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Use the Pythagorean identity, (×^2 - y^2)^2 + (2xy)^2 = (×^2 + y^2)^2 to create a Pythagorean triple.

Follow these steps:

Choose two numbers and identify which is replacing a and which is replacing y.

How did you know which number to use for a and for y?

Explain how to find a Pythagorean triple using those numbers.

Explain why at least one leg of the triangle that the Pythagorean triple represents must have an even-numbered length.

it A

Step-by-step explanation:

Answer: a= -3 and b= -1

a. The population function that shows a growth of 70 people per year is P(t) = 1650 + 70t

b. The population function that shows an annual growth rate of 3% is

P(n) = 1650 * (1 + 0.03)ⁿ

c. The population function that shows a shrinkage of 50 people per annum is P(t) = 1650 - 50t

d. The population function that shows an annual shrinkage rate of 8% per annum is P(n) = 1650 * (1 - 0.08)ⁿ

a. In this case, where the town grows by 70 people a year, we can represent the population as a linear function of time:

P(t) = 1650 + 70t

b. When the town grows at an annual rate of 3 percent, we can express the population using exponential growth:

P(n) = 1650 * (1 + 0.03)ⁿ

c. If the town shrinks by 50 people each year, we can represent the population as a linear function of time:

P(t) = 1650 - 50t

d. When the town shrinks at an annual rate of 8 percent, we can express the population using exponential decay:

P(n) = 1650 * (1 - 0.08)ⁿ

In each case, "P(t) or P(n)" represents the population of the town after "t" or "n" years, starting with an initial population of 1650 people. The formulas provide different models for how the population changes over time based on the given conditions.

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Answer:

y=3x+8

Step-by-step explanation:

Perpendicular to -1/3, is 3.

y-5=3(x+1)

y-5=3x+3

y=3x+8

Answer:

y - 5 = 3(x + 1).

Step-by-step explanation:

y = -1/3x - 6

The slope of this line is -1/3 so the slope of the perpendicular line to it is -1/-1/3

= 3.

Using the point-slope form of a straight line:

y - y1 = m(x - x1)  where m = the slope and (x1, y1) is a point on the line:

Here m = 3 and (x1, y1) is (-1, 5) so we have:

y - 5 = 3(x - (-1))

y - 5 = 3(x + 1).

Answer:

x=-4 is the answer

Step-by-step explanation:

-7x+9=3x+49

Subtracting 3x on both sides

-7x-3x+9=49

Subtracting 9 on both sides

-10x=49-9

-10x=40

x=-4

I hope this will help you :)

Answer:

i can see

Step-by-step explanation:

UKDIAMOND is a great place for the people of sentence to get it 4out in a sense that you are a very

Answer:

b = 99°

Step-by-step explanation:

XY is a line segment and so it is a straight line which means that it is a straight angle - 180°

a = 28°

c = 53°

b = ?

=> a + b + c = 180°

=> 28° + b + 53° = 180°

=> b = 180° - (53 + 28)°

=> b = 180° - 81°

=> b = 99°

Therefore b = 99°

Hope it helps :)

Answer:

points are free?

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

clockwise is rotating it to the right. And then 180 rotation would cause the image to be flipped upside down

The length of the spiraling polar curve \(r = 65e^{(2\theta)}\) from θ = 0 to θ = 2π is approximately 2.084×10⁷ units.

To find the length of the spiraling polar curve \(r = 65e^{(2\theta)}\) from θ = 0 to θ = 2π, you can follow these steps:

1. Use the polar curve arc length formula:

\(L=\int \sqrt{r^2+\left(\frac{d r}{d \theta}\right)^2} d \theta\) from θ = 0 to θ = 2π, where r is the polar curve equation and dr/dθ is its derivative with respect to θ.

2. Differentiate the given polar curve with respect to θ:

\(dr/d\theta = 130e^{2\theta}\).

3. Calculate r² + (dr/dθ)²:

\((65e^{(2\theta)})^2 + (130e^{(2\theta)})^2 = 65^2 \times e^{(4\theta)} + 130^2 \times e^{(4\theta)}\).

4. Factor the common term and simplify:

\(e^{(4\theta)}(65^2 + 130^2) = 21125  e^{(4\theta)}\).

5. Now, find the square root of the expression:

\(\sqrt{(21125 \times e^{(4\theta)})} = 145.34 e^{(2\theta)}\).

6. Integrate the expression with respect to θ from 0 to 2π:

\(\int145.34 e^{(2\theta)}d\theta\) from θ = 0 to θ = 2π.

