i need to simplfiy the answer can someone help me with the question

Pythagoras was an ancient Greek mathematician who founded the Pythagorean school of thought. The Pythagorean theorem is a fundamental concept in mathematics that is attributed to Pythagoras and his followers.

It states that in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides. While this theorem is considered a cornerstone of mathematics today, it is important to understand that Pythagoras did not have access to the advanced mathematical tools and methods that we have today.

He had to rely on geometric constructions and reasoning to prove his theorem. Furthermore, Pythagoras believed that all numbers could be expressed as ratios of whole numbers, which is not always true in reality. Despite these limitations, the Pythagorean theorem has stood the test of time and continues to be a crucial tool in mathematics and other fields.

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Answer:

\(\bigodot\:a \:\) The additional fee per hour of tutoring is $10

Step-by-step explanation:

Option a is the correct answer.

Answer:

1/4

Step-by-step explanation:

Use the slope formula to find the slope.

slope = (y2-y1)/(x2-x1)

slope = -1 - -2 / -2- -6

= 1/4

Answer:

C

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

I think its because 5x2=10 and then its three dollars times the amount of eggs he buys. Im not entirely sure though

Answer: it’s the third option

Step-by-step explanation:

Answer:

y – 7 = 4(x – 1)

Step-by-step explanation:

Third option

Answer:

72°

Step-by-step explanation:

→ Recall how many degrees are within an interior angle

180

→ Minus the angle from 180

180 - 108 = 72°

Answer:

6

Step-by-step explanation:

diameter = 2 radius

3*2 = 6

Answer:

6

Step-by-step explanation:

r = d/2        Multiply both sides by 2

2*r = d

r = 3

2*3 = d

d = 6

Answer:

The answer should be 12

Step-by-step explanation

he has 60 in his account already so add 35 and 15 (60+35+15=110) then add 48+24+50 which equals 122. Now subtract 110-122 and you'll get 12. so the answer is 12.

Answer:

y=-1x-6

Step-by-step explanation:

y-y1=m(x-x1)

y-(-5)=-1(x-(-1)

y+5=-1(x+1)

y+5=-1x-1

y=-1x-5-1

y=-1x-6

Answer:

y < -19/2

Step-by-step explanation:

-18 - 4y > 20

Add 18 to each side

-18+18 - 4y > 20+18

-4y > 38

Divide each side by -4, remembering to flip the inequality

-4y/-4 < 38/-4

y < -19/2

Answer:

y < -9.5

Step-by-step explanation:

-18 - 4y > 20

Add 18 to both sides of the inequality.

-18 + 18 - 4y > 20 + 18

Add -18 + 18 which gets you 0.

0 - 4y > 20 + 18

Subtract 0 - 4y which gets you -4y.

-4y > 20 + 18

Add 20 + 18 to get 38.

-4y > 38

Divide both sides by -4 and change the inequality direction.

y < 38/-4

Cancel out 2 as a common factor from 38/-4.

y < 19/-2

Divide 19 / -2 which gets you -9.5.

-9.5

Recapturing a higher percent of marked alligators affects the estimated total population by making it high enough to support an accurate estimate.

This is referred to as the total number of species or organisms in an area at a given period of time.

Recapture rates are high enough to support an accurate estimate. The Lincoln-Peterson calculation tends to overestimate the population size, especially if the number of recaptures is small.

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Answer:

35 meters

Step-by-step explanation:

Since 1cm=10meters, we can do 3.5cm=how many meters?

To get from 1 to 10 we multiply by 10.

So we can do 3.5x10 to get 35 meters.

Hope this helps!

Answer: The length of AB =4 units

               The length of BD = 2.4 units.

Step-by-step explanation:

Given data,

                  AD = 3.2 unit

                  BC  = 3 unit

                 CD  = 1.8 units

Find :         AB =? units

                  BD=? units

We can use the formula of Pythagorean theorem,

Define Pythagorean theorem :

Pythagoras theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“. The sides of this triangle have been named Perpendicular, Base and Hypotenuse.

Hypotenuse2 = Perpendicular2 + Base2

                  c2 = a2 + b2

Where “a” is the perpendicular,

“b” is the base,

“c” is the hypotenuse.

