AnimeGhoul8863:

last two questions Given the two expressions shown below: square root of 4 plus square root of 25 square root of 4 plus square root of 9 Which statement best describes the two expressions? Both are rational. Both are irrational. A is rational, but B is irrational. A is irrational, but B is rational. ----- What is the value of y in the solution to the following system of equations? 2x + y = −4 5x + 3y = −6

10 months ago
AnimeGhoul8863:

Hey Dude you think you can help me

10 months ago
vannieduval:

for one please explain it for me

10 months ago
dude:

Well what is $\sqrt{4}+\sqrt{25}?$

10 months ago
dude:

Do you have to show work for each question?

10 months ago
AnimeGhoul8863:

no but i have 4 after this that do

10 months ago
AnimeGhoul8863:

7

10 months ago
dude:

Well $\sqrt{4}+\sqrt{9}?$

10 months ago
AnimeGhoul8863:

5

10 months ago
dude:

Are 5 and 7 rational or irrational numbers?

10 months ago
AnimeGhoul8863:

i think irrational

10 months ago
dude:

Oh, define irrational

10 months ago
AnimeGhoul8863:

An irrational number is a number that cannot be expressed as a fraction

10 months ago
dude:

Right, can you rewrite 5 and 7 as a fraction?

10 months ago
AnimeGhoul8863:

omg i think i was thinking irrational numbers were odd numbers

10 months ago
dude:

No no lol

10 months ago
AnimeGhoul8863:

5/7 right so yes

10 months ago
dude:

No $5=\frac{5}{1}\\ ~\\ 7=\frac{7}{1}$ Do you understand this?

10 months ago
AnimeGhoul8863:

i think so

10 months ago
AnimeGhoul8863:

so the answer would be A

10 months ago
dude:

Yes but do you understand why I can rewrite those numbers as fractions?