Question

Wow, I am actually clueless on this.
A right triangle has base (x - 7) units and height (2x - 10) units.

Part A: What is the square of the length of the hypotenuse of the triangle? Show your work.

Answer 1

I'll put the other two parts when I'm finished with A.

Answer 2

@e.mccormick

Answer 3

jim :DDDDD

Answer 4

pythagorean theorem

a^2 + b^2 = c^2

Answer 5

Yes, but I'm not sure how to apply.

Answer 6

so

\[\Large a^2 + b^2 = c^2\]

\[\Large (2x-10)^2 + (x-7)^2 = c^2\]

solve for c

Answer 7

Then I'm factoring it, then.

Answer 8

Correct?

Answer 9

no just isolating c

Answer 10

oh nvm

Answer 11

C = 5x^2 - 54x + 149 ?

Answer 12

What is the SQUARE of the length of the hypotenuse of the triangle?

Answer 13

they want c^2 and not c

Answer 14

How can we find the square of the length?

Answer 15

Jim? D:

Answer 16

I don't know how to find the square of the length.

Answer 17

you see how I plugged in the stuff for a and b right?

Answer 18

YEs.

Answer 19

you just need to simplify that left side to find c^2

Answer 20

expand things out, combine like terms

Answer 21

I see.

Answer 22

But isn't it the same answer I got earlier?

Answer 23

5x^2 - 54x + 149

Answer 24

yeah when you expand then simplify, you get

\[\Large c^2 = 5x^2-54x+149\]

Answer 25

you don't need to isolate c since they want the square of the hypotenuse length

Answer 26

So my answer right there is the complete answer>

Answer 27

yeah

Answer 28

Ok, awesome. Ready for part B? 2/3 of the way through.

Answer 29

ok

Answer 30

Part B: What is the area of the triangle?

Answer 31

A = 1/2 B * H

Answer 32

I just need the numbers, and I'm good.

Answer 33

the base is x-7 and the height is 2x-10

Answer 34

Thank ya.

Answer 35

honestly, it doesn't matter because you can easily turn the triangle sideways (or turn your head sideways). So you could say base = 2x-10 and height = x-7

Answer 36

2x^2 - 24x + 70 ?

Answer 37

that looks incorrect

Answer 38

yeah it is

Answer 39

you forgot to multiply by 1/2

Answer 40

Aha.

Answer 41

x^2 - 12x + 35 ?

Answer 42

yes

Answer 43

Thank you! And the final part, and we can... wait for it... PART WAYS.

Answer 44

hah i get it c:

Answer 45

Part C: Using the solution obtained in Part B, explain the closure property of multiplication of polynomials.

uh oh

Answer 46

what does closure mean

Answer 47

hahah you feel my pain XD

Answer 48

Let me look it up and I can give some insight. Maybe you can help me then

Answer 49

no, I know what it means, I need you to explain it to me so I can see if you know or not

Answer 50

it helps you frame it better in your mind if you explain it out

Answer 51

The sum, difference, or product of any two integers is another integer,
also the sum difference or multiplication of any two polynomials is once again, a polynomial.
the ratio of two integers will not always be an integer
and the ratio of two polynomials is not always a polynomial.

Answer 52

so in general, what is closure?

Answer 53

Just looked in my notes, and that's what's there.

Answer 54

Closure is the act of closing something.

Answer 55

in the mathematical sense, it means that if you have 2 things from a set, and you do some operation to them, then you should get another thing from that same set

Answer 56

oh

Answer 57

i totes knew that

Answer 58

INTEGER plus INTEGER = INTEGER

pick any two integers, add them, you get an integer

Answer 59

I got it!

Answer 60

Polynomial + Polynomial = Polynomial

Answer 61

no wait though

Answer 62

INTEGER plus INTEGER = INTEGER

pick any two integers, add them, you get an integer

Answer 63

Polynomial * Polynomial = Polynomial

Answer 64

yes, take any two polynomials and multiply them

the result is a polynomial

Answer 65

That's my answer, then?

Answer 66

the basics of it, you have to explain in words what is going on

Answer 67

you probably don't have to write a 5 paragraph essay or anything

Answer 68

haha, yeah. Thanks, jim.