Let be a ΔABC,

                           \((AB)^{2} = (BC)^{2} +(AC)^{2}\)

From the above formula now  determined  the value of AB and BD,

Firstly , find the value of BD

In ΔBDC, by applying Pythagorean theorem,

                             \((BC)^{2} = (BD)^{2} + (DC)^{2}\)             (Eq - 1)

Substitute BC and CD values in equation 1,

            BC  = 3 units and CD = 1.8 units

So,

We can write,

                            \(3^{2} = (BD)^{2} +(1.8)^{2}\)

                            9 = \((BD)^{2}\) + 3.24

                            \((BD)^{2}\) = 9 - 3.24

                            \((BD)^{2}\) = 5.76

                             \(BD = \sqrt{5.76}\)

                             BD = 2.4 units             (Eq - 2)

Now find the value of AB,

In ΔABD, by applying Pythagorean theorem,

                               \((AB)^{2} = (AD)^{2} +(BD)^{2}\)           (Eq - 3)

Substitute AD and BD values in equation 3,

            AD  = 3.2 units and BD = 3 units

So,

We can write,

                                \((AB)^{2} = (3.2)^{2} + 3^{2}\)

                                 \((AB)^{2}\) = 10.24 + 5.76

                                 \((AB)^{2}\) = 16

                                  AB = \(\sqrt{16}\)

                                   AB = 4 units

Therefore,

The length of AB =4 units

The length of BD = 2.4 units.

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Answer:

0.8 or Tenths place. I hope this helped.

From the picture, we can see that we have a right triangle. The hypontenuse (the side opposite to the right angle) is the side whose length of 14, where the side whise length is 11, and the one whose length is x, are the two hicks. We can establish the relationship of the Pythagoras theorem for this triangle:

We can solve for x:

To find the square root of 75, we can decompose it:

75/5 = 15

15/5 = 3

3/3 = 1.

Then, 75 can be expressed the following way:

Then:

Since the square root of a product is the product of the square roots:

The value of x is approximately 8.66,

Answer: m<c is 57 degrees

Step-by-step explanation: A parallelogram must have equivalent opposite interior angles, and <c is a diagonal to <a

therefore its 57

Hope this helps! <3

Answer:

x = 16

Step-by-step explanation:

hypotenuse=  a /sin(α)

= 22.62742

= 16√2

So using this to calculate x:

x = √c2 - a2

= √22.627416997972 - 162

= √256

= 16

Hope this helps you :)

Answer:

y-intercept: 1

slope: -2

Step-by-step explanation:

According to the given percentages, 18% of the students at the orientation are male arts majors.

The statement correctly calculates that 60% of the students at the orientation are men and 30% are arts majors.

To determine the percentage of students who are male arts majors, we multiply these two percentages together: 60% x 30% = 18%. Therefore, 18% of the students at the orientation are male arts majors.

This calculation follows the principles of probability, where the intersection of two events (being a male and being an arts major) is determined by multiplying the probabilities of each event occurring individually.

In this case, it results in 18% of the students meeting both criteria.


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Question - Sixty percent of the students at an orientation are men and 30% of the students at the orientation are arts majors. Therefore, 60% X 30% = 18% of the students at the orientation are male arts majors.

The polynomial equation  0 = 3x⁵ − x⁴ − 5x² + 1 contains 2 complex roots as a result.

Describe a polynomial.

A mathematical expression that contains at least two terms with variables or integers is referred to as a polynomial. A polynomial may include several terms.

Below is a polynomial equation that is given:

0 = 3x⁵ − x⁴ − 5x² + 1

Which can also be written as

3x⁵ − x⁴ − 5x² + 1 = 0

A polynomial of degree 5 is used in the accompanying polynomial equation.

Using a graphing application to solve it graphically is the simplest approach.

The polynomial equation obviously has a maximum of 5 roots because it is an equation of degree 5.

Now that we have the graph, we can use it to find the equation's roots.

There are 2 complex roots because there are only 3 real roots and 2 remaining are complex roots.

The polynomial equation  0 = 3x⁵ − x⁴ − 5x² + 1 contains 2 complex roots as a result.

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The value of √(25) x 3² - ∛(-8) ÷ 2² is 46.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

√(25) x 3² - ∛(-8) ÷ 2²

[ √(25) = 5 ]

[ ∛(-8) = -2 ]

= 5 x 9 - (-2) ÷ 4

= 45 + 2 ÷ 2

= 45 + 1

= 46

Thus,

The value of the expression is 46.

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The unit of the right-hand side of the equation is s⁰ * s⁻¹ = s⁻¹.The SI unit of the quantity f is s⁻¹.

Given that the motion y(x, t) of a vibrating system is described by

                                     y(x, t) = A0e^(-πt) sin((2πx/λ)−2πft).

Denoting units with fractions using the "/" operator and units with products using the "*" operator, numbers.

We are given that

                                          y(x, t) = A0e^(-πt) sin((2πx/λ)−2πft)where x denotes a distance in meters and t denotes a time in seconds.

The SI unit for time t is the second (s).We need to find the unit of the quantity f, given that the formula is

                                        y(x, t) = A0e^(-πt) sin((2πx/λ)−2πft)

Comparing the argument of sin in the above equation,(2πx/λ) − 2πft

The unit of the first term is m/m = 1The unit of the second term is s⁻¹ * s = s⁻¹

Therefore, the unit of the argument of sin is s⁻¹.

Now, sin(x) is a dimensionless quantity.

Hence, the unit of A₀e^(-πt) is s⁰ or 1.

