What are the next two numbers in the pattern of numbers;
45, 15, 44, 17, 40, 20, 31, 25, …

The length of missing side is 39.

Pythagoras theorem is a mathematical statement that states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the two other sides (the legs).

It can be expressed as a2 + b2 = c2, where a and b are the two legs of the triangle and c is the hypotenuse. The theorem is named after the ancient Greek mathematician Pythagoras, who is believed to have discovered it.

Pythagoras theorem is an important concept in geometry, and is used to calculate the length of the hypotenuse in a right triangle when the lengths of the other two sides are known.

It can also be used to determine the lengths of the other two sides when the length of the hypotenuse is known. In addition, it can be used to find the angles of a right triangle when the lengths of the sides are known.

Pythagoras theorem has many applications in everyday life. For example, it can be used to calculate the height of a building, or the distance between two points.

It can also be used in carpentry, engineering, and architecture to measure distances and angles. In addition, it can be used in trigonometry to find the values of trigonometric functions.

Finally, it can be used in navigation to calculate distances and angles.

Let c be the length of missing side,

According to Pythagoras theorem,

a² + b² = c²

36² + 15² = c²

c = √1521

c = 39

So, the length of missing side is 39.

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By finding all the four slopes, we can see that the word is ECHA.

We know that the general linear equation can be written as:

y = a*x + b

Where a is the slope and b is the y-intercept.

We know that if the line passes through (x₁, y₁) and (x₂, y₂) then the slope is:

s = (y₂ - y₁)/(x₂ - x₁)

With that formula we can get the slopes.

1) Using the points (0, 3) and (2, 4).

m = (4 - 3)/(2 - 0) = 1/2, so the letter is E.

2)Using (-1, -12) and (1, -8)

m = (-8 + 12)/(1 + 1) = 4/2 = 2, so the letter is C.

3) We have (2, -6) and (-4, -3) so:

m = (-3 + 6)/(-4 - 2) = 3/-6 = -1/2, so the letter is H

4)we can use the points (0, 3) and (1, 1), so:

m = (1 - 3)/(1 - 0) = -2, so the letter is A

Then the word is ECHA

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Answer:

B. 0.57 repeating

Step-by-step explanation:

Question 1:

(a) The equation representing Elaine's total parking cost is:

C = x * t

(b) So the cost of parking for a full 24 hours would be 24 times the cost per hour.

Question 2:

The given system of equations is inconsistent and has no solution.

(a) To represent Elaine's total parking cost, C, in dollars for t hours, we need to know the cost per hour. Let's assume the cost per hour is $x.

(b) If Elaine wants to park her car for a full 24 hours, we can substitute t = 24 into the equation from part (a):

C = x * 24

Question 2:

To solve the linear system:

-x - 6y = 5

x + y = 10

We can use the elimination method.

Multiply the second equation by -1 to create opposites of the x terms:

-x - 6y = 5

-x - y = -10

Add the two equations together to eliminate the x term:

(-x - 6y) + (-x - y) = 5 + (-10)

-2x - 7y = -5

Now we have a new equation:

-2x - 7y = -5

To check the answer, we can substitute the values of x and y back into the original equations:

From the second equation:

x + y = 10

Substituting y = 3 into the equation:

x + 3 = 10

x = 10 - 3

x = 7

Checking the first equation:

-x - 6y = 5

Substituting x = 7 and y = 3:

-(7) - 6(3) = 5

-7 - 18 = 5

-25 = 5

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Answer:

Three

Step-by-step explanation:

Assuming the grade score from 70 to 100 is A; for grade score from 60 to 69 is B and grade score from 50 to 59 is C. Well it is certain there are three peaks in the distribution of scores

The angle between the ground and the steepest slope on the real rollercoaster is approximately 89.998°.

A model rollercoaster is built to a scale of 1:32. In the model rollercoaster, the angle between the ground and the steepest slope is 110°.What is the angle between the ground and the steepest slope on the real rollercoaster?

To determine the angle between the ground and the steepest slope on the real rollercoaster, you need to consider the scale of the model rollercoaster.To find the real rollercoaster angle, you should use a scale factor that relates the model rollercoaster to the real one.

The scale factor should multiply the model angle to obtain the real one. Since the scale factor relates the model length to the real length, it should relate the horizontal distance and the vertical height.

The horizontal and vertical lengths are in a ratio of 32:1 for the model. This means that for every 32 units in the model, there is one unit in the real rollercoaster. Therefore, we can say that the horizontal length of the real rollercoaster is 32 times the horizontal length of the model rollercoaster.

That is:h(real) = 32h(model)Similarly, the vertical height of the real rollercoaster is 32 times the vertical height of the model rollercoaster. That is:v(real) = 32v(model)

The tangent of an angle equals the vertical height divided by the horizontal distance. Therefore, the tangent of the real angle equals the tangent of the model angle times the scale factor.

That is:tanθ(real) = 32tanθ(model)By substitution,θ(real) = arctan(32tanθ(model))For the given model angle of 110°,

the corresponding real angle is:θ(real) = arctan(32tan110°)θ(real) = arctan(32(-2.74747741945462))θ(real) = arctan(-87.91927694142864)θ(real) ≈ -89.998°

The negative sign indicates that the angle is measured below the horizontal line.

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Answer:

I have this copied to my clipboard for me to past in comments!

Step-by-step explanation:

And it is CHRISTMAS do not X out Christ.

Mwah

Answer:

is this the All I want for christmas is you by mariah carey( I love the song )

The slope of the line, using two points (2, 2) and (-2, -3), is calculated as: 5/4.

Using two points on a line, the slope of a line can be calculated by applying the slope formula below:

Slope (m) = change in y / change in x = \(\frac{y_2 - y_1}{x_2 - x_1}\).

Pick two points on the line in the graph given to find the slope of the line. The two points that are marked on the line are:

(2, 2) = \((x_1, y_1)\)

(-2, -3) = \((x_2, y_2)\)

Substitute the values into the slope formula:

Slope (m) = (-3 - 2) / (-2 - 2)

Slope (m) = -5/-4 = 5/4

The slope of the line is: 5/4.

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The value of angle BCD is determined as 108⁰.

option B is the correct answer.

The value of angle BCD is calculated by applying intersecting chord theorem, which states that the angle at tangent is half of the arc angle of the two intersecting chords.

Also this theory states that arc angles of intersecting secants at the center of the circle is equal to the angle formed at the center of the circle by the two intersecting chords.

arc AB =  m∠ACB

m∠ACB =  72⁰

The value of angle BCD is calculated as follows;

angle BCD = 180 - 72⁰ (sum of angles in a circle)

angle BCD = 108⁰

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Answer:

problem list

Step-by-step explanation:

huguih

Answer:

40.6

Step-by-step explanation:

Use the pythagorean theorem a^2+b^2=c^2

25^2+32^2=1649

The square root of 1649 is 40.607

Answer:

D) 40.6

Step-by-step explanation:

When finding the hypotenuse, you square the two leg values (in this case, 25 and 32). Then, you add them together and find the square root of the sum. Use the Pythagorean theorem: a²+b²=c²

Answer:

-12≥x

Step-by-step explanation:

-10≥2x+14

-24≥2x

-12≥x

STEP - BY - STEP EXPLANATION

What to find?

Average rate of change of the given function.

Given:

We solve following the steps below:

Step 1

State the formula.

Step 2

Pick a point within the given interval and identify its coordinates.

That is;

(0, 71) and (3, 47)

⇒a=0 b=3

f(a) = 71 f(b)=47

Step 3

Substitute the values into the formula and simplify.

ANSWER

The rate of change = -8

Answer:

b = − 3

m = 5 ( 39 + 2 m ) /23

Answer:

3.6661

3.6661

A, Adding a constant does nothing to the standard deviation

Step-by-step explanation:

I'm gonna assume s=standard deviation

The standard deviation is just the square root of the second moment minus the first moment squared

Because we were not told otherwise I think it's pretty safe to assume that all events are equally likely

Let's start by calculating the first moment (AKA The mean)

1/5(8+16+14+8+16)= 12.4

Let's then find the second moment

1/5(8²+16²+14²+8²+16²)= 167.2

√(167.2-12.4²)=3.6661

b.

While I could just tell you that adding something to the standard deviation (and the variane as well) doesn't do anything let's calculate it for fun

same process

.2(16+24+22+16+24)= 20.4

.2(16²+24²+22²+16²+24²)=429.6

√(429.6-20.4²)= 3.6661

Answer:

150 feet

Step-by-step explanation:

A rectangle has 2 pairs of equal sides.

One of the sides is 100 feet, meaning another side is 100 feet.

If we subtract 200 feet we are left with 300, which are the last two sides.

Divide 300 by 2 to get each side length.

150 feet

Answer:

90  berries

Step-by-step explanation:

Answer:

x =6.0

The base is 6x  = 35.8

The side is 3x =  17.9

Step-by-step explanation:

We can use the pythagorean theorem

a^2 + b^2 = c^2

(6x)^2 +(3x)^2 = 40^2

36x^2 + 9x^2 = 1600

Combine like terms

45x^2 = 1600

Divide each side by 45

45x^2 /45 =1600/45

x^2 =35.555555555

Take the square root of each side

sqrt(x^2) = sqrt(35.555555555)

x =5.96284794 = 6.0

The base is 6x = 6*5.9628479 =35.77708 = 35.8

The side is 3x = 3*5.9628479 =17.88854382= 17.9

Answer:

x = 6.0

3x = 17.9

6x = 35.8

Step-by-step explanation:

Using pythagoras theorem

40² = (3x)² + (6x)²

1600 = 9x² + 36x²

1600 = 45x²

x² = 320/9

x = 5.96284794

3x = 17.88854382

6x = 35.77708764

Answer:

32.4

Step-by-step explanation:

i knoiw it

Step-by-step explanation: To fill in the table, we will need to first count the number of times each wait time appears in the given data. We can then use these counts to fill in the Frequency column of the table. We will also need to calculate the relative frequency of each wait time, which is the number of times it appears in the data divided by the total number of data points. We can then use these relative frequencies to fill in the Relative Frequency column of the table, expressed as a percentage.

Here is the completed table:

Wait Time (minutes) Frequency Relative Frequency (%)

5                                     5                 11.36

10                                 4                  9.09

15                                 7                  15.91

20                                6                   13.64

25                                7                   15.91

30                                 4                   9.09

35                                5                    11.36

40                                3                    6.82

45                                 2                    4.55

50                                 1                    2.27

60                                  2                    4.55

75                                  1                       2.27

Note that the total number of data points is 44, so each relative frequency is calculated as the corresponding frequency divided by 44.

I hope this helps! Let me know if you have any other questions.

Given the figure of a right-angle triangle

As shown, the hypotenuse = 15 yd

And one of the legs = 13 yd

We will find the side (x) using the Pythagorean theorem as follows:

Solve the equation to find (x):

So, the answer will be 2√14

By applying the concept of corresponding angles in similar triangles, we were able to establish the value of x as 25 in the given scenario.

In the given problem, we are provided with information about the angles in two similar triangles: triangle ABC and triangle STU. It is stated that angle UTS in triangle STU is 100 degrees, and since corresponding angles of similar triangles are congruent, we can conclude that angle STU is also 100 degrees.

Next, we examine angle BAC in triangle ABC, which is given as 4x. Using the same logic, we know that angle BAC is also congruent to angle STU. Therefore, we can equate the two angles:

angle BAC = angle STU

4x = 100

To find the value of x, we divide both sides of the equation by 4:

x = 100/4

x = 25

Hence, we determine that x is equal to 25. This method allows us to leverage the known information about one triangle to infer the measurements of corresponding angles in the other similar triangle.

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The correct answer is B. The sample represents a proportion of the population.

A point estimate is a single value used to estimate a population's unknown parameter. The sample proportion (denoted by p), in the context of determining the population proportion, is a widely used point estimate. The sample proportion is determined by dividing the sample's success rate by the sample size.

The sample must be representative of the population for it to be a reliable point estimate of the population proportion. To accurately reflect the proportions of various groups or categories present in the population, the sample should be chosen at random.

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Answer:

the direction of the road

Step-by-step explanation:

To calculate the net force, we need to know the direction through which the forces are acting.

Are the forces directed towards one another or against each other?

  Net force is a vector sum of forces that acts on a body. It is that single force that can replace two or more forces acting on a body.

So, without knowing the direction, we cannot calculate the net force.

Answer:

x = ±9.899....

Step-by-step explanation:

since x^2 = 98

x = ±7√2

so x = 9.89949..., -9.89949...

hope this helps:)

Answer:

$1275.00

Step-by-step explanation:

600/40=15

15x85=1275

Answer:

1208

Step-by-step explanation:

You have to multiply 600 x2 =1200 then you have to do 40÷5 witch it 8. Then add 1200 and 8 and you get 1208