A Pythagorean triple is a set of three positive integers a, b, and c that satisfy the equation a² + b² = c².

The numbers 3, 4, and 5 are a Pythagorean triple because 3² + 4² = 5². Pythagorean triples are usually written in parentheses, such as (3, 4, 5) .

You can determine other Pythagorean triples by multiplying every number in (3, 4, 5) by the same positive integer. This creates similar triangles where the number you multiplied every triple by is the scale factor.

To create Pythagorean triples that are not similar to a triangle with side lengths of 3, 4, and 5, follow these steps.

Choose two positive integers, m and n, where m>n .
Determine a using a=m2−n2 .
Determine b using b=2mn .
Determine c using c=m2+n2

.
Write the triple (a, b, c) .

a. What Pythagorean triple results when m = 3 and n = 2? Explain.

b. Determine two other Pythagorean triples by multiplying every triple in part a by the same number.

c. Choose your own values for m and n. What Pythagorean triple results? Explain.

The value of a using integration is 2, such that the area of the region bounded by the curve y^2 =4ax and the line x= 4a is 256/3 Sq units

The given parameters are:

Curve, y² = 4ax

Line, x = 4a

Substitute x = 4a in y² = 4ax

y² = 4a * 4a

Take the square root of both sides

y = ±4a

This means that the point of intersection between the line and the curve is (4a, -4a) and (4a, 4a)

Remove the negative interval

So, we have: (4a, 0) and (4a, 4a)

The area is then calculated as

[tex]A =2 \int\limits^{4a}_0 {\sqrt y} \, dx[/tex]

This gives

[tex]A =2 \int\limits^{4a}_0 {\sqrt {4ax}} \, dx[/tex]

Remove the constant

[tex]A = 2\sqrt{4a}\int\limits^{4a}_0 {\sqrt {x}} \, dx[/tex]

Integrate

[tex]A = 2\sqrt{4a} * \frac 23 x^\frac32 |\limits^{4a}_0[/tex]

Evaluate the exponent

[tex]A = 4\sqrt{a} * \frac 23 x^\frac32 |\limits^{4a}_0[/tex]

Expand

[tex]A = 4\sqrt{a} * \frac 23 (4a)^\frac32[/tex]

Rewrite as:

[tex]A = 4 * a^\frac12 * \frac 23 * 4^\frac32 * a^\frac32[/tex]

Evaluate the exponents by the laws of indices

[tex]A = 4 * \frac 23 * 8 * a^2[/tex]

Recall that the area is:

A = 256/3

So, we have:

[tex]\frac{256}3 = 4 * \frac 23 * 8 * a^2[/tex]

Evaluate the quotients

[tex]256 = 4 * 2 * 8 * a^2[/tex]

Divide both sides by 64

4 = a²

Take the square root of both sides

2 = a

Rewrite as:

a = 2

Hence, the value of a is 2

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The total weight of the 100 cantaloupe is 324 pounds

The given parameters are:

Since the number of zeros in 100 is 2;

All Evans needs to do is to move the decimal point in 3.24 two places forward.

i.e. 3.24 becomes 324 when the decimal point is moved

Hence, the total weight of the 100 cantaloupe is 324 pounds

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Step-by-step explanation:

Hello there!

This is how we solve this problem

7/8 ÷ 2 1/4

[tex] \frac{7}{8} \div 2 \frac{1}{4} \: conveting \: to \: improper \: faction\\ \\ = \frac{7}{8} \div \frac{9}{4} \\ = \frac{7}{8} \times \frac{4}{9} \: multiply \: through \\ = \frac{7}{18} [/tex]

= 7/18

I hope this helps.

Have a nice studies.

Answer:

y=12×3(-2)

y=-72

Step-by-step explanation:

please mark me as brainlest

The first tip is to travel by public transport instead of using your own vehicle. The second tip would be to stop smoking and drinking it is a total waste of money and health.

Saving is the method of saving your money for the future. We can not predict the future if anything bad happens and we need a large amount of money these savings will help us.