Therefore, the unit of the right-hand side of the equation is s⁰ * s⁻¹ = s⁻¹.The SI unit of the quantity f is s⁻¹.

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Answer:

0.0108 kg

Step-by-step explanation:

Jiri is on a special diet

Over 5 days he eats 0.054

Therefore the food consumed in a day can be calculated as follows

5 days= 0.054

1 day= 0.054/5

= 0.0108kg

For this case we have the following variables:

x: represents time, in seconds at the start of the test.

y: represents the speed, in miles per hour.

We have then that:

x = 0 ---> y = 0

x = 12 ---> y = 0

Answer:

the electric car is not moving at 0 seconds and 12 seconds

I hope this helps!

the electric car is not moving at 0 seconds and 12 seconds

I hope this helps!

A two-tailed test is used in sample of 10 observations with an alpha level of 0.10. The critical value for this test is ± 1.697. These critical values are used to determine the rejection region of your hypothesis test.

In a two-tailed test with a sample of 10 observations and alpha equal to 0.10, the critical value would be ±1.697. This means that if the test statistic falls outside of this range, it would be considered statistically significant and we would reject the null hypothesis. The use of a two-tailed test means that we are interested in testing for the possibility of a difference in either direction, as opposed to a one-tailed test where we would only be interested in a difference in one specific direction.

Among the significance tests, single-ended and two-tailed tests are other ways of calculating the significance of the measurements determined from the data set under the test. A two-tailed test is appropriate if the predicted value is greater or less than the value on a test, i.e. whether the test taker will score some points higher or lower. This method is used to test the null hypothesis, if the predicted value is in the critical region, it accepts the alternative hypothesis instead of the null hypothesis. A one-tailed test is appropriate if the estimated value differs from the reference value in one direction (left or right) but not in two directions.

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Answer:

x=3-3y

Step-by-step explanation:

Answer:

84 ft

Step-by-step explanation:

16 + 16 + 26 +26 = 84

The function F(x, y) has a local maximum at (-2, -3), saddle points at (2, -3) and (-2, 1), and a local minimum at (2, 1).

To find the critical points and classify them as local maxima, local minima, or saddle points, we need to find the partial derivatives of the function F(x, y) and evaluate them at each critical point.

Given the function F(x, y) = x³ - 12x + y³ + 3y² - 9y, let's find the partial derivatives:

∂F/∂x = 3x² - 12

∂F/∂y = 3y² + 6y - 9

To find the critical points, we set both partial derivatives equal to zero and solve the resulting system of equations:

3x² - 12 = 0 --> x² = 4 --> x = ±2

3y² + 6y - 9 = 0 --> y² + 2y - 3 = 0 --> (y + 3)(y - 1) = 0 --> y = -3 or y = 1

Therefore, the critical points are (-2, -3), (2, -3), and (-2, 1).

To classify these critical points, we use the second partial derivatives test. The second partial derivatives are:

∂²F/∂x² = 6x

∂²F/∂y² = 6y + 6

Now, let's evaluate the second partial derivatives at each critical point:

At (-2, -3):

∂²F/∂x² = 6(-2) = -12 (negative)

∂²F/∂y² = 6(-3) + 6 = -12 (negative)

Since both second partial derivatives are negative, the point (-2, -3) corresponds to a local maximum.

At (2, -3):

∂²F/∂x² = 6(2) = 12 (positive)

∂²F/∂y² = 6(-3) + 6 = -12 (negative)

Since the second partial derivative with respect to x is positive and the second partial derivative with respect to y is negative, the point (2, -3) corresponds to a saddle point.

At (-2, 1):

∂²F/∂x² = 6(-2) = -12 (negative)

∂²F/∂y² = 6(1) + 6 = 12 (positive)

Since the second partial derivative with respect to x is negative and the second partial derivative with respect to y is positive, the point (-2, 1) corresponds to a saddle point.

Therefore, the critical points are classified as follows:

Local maximum: (-2, -3)

Saddle points: (2, -3) and (-2, 1)

Local minimum: (2, 1)

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Influential scores, indicated by large residuals, have a significant impact on the regression line when removed from the data. These points, characterized by extreme x or y-values, can alter the slope and intercept of the regression line, emphasizing their importance in regression analysis.

The correct statements about influential scores are i and ii.

i. Influential scores have large residuals because they have a strong effect on the regression line. This means that if we remove an influential score from the data, it will significantly change the slope and intercept of the regression line.

ii. Removal of an influential score sharply affects the regression line because influential scores have a large impact on the regression line. If we remove an influential score, it will significantly change the slope and intercept of the regression line.

iii. This statement is not true. An x-value that is an outlier in the x-variable may be indicative of a point being influential, but a y-value that is an outlier in the y-variable can also be indicative of a point being influential.

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Answer:

The statement is true

Step-by-step explanation: