is used to evaluate a small data set such as the grades of a small group of students.

The range is the difference of the maximum and minimum values of a data set. The range is calculated by subtracting the smallest value from the largest value in a data set.

For example, if the smallest value in a data set is 2 and the largest value is 10, the range would be 8 (10-2=8).

However, the range is also the most imprecise measure of variability because it only takes into account the two extreme values in the data set and does not consider the values in between.

The range is most useful when you want to quickly assess the dispersion of a data set or when the data set is small and does not have any outliers. It is also useful when you want to compare the dispersion of two or more data sets. However, if the data set is large or has outliers, it is better to use other measures of dispersion and variability, such as the standard deviation or interquartile range.

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To create a sign chart for the polynomial function F(x) = -(x+5)(x-2)(2x-4)(x-4)², we will examine the intervals defined by the critical points and the zeros of the function.

1. Determine the critical points  -

  - The critical points occur where the factors of the polynomial change sign.

  - The critical points are x = -5, x = 2, x = 4, and x = 4 (repeated).

2. Select test points within each interval  -

  - To evaluate the sign of the polynomial at each interval, we choose test points.

  - Common choices for test points include values less than the smallest critical point, between critical points, and greater than the largest critical point.

  - Let's choose test points  -  x = -6, x = 0, x = 3, and x = 5.

3. Evaluate the sign of the polynomial at each test point

  - Plug in the test points into the polynomial and determine the sign of the expression.

The sign chart for F(x) = -(x+5)(x-2)(2x-4)(x-4)² would look like this

Intervals              Test Point         Sign

-∞ to -5                  -6                    -

-5 to 2                   0                       +

2 to 4                    3                      -

4 to ∞                    5                      +

Note  - The signs in the "Sign" column indicate whether the polynomial is positive (+) or negative (-) in each interval. See the attached sign chart.

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An indication of the inequality negative 2 over 3 > −1 about the positions of negative 2 over 3 and −1 on the number line is that: A. negative 2 over 3 is located to the right of −1.

A number line can be defined as a type of graph that is designed and developed with a graduated straight line containing both positive and negative numbers (numerical values), that are placed at equal intervals along its length.

This ultimately implies that, a number line can be used for the comparison of two or more numbers such as -2/3 and -1. Also, a number line typically decreases in numerical value towards the left and increases in numerical value towards the right.

Note: negative 2 over 3 = -2/3.

By comparison, we have:

-2/3 > -1

In conclusion, the above inequality simply means that -2/3 is greater than -1 and it would be located to the left of 0 and right of -1 on a number line as shown in the image attached below.

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Answer: Pacco is right

Step-by-step explanation: 1st cube:

42 ft^2 2nd cube: 52 ft^2 3rd cube: 62 ft^2

42+52+62=156 ft^2 156 ft^2<160 ft^2

Answer:

-9a + b

Step-by-step explanation:

For this problem, let us factor out the variable a from the terms containing the variable, and apply addition and the distributive property to simplify the terms.

-5a - 4a + b

= a ( -5 + -4 ) + b

= a ( -9 ) + b

= -9a + b

Hence, the simplified expression for -5a - 4a + b is -9a + b.

Cheers.

Answer:

= -9a+b

Step-by-step explanation:

-5a+-4a =b

(-5a+-4a)+(b)

Answer:

b = 12

Step-by-step explanation:

a² + b² = c²

a and b are the length of the sides in the right triangle and c is the hypotenuse.

since we know one leg and the hypotenuse, we can find the other leg.

9² + b² = 15²

81 + b² = 225

b² = 225 - 81

b² = 144

b = 12

Answer:

The answer is 12

Step-by-step explanation:

the formula is A^2+B^2=c^2

9² + b² = 15²

81 + b² = 225

b² = 225 - 81

b² = 144

b = 12

Plotting the data on a graph can help you identify the outliers or points that don't fit the pattern.

The dataset, you can use it to identify the points that don't fit the pattern.

The points that don't fit the pattern in a dataset.

The points that don't fit the pattern in a dataset, you can use several methods such as:

Visualization:

Plotting the data on a graph can help you identify the outliers or points that don't fit the pattern.

You can use various graph types such as scatter plots, line graphs, box plots, etc., to visualize the data.

Statistical methods:

You can use statistical methods such as standard deviation, z-score, or regression analysis to identify the outliers or points that don't fit the pattern.

Domain knowledge:

If you have domain knowledge about the dataset, you can use it to identify the points that don't fit the pattern.

If you know that a particular event occurred during a specific period, you can use it to explain the anomaly in the data.

The points that don't fit the pattern, you can investigate why they don't fit the pattern.

It could be due to measurement errors, data entry errors, or a genuine anomaly in the data.

Understanding why certain data points don't fit the pattern can provide insights into the data and improve the accuracy of the analysis.

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Answer: 0.06 repeated, I'm sorry if it's wrong! I used a calculator.

Step-by-step explanation:

Calculating 2 divided by 5 / 6 should give you the answer 0.06666666666.

Answer:

x ≤ 15

Hope you could get an idea from here.

Doubt clarification - use comment section.