The first tip is to travel by public transport instead of using your own vehicle. The second tip would be to stop smoking and drinking it is a total waste of money and health.

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Answer:

2 good scoops

Step-by-step explanation:

I got you I think

Answer:

y= x + b

-6 > 2x+6- graph a doted line that crosses through -6, and 2 shade below the dotted line going to the negative

18 >< 2x+6 graph a solid line through 18 and 2 and shade everything above the line going positive

have a good day hope this helped

Step-by-step explanation:

Answer:

y = 6

Step-by-step explanation:

-7 (4) + y = -22

-28 + y = - 22

+28 + 28

y = 6

Answer: D

Step-by-step explanation:

Answer: Choice D

Plot the points given for choice D. See below.

It is impossible to draw a single straight line through all of the points.

Therefore, this set of points do not represent a linear function.

Answer: b1/b1=h1/h2=10/12=15/h2 so use criss cross and equel to 15×12=10h2 both sides devide by 10 and equel 180/10=18

so h2=18

Answer:

Dilation

Step-by-step explanation:

it’s a dilation because the dilation changes how big the image is or what it looks like after the original image.

Answer:

For the answer to the question above, the numbers of pages in the books in a library follow a normal distribution. If the mean number of pages is 180 and the standard deviation is 30 pages, you can conclude that about 16% of the books have fewer than 150 pages.

Step-by-step explanation:

remember, a probability is ultimately always

desired cases / total possible cases

what are the total possible cases for our question here ?

all registered voters in 2009 :

640 + 960 + 320 = 1920

the desired cases (not republican) out of all these 1920 possibilities are

640 + 320 = 960

so, the probability for a registered voter to not be republican was

960 / 1920 = 1/2 = 0.5

Looking at the problem statement, the question is asking us to determine what the missing reasons are.  The information that is given to us is a step-by-step process of solving an expression for an unknown. There are also two blanks in the reasons column for steps 3 and 5 which we will need to determine.

For step #3, we can see that they subtracted 6x from both sides which means that options 3 and 4 are automatically out since they reference addition in the first part.  The correct reasoning for this part would be Subtraction Property of Equality which states that we subtract the same item from both sides of the expression.

We can see this being done in the following actions

For step #5, we can see that they divided both sides by -2 which means that option 1 is out since it references the multiplication property of equality. The correct reasoning for this part would be Division Property of Equality which states that we divide both sides by the same item.

We can see this being done in the following actions

Therefore, the option that would best fit the description that we provided during our work would be option 2 (3. subtraction property of equality; 5. division property of equality).

Answer:

b) 3. addition property of equality; 5. division property of equality.

Step-by-step explanation:

Given: 4(x - 2) = 6x + 18

Prove: x = -13

Algebraic Properties:

Steps:

1. Given:

⟹ 4(x - 2) = 6x + 18

2. Distribute property:

4(x) + 4(-2) = 6x + 18 [distribute 4]

⟹ 4x - 8 = 6x + 18

3. Subtraction property of equality:

4x - 6x - 8 = 6x - 6x + 18 [subtract 6x from both sides]

⟹ -2x - 8 = 18

4. Addition property of equality:

-2x - 8 + 8 = 18 + 8 [add 8 to both sides]

⟹ -2x = 26

5. Division property of equality:

-2x ÷ -2 = 26 ÷ -2 [divide both sides by -2]

⟹ x = -13

In conclusion, the missing reasons are the subtraction and division properties of equality.

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Answer:

X * H

-----------

  2

Step-by-step explanation:

Base of the triangle (X) times height of triangle, divided by 2

-- Gage Millar, Algebra 1/2 Tutor (Pending Pre-Calc Tutor)

The area of the isosceles triangle will be A(x) = √15(x² / 4).

A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.

In an isosceles triangle, the two legs of the triangle are congruent and their opposite angles too.

The base of an isosceles triangle is half as long as each of the two equal sides.

Let the base length be x. Then the length of each other legs will be 2x.