7. Perform the integration:

\((145.34/2) [e^{4\pi}-e^0]\) = 2.084×10⁷ units.

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The Area of triangle with the given height 10 cm and base 6 cm is calculated to be  30 square centimeters.

To calculate the area of a triangle with height 10 cm and base 6 cm, we can use the formula:

Area = (1/2) x Base x Height

Substituting the given values, we get:

Area = (1/2) x 6 cm x 10 cm

Area = 30 square cm

Therefore, the area of the triangle is 30 square centimeters.

We can see that the area of the triangle is calculated by multiplying the base and height and then dividing the result by 2. In this case, the height of the triangle is 10 cm and the base is 6 cm, so the area is 30 square cm. This formula can be used to calculate the area of any triangle, regardless of its size or shape.

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The complete question is :

Calculate the Area of triangle with the height 10 cm and base 6 cm .

In statistics, comparing an individual’s performance to the class average is a very common question. To solve the given problem, we will compare Ella’s math and Spanish scores to the class averages. We will calculate the z-score to compare her performance and see which score was relatively better.

The z-scores for Ella’s test scores.z math =(66 – 55) / 5= 2.2 z Spanish =(95 – 82) / 7= 1.86 Now let’s explain the z-score obtained: For the math test, Ella’s z-score is 2.2 which means that she scored 2.2 standard deviations above the class average. For the Spanish test, Ella’s z-score is 1.86 which means that she scored 1.86 standard deviations above the class average. A positive z-score indicates that Ella performed better than the class average and a negative z-score indicates that she performed worse.Now, let’s compare the z-scores obtained for each test. Since Ella’s z-score for math is higher than her z-score for Spanish, Ella did better on the math test than the Spanish test.

Therefore, we can say that Ella performed better on the math test than on the Spanish test when compared to the class average.

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Answer:

B. False

Step-by-step explanation:

5x² - 6x + 4 | 5 × 4 = 20

Can't factor it normally

           √b² - 4ac

 -b  ±   ---------------

                2a

           √(-6)² - 4(5)(4)

 -(-6)  ±   ---------------

                   2(5)

           √36 - 80

 6  ±   ---------------

                 10

    6 ± √-44

  ---------------

         10

    6 ± √-4 × 11

  ---------------

         10

    6 ± 2i√11

  ---------------

         10

The answer is actually

    3 ± i√11

  ---------------

         5

I hope this helps!

Answer:

  B.  False

Step-by-step explanation:

You want to know if (x -2) is a factor of 5x² -6x +4.

There are a couple of ways you can determine whether (x -2) is a factor. One is to look at the polynomial value at x=2:

  5x² -6x +4 = (5x -6)x +4 = (5(2) -6)(2) +4 = 4(2) +4 = 12

The value is not 0, so (x -2) is not a factor.

Another way to tell is to determine what the other factor would be.

The product of roots is the ratio c/a = 4/5 in the polynomial. If 2 is a root, then (4/5)/2 = 2/5 is the other root. That would mean the factorization of the polynomial is ...

  (5x -2)(x -2) = 5x² -12x +4 . . . . . . not the same polynomial

The polynomial 5x² -6x +4 does not have a factor (x -2).

The graph of the polynomial has no x-intercepts, so (x -2) cannot be a factor.

Answer:

16/55

Step-by-step explanation:

Answer: 16/55

Step-by-step explanation:1

5

+

2

22

=  

1 × 22

5 × 22

+

2 × 5

22 × 5

=  

22

110

+

10

110

=  

22 + 10

110

=  

32

110

=  

32 ÷ 2

110 ÷ 2

=  

16

55

An analysis of variance comparing three treatment conditions produces dftotal = 32. It is possible for the samples to be the same size. The correct answer is b.

To determine the number of individuals in each sample when the total degrees of freedom (dftotal) is 32,

we need to divide the total degrees of freedom equally among the three treatment conditions.

Start with the assumption that each sample has an equal size, denoted as n.

Calculate the degrees of freedom within each sample, denoted as dfwithin.

Since there are three treatment conditions,

each sample has (n-1) degrees of freedom within, resulting in a total of 3(n-1) degrees of freedom within the three samples.

Calculate the degrees of freedom between the samples, denoted as dfbetween.

The dfbetween is equal to the total degrees of freedom (dftotal) minus the degrees of freedom within (dfwithin): dfbetween = dftotal - 3(n-1).

Set up the equation: dftotal = dfwithin + dfbetween.

Substituting the values,

we get: 32 = 3(n-1) + (dftotal - 3(n-1)).

Simplify the equation: 32 = 3(n-1) + (32 - 3(n-1)).

