The Pythagoreans changed mathematics from a science into a set of problem-solving techniques. True or false

Find the value of x. Give your answer in simplest radical form.

MrMuchimi

Answer: x = 5*sqrt(10)
"sqrt" stands for "square root"

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Refer to the attached image. The figure is not to scale. Notice how I've added in y and z (blue and red respectively)
The length y is the bottom horizontal leg for the triangle on the right.
The length z is the bottom horizontal leg for the triangle on the left.

To find x, we need to find y first, which will help us find z, and then we can finally get to x.

Let's find y first
To do this, we use the pythagorean theorem
a^2 + b^2 = c^2
y^2 + 9^2 = 15^2
y^2 + 81 = 225
y^2 + 81-81 = 225-81
y^2 = 144
sqrt(y^2) = sqrt(144)
y = 12 ... keep in mind that y is a length, so it needs to be positive

Notice how the y and z lengths combine to form a total length of 25 units
Therefore,
y+z = 25
12+z = 25
12+z-12 = 25-12
z = 13

Now that we know z = 13, we can find x. Again we use the pythagorean theorem one last time
a^2 + b^2 = c^2
z^2 + 9^2 = x^2
13^2 + 9^2 = x^2
169 + 81 = x^2
250 = x^2
x^2 = 250
sqrt(x^2) = sqrt(250)
x = sqrt(250)
x = sqrt(25*10)
x = sqrt(25)*sqrt(10)
x = 5*sqrt(10)
This is in simplest radical form as we can't factor 10 any further (there are no perfect square factors that go into 10). This is the exact length of side x

Note: using a calculator, 5*sqrt(10) = 15.8113883008419 approximately

6 0

2 years ago

Can you explain to me how exponents work?

LuckyWell [14K]

Answer:

1^2 is one squared which means

1x1

1^3 is

1x1x1

2^4 is

2x2x2x2 which equals 16

Step-by-step explanation:

4 0

2 years ago

Read 2 more answers

Explanation of Baye's theorem.

ELEN [110]

I will be including both an basic explanation of what it is and its proof.

I'm guessing you are either learning about conditional probability at school or preparing for competitions.

Baye's theorem states:

$P(A|B)=\frac{P(B|A)P(A)}{P(B)}$

That is the theorem itself and it means that the probability that event A happens given B is true equals the probability event B happens given A is true times the probability event A happens divided by the probability B happens.

That was the basic of the theorem and the proof of this is basically just testing how well you understand what conditional probability is.

$P(A|B)=\frac{P(AintersectB)}{P(B)}$

$P(B|A)=\frac{P(BintersectA)}{P(A)}$

Now we know that the probably that A and B both happens is the same as the probably that B and A both happens.

Therefore P(A|B) can be seen as P(B|A) multiplied by P(A) and then divided by P(B) which gives the right hand side of the first equation. And this is basically the theorem.

$P(A|B)=\frac{P(B|A)P(A)}{P(B)}$

**Note P(B) have to be not equal to 0 because having a 0 in the denominator would make this equation undefined.

If you have any questions or need further explanations please ask me in the comments of the answer, I hope this helped!

6 0

3 years ago

Is 290.45 higher than 2867.5

tekilochka [14]

2867.5 is bigger

Even though they both show 5 numbers, the second one has only one decimal place versus 2 on the first

If you ignore the decimal, your left with
290 vs 2867

2867 is much bigger than 290 so this is the answer

5 0

2 years ago

How important is writing the polynomial in standard form when dividing polynomial

Novay_Z [31]

It is verg important because once diving "The length of one cathetus in a right triangle with equal catheti is the squareroot of half of the squared hypotenuse. And yeah

6 0

2 years ago