A(x) = √[s(s - x)(s - 2x)(s - 2x)]

The value of s is half of the perimeter.

s = (x + 2x + 2x) / 2

s = 5x / 2

Then the area of the isosceles triangle will be

A(x) = √[5x / 2(5x / 2 - x)(5x / 2 - 2x)(5x / 2 - 2x)]

A(x) = √[5x / 2(3x / 2)(x / 2)(x / 2 )]

A(x) = √(15x⁴ / 16)

A(x) = (x² / 4)√15

The area of the isosceles triangle will be A(x) = √15(x² / 4).

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Angle C and the 112 degree angle are supplementary, so angle C measures 180-112=68 degrees.

This means that by the exterior angle theorem, [tex]m\angle B=51^{\circ}+68^{\circ}=\boxed{119^{\circ}}[/tex]

Area of base

Volume

Answer:

x = 14 units

Step-by-step explanation:

Answer: [tex]\angle A+\angle D=180^{\circ}[/tex]

Step-by-step explanation:

Adjacent angles of a parallelogram are always supplementary.

There were 2350 people supporting the home team

The given parameters are:

Total = 2500

Proportion that supports the visiting team= 6%

Let the number of people that supports the team be x.

So, we have:

x = (1 - Proportion that supports the visiting team) * Total

This gives

x = (1 - 6%) * 2500

Evaluate

x = 2350

Hence, there were 2350 people supporting the home team

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The statement that is true for ΔXYZ and ΔX''Y''Z'' is; 2: ΔXYZ and ΔX''Y''Z'' are congruent

We are told that;

- Triangle XYZ is rotated 90º clockwise about the origin to form triangle X'Y'Z'.

- Thereafter, reflected across the x-axis to form triangle X''Y''Z''

Now, in transformation, Reflection is flipping an object across a line without changing its size or shape while Rotation is rotating an object about a fixed point without changing its size or shape. Thus, it means that the size and shape of the triangle formed is not different from the original one.

Thus, we can say that both triangles are congruent because the shape and size didn't change.

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Answer:

1

Step-by-step explanation:

f(x)=(x-1)²+1

f(1)=(1-1)²+1

f(1)=0²+1

f(1)=0+1

f(1)=1

Reason:

There are 7 outcomes we don't want vs 1 outcome we do want

outcomes we don't want = rolling one of the following {1,2,3,4,5,6,7}

outcome we want = rolling an 8

Answer:

13.5

Step-by-step explanation:

c = 2πr

42.3 = 2(3.14)r

42.3 = 6.28r

6.74 = r

d = r + r

d = 6.74 + 6.74

d = 13.5

The transformation is (b) The graph will reflect across the y-axis and then shift 5 units down.

The missing phrase in the question is: "If f(x) = 2ˣ + 1 is modified as g(x) = 2⁻ˣ + 1 - 5"

The functions are given as:

f(x) = 2ˣ + 1

g(x) = 2⁻ˣ + 1 - 5

First, the function f(x) is reflected across the y-axis (this eliminates options a and c)

The rule of this transformation is

(x,y) ⇒ (-x,y)

So, we have:

f'(x) = 2⁻ˣ + 1

Next, the function f(x) is shifted down by 5 units (this eliminates options d)

The rule of this transformation is

(x,y) ⇒ (x,y - 5)

So, we have:

f''(x) = 2⁻ˣ + 1 - 5

By comparing the functions f"(x) and g(x), we have:

g(x) = f''(x) = 2⁻ˣ + 1 - 5

Hence, the transformation is (b) The graph will reflect across the y-axis and then shift 5 units down.

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Answer:A

Step-by-step explanation:

-23/6 - 7/3 =-6.16666666667

-37/6 = -6.16666666667

Answer:

[tex] \frac{ - 37}{6} [/tex]

Step-by-step explanation:

[tex] \frac{23}{6} - \frac{7}{3} \\ lcm = 6 \\ \frac{ - 23 - 14} {6} = - \frac{ - 37}{6} \\ final \: answer \\ = \frac{ - 37}{6} [/tex]