Solve for n: 32 = 3n - 3 + 32 - 3n + 3.

Combine like terms and simplify: 32 = 32.

Since the equation is true regardless of the value of n, it means that the size of each sample can be any positive number, and the samples can be the same size.

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Yes...

x/3 > -1

what values of x make x/3 > -1

hint... your answer will look like like x > (number)

Answer:

-2.23, -2 2/5, -0.95

Step-by-step explanation:

-15/16 = -0.9375 (greater than -0.94)

0.24 (greater than -0.94)

-2.23 (less than -0.94)

97% = 0.97 (greater than -0.94)

-2 2/5 = -2.4 (less than -0.94)

-0.95 (less than -0.94)

To calculate the Value-at-Risk (VaR) for this investment at a 99% confidence level, we need to determine the loss amount that will be exceeded with a probability of only 1% (i.e., the worst-case loss that will occur with a 1% chance).

Given that there is a 0.5% chance of a loss of $10 million and a 99.5% chance of a loss of $1 million, we can express this as:

Loss Amount | Probability

$10 million | 0.5%

$1 million | 99.5%

To calculate the VaR, we need to find the loss amount that corresponds to the 1% probability threshold. Since the loss of $10 million has a probability of 0.5%, it is less likely to occur than the 1% threshold. Therefore, we can ignore the $10 million loss in this calculation.

The loss of $1 million has a probability of 99.5%, which is higher than the 1% threshold. This means that there is a 1% chance of the loss exceeding $1 million.

Therefore, the Value-at-Risk (VaR) for this investment at a 99% confidence level is $1 million.

The Value-at-Risk (VaR) for this investment at a 99% confidence level is $1,045,000.

To calculate the Value-at-Risk (VaR) for this investment at a 99% confidence level, we need to determine the loss amount that will be exceeded with only a 1% chance.

Given that the investment has a 0.5% chance of a loss of $10 million and a 99.5% chance of a loss of $1 million, we can calculate the VaR as follows:

VaR = (Probability of Loss of $10 million * Amount of Loss of $10 million) + (Probability of Loss of $1 million * Amount of Loss of $1 million)

VaR = (0.005 * $10,000,000) + (0.995 * $1,000,000)

VaR = $50,000 + $995,000

VaR = $1,045,000

Therefore, the Value-at-Risk (VaR) for this investment at a 99% confidence level is $1,045,000.

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Answer:

I tried but soory I can't understand

Answer:

D-60°

Step-by-step explanation:

K,L,M is collinear and JM=JL

M can only be extend to the left of K, otherwise it will overlap with L

JM = JL     ΔJML is isosceles triangle    ∠JML ≅ ∠JLM

∠JLM = 90 - ∠KJL = 90 - 30 = 60

∠JML = 60°

The possible solution set for the system is (- 1, 4) and (4, - 1).

Given are the equations as -

x + y = 3

x² + y² = 17

Refer to the graph of the function attached. The points of intersection represents the possible solution set.

Therefore, the possible solution set for the system is (- 1, 4) and (4, - 1).

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The volume of the stucture made from three rectangular prism is 4080 ft³

Volume is the amount of space occupied by a three dimensional shape or object.

The volume of the rectangular prism = length * width * height = 12 * 10 * 5 = 600 ft³

The volume of the other prism = length * width * height = 10 * 8 * 36 = 2880 ft³

Volume of the structure = 600 ft³ + 600 ft³ + 2880 ft³ = 4080 ft³

The volume of the stucture made from three rectangular prism is 4080 ft³

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While making a perfect square for the given quadratic equation \(\rm x^2+3x+c=\frac{7}{4} +c\) the value of c is 9/4

It is given that the quadratic equation  \(\rm x^2+3x+c=\frac{7}{4} +c\) while forming the perfect square.

It is required to find the value of c.

It is defined as the equation of polynomial of degree two. The standard form of the quadratic equation is as follows:

\(\rm ax^2+bx+c=0\)  where \(\rm a\neq 0\)

We have a quadratic equation:

\(\rm x^2+3x+c=\frac{7}{4} +c\)

We know that we can make any quadratic equation into a perfect square by the perfect square trinomial method as follow:

\(\rm ax^2+bx+c=0\\\rm ax^2+bx=-c\\\rm ax^2+bx+(\frac{b}{2a})^2 =-c+(\frac{b}{2a})^2\\\)

So, the value of 'c' would be:

\(\rm c=(\frac{b}{2a})^2\\\)  here b=3 and a=1 by comparing the equation to the standard equation.

