MATHEMATICS MIDDLE SCHOOL

Pythagorean triples are given by the formula x^2-y^2, 2xy, and x^2+y^2. Use the formulas for the Pythagorean triples to find a right triangle with leg lengths of 16 and an odd number. Show all of your work for full credit.

Answers

Answer 1

Answer:

Answer:

Let the unknown length be x

We have a formula to find the triplet of a right angle triangle

Put the given length equal to all three terms in the triplet

$2m,m^2-1,m^2+1$

put 16 equal to all above three but number comes out has to be integer.

$2m=16$

$\Rightarrow m=8$

Now, $m^2-1=16$

$m^2=17$ will not give integer.

And now, $m^2+1=16$

$m^2=15$ will not get integer value

Hence, the value of m will be 8

And substituting the value in the triplet formula we get

$2m=2\cdot 8=16$ which is given.

$m^2-1=64-1=63$ the other leg and is odd.

And $m^2+1=64+1=65$ the hypotenuse or the longest side.

Hence, 16,63 and 65 will form a right triangle

Pythagoras theorem is:

$\text{one side}^2+\text{other side}^2=hypotenuse^2$

Here, 16 and 63 are sides or legs and 65 is the hypotenuse.

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What is 18/25 simplified

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18/25 is already simplified. There is no number that can go in both 18 and 25.

18/25 is already simplified. you cant simplify it more

Olivia orderd 5 books online each book weighed 2 1/3.what is tge total weight altogether

Answers

11 2/3, I think. 2*3 + 1 = 7 & 7/3*5/1 (where you do straight multiplication) you get 35/3 which simplifies to 11 2/3. Hope this helped, but um what is the weight measurement or is that not mentioned?

Weight of each book = 2 ⅓ = 7/3

Weight of 5 books = 5 × 7/3
= 35/3

A triangle is inside a circle where the triangle's base is on the circle's diameter as shown.What is the area of the shaded region?

Use 3.14 for π .

Enter your answer as a decimal in the box.

Answers

Answer:

$A_(shaded)= 136.96 ft^(2)$

Step-by-step explanation:

We will find the shaded area if we subtract the area of the triangle from the area of the circle.

We know that the area of the circle is defined as

$A= \pi r^(2)$

Where $r$ is half the diameter, that is

$r=(16ft)/(2)=8ft$

The area of the circle is

$A= \pi r^(2)\nA= 3.14 (8ft)^(2) =200.96ft^(2)$

Now, we have to find the area of the triangle, which is defined as

$A_(\triangle) =(bh)/(2)$

Where $b$ is the base of 16 feet, and $h$ is the height of the triangle which is on the radius. So, we have $b=16ft$ and $h=8ft$ .

The area of the triangle is

$A_(\triangle) =(16ft(8ft))/(2)=64ft^(2)$

Now, the shaded is the difference as we said before, that is

$A_(shaded)=A-A_(\triangle)$

Replacing both areas, we have

$A_(shaded)=200.96 ft^(2) - 64ft^(2)= 136.96 ft^(2)$

Therefore, the shaded area is $A_(shaded)= 136.96 ft^(2)$

area of a circle=pi x r^2= 3.14 x 8^2(half of the radius)=3.14 x 64=200.96

area of triangle= 1/2 bh=1/2(16)(8)=1/2(128)=64

200.96-64=136.96 sq.ft

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Answers

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You would write a penny in decimal from as 0.1
If you think about it, a penny is always “0.1” when added to an amount. (3 pennies= 0.3) For example, $5.01, you would read this as five dollars and one cent. Another example could be $3.05, which would be read as three dollars and five cents. I hope this helped :)

.01 is how you would write a peny in a decimal

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Answers

Answer:

Step-by-step explanation:

I had to look up how many cards in a deck to answer this question XD

This proves how little I play cards

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