The equation that is required to be solved is: \($$\sqrt{2t} 2t - 1 + t = 53.56$$$$\sqrt{3t}+ 3 = 5x$$\)

Solving the first equation: \($$\begin{aligned}\sqrt{2t} 2t - 1 + t &= 53.56\\2t^2 + t - 53.56 &= 1\\2t^2 + t - 54.56 &= 0\end{aligned}$$\)

Now we can apply the quadratic formula to solve for t. The quadratic formula is:\($$x = \frac{-b \pm \sqrt{b^2-4ac}}{2a}$$\)

Using the quadratic formula for the equation above, we can substitute the values of a, b and c as follows: \($$\begin{aligned}a &= 2\\b &= 1\\c &= -54.56\\\end{aligned}$$\)

Substituting the values into the quadratic formula gives us:\($$t=\frac{-1 \pm \sqrt{1-4(2)(-54.56)}}{2(2)}$$$$t=\frac{-1 \pm \sqrt{1+436.48}}{4}$$$$t=\frac{-1 \pm \sqrt{437.48}}{4}$$\)

The solutions are:\($$t_1 = \frac{-1 + \sqrt{437.48}}{4}$$$$t_2 = \frac{-1 - \sqrt{437.48}}{4}$$\)

Calculating t1 and t2 using a calculator gives:\($$t_1 \approx 3.743$$$$t_2 \approx -7.344$$\)

However, since we are dealing with time, a negative value for t is not acceptable. Therefore, the only solution is

\($$t = t_1$$\)

Substituting t into the second equation gives: \($$\sqrt{3(3.743)}+ 3 = 5x$$$$\sqrt{11.229}+ 3 = 5x$$$$5x = \sqrt{11.229}+ 3$$$$5x = 6.345$$$$x \approx 1.269$$\)

Therefore, the solution to the equations is\($$t \approx 3.743$$and$$x \approx 1.269$$\)

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Answer:

Step-by-step explanation:

Given function:

a)  g(2)

b)  g(t - 2)

c)  g(t) - g(2)

In the theater, that have 1,464 seats.

1426 seats are in "regular" sections

38 seats are  "premium" front-row section

The seat arrangement is solved by division. In this case the 62 equal spaced is the divisor while the number of seats is the in each row is the quotient

The division is as follows

1464 / 62

= 23 19/31

The number of seats in the regular section is 23 * 62 = 1426

The remainder will be arranged in premium front row

using equivalent fractions

19 / 31 = 38 / 62

the remainder is 38 and this is the seat for the premium front row section

OR 1464 - 1426 = 38 seats

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Therefore , the solution of the given problem of area comes out to be section has a size of about 164.07 square centimetres.

Calculating how much space would be needed to fully cover the outside will reveal its overall size. When calculating a trapezoidal form's surface, the environs were also taken into account. The surface area of something determines its overall measurements. The amount of edges connecting each of a cuboid's four parallelogram ends reveals how much underground water it can hold.

Here,

The following algorithm determines a sector's area:

=> A = (θ/360°) * π * r²

where is the mathematical constant pi, r is the radius, and is the centre angle (approximately 3.14).

If we substitute the numbers provided, we get:

=> A = (30/360) * 3.14 * (12.5)^2

By condensing and computing, we arrive at:

=> A ≈ 164.06

To the closest hundredth, we have the following:

=> A ≈ 164.06 ≈ 164.07

Consequently, the section has a size of about 164.07 square centimetres.

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Answer:

I don't know if you typed the question wrong, but coordinates are written as (x, y).

A (1, -3)

B (-3, 1)

C (-1, 3)

D (3, -1)

Hope I helped!

Step-by-step explanation:

To determine the maximal velocity from an acceleration vs. time graph, you need to follow these steps:

Identify the time interval during which the acceleration remains constant or nearly constant. This interval can be identified as a straight line on the graph.

Calculate the acceleration value during this interval by finding the slope of the line. The slope is the change in acceleration divided by the change in time.

Use the acceleration value and the time interval to calculate the change in velocity during this interval using the formula:

Δv = aΔt

Where Δv is the change in velocity, a is the acceleration, and Δt is the time interval.

Add the change in velocity to the initial velocity at the start of the time interval to obtain the maximal velocity. If the initial velocity was zero, then the maximal velocity will be equal to the change in velocity.

vmax = vi + Δv

Where vmax is the maximal velocity and vi is the initial velocity.

Note that this method assumes that the acceleration is constant or nearly constant during the time interval of interest. If the acceleration changes significantly during this time interval, you will need to break it down into smaller intervals and repeat the above steps for each interval to determine the maximal velocity.

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No, not every five measurements of a quadrilateral can determine a quadrilateral uniquely. The choice of measurements depends on the properties of the quadrilateral.

For instance, the measurements for a parallelogram are different from the measurements for a trapezoid, and so on. Therefore, the five measurements must be selected based on the properties of the quadrilateral in question.

Let's see how five measurements can uniquely determine a quadrilateral?

A quadrilateral has 4 sides and 4 angles. The sum of the angles in a quadrilateral is 360°. Therefore, three of the angles can be measured. The fourth angle can be found by subtracting the sum of the other three angles from 360°. In other words, any three angles of a quadrilateral can determine the fourth angle. This gives us four measurements.

The fifth measurement can be any one of the following:

Diagonal length - A quadrilateral has two diagonals. The length of one diagonal can be measured to give us the fifth measurement. This is useful for quadrilaterals with perpendicular diagonals, such as a rhombus or a square.

Length of one side and two diagonals - This is useful for quadrilaterals with two diagonals that bisect each other at right angles, such as a kite.

Lengths of all four sides - This is useful for quadrilaterals with all four sides of equal length, such as a square or a rhombus.

Lengths of three sides and an angle - This is useful for quadrilaterals with two sides of equal length and two adjacent angles of equal measure, such as an isosceles trapezoid.

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