\(c=(\frac{3}{2\times1} )^2\\c=(\frac{3}{2} )^2\\c=\frac{9}{4}\)

Thus,  while making a perfect square for the given equation the value of c is 9/4

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Answer:

9/4

Step-by-step explanation:

correct on edge

The required work done in lifting the laptop to a height of 2 feet will be 263.79 foot-poundal.

Total weight of the laptop is 4.1 pounds

Acceleration due to gravity = 32.17 ft/\(s^{2}\)

Now the height to which the laptop has been lifted = 2 feet

Since, there is no mentioned velocity of the laptop, therefore the kinetic energy will be zero

Therefore, the total work in lifting the laptop will be equal to the change in potential energy.

Potential energy is the energy that comes by virtue of its position with reference to other

Therefore, potential energy = mgh

Where, m = mass of the laptop = 4.1 pounds

g = acceleration due to gravity = 32.17 ft/\(s^{2}\)

h = height to which the laptop is lifted =  2 feet

Therefore potential energy = (4.1)(32.17)(2) = 263.79 foot-poundal

263.79 foot-poundal is the required work done.

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The value of the function 8s/ 2s^2−25s using inverse  Laplace transform  is equal to 4e^(25t/2).

Function is equal to,

8s/ 2s^2−25s

Value of 's' after factorizing the denominator we get,

2s^2−25s = 0

⇒ s( 2s -25 ) =0

⇒ s =0 or s =25/2

Now apply partial fraction decomposition we get,

8s/ 2s^2−25s = A/s + B /(2s -25)

Simplify it we get,

⇒ 8s = A(2s -25) + Bs

Now substitute s =0 we get,

⇒ 0 = A (-25) + 0

⇒ A =0

and s = 25/2

⇒8(25/2) = A(2×25/2 -25 ) + B(25/2)

⇒100 = B(25/2)

⇒B = 8

Now ,

8s/ 2s^2−25s = 0/s + 8 /(2s -25)

⇒ 8s/ 2s^2−25s = 8 /(2s -25)

Take inverse Laplace transform both the side we get,

L⁻¹ [8s / (2s^2 - 25s)] = L⁻¹ [8/(2s - 25)]

Apply , L⁻¹ [1/(as + b)] = (1/a)e^(-bt/a),

here,

a = 2 , b = -25

L⁻¹ [8s / (2s^2 - 25s)]

= L⁻¹ [8/(2s - 25)]

= (8/2) e^(25t/2)

= 4e^(25t/2)

Therefore, the value of  inverse Laplace transform for the given function is equal to 4e^(25t/2)

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The above question is incomplete, the complete question is:

Find the inverse Laplace transform of 8s/ 2s^2−25s.

Answer:

8 tricycles

Step-by-step explanation:

Let x be the amount of bicycles and y be the amount of tricycles

We can set up a system of equations:

x=3y+6

2x+3y=84

We can solve using substitution

2(3y+6)+3y=84

Distribute

6y+12+3y=84

Combine like terms

9y+12=84

Subtract 12 from both sides

9y=72

Divide 9 from both sides

y=8

There were 8 tricycles at the yard sale

Answer:
D

Step-by-step explanation: 5 are crossed rows by 3 and then 7 by 5 are shaded in and than is 2 different numbers in together multiplied equals 1.500 which is D

The series is convergent because sn can be expressed as a telescoping sum, which means that the series will approach a finite value as n approaches infinity.

To determine whether the series [infinity] cos 4n − cos 4n/2n=1 is convergent or divergent by expressing sn as a telescoping sum, we can rewrite the terms using the identity cos 2x = 2cos²ˣ − 1:

cos 4n − cos 4n/2n=1 = 2cos^24n/2 − 1 − 2cos^24n/2n+1 + 2cos^24n+2/2n+2 − 1

This expression has a telescoping sum because each term cancels with the previous and next terms. So we can simplify it as:

s_n = (2cos² 2n − 1) − (2cos² 2n+1 − 1)

s_n = 2(cos² 2n − cos² 2n+1)

s_n = −2(cos² 2n+1 − cos² 2n)

Therefore, the series is convergent because sn can be expressed as a telescoping sum, which means that the series will approach a finite value as n approaches infinity.

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it will be 20 squares in step four

Answer:

0.0625 miles

Step-by-step explanation:

There is a faster way but this way makes more sense

1/4 miles = 440 yards

440/4 (since 4 people)

110 yards per person

Put back into miles

Everyone ran 0.0625 miles

Step-by-step explanation:

19 tens

18 hundreds

false

true

true

true

Answer:

1/1001,49/100,357/10,4/10 is the ascending order

Step-by-step explanation:

i hope this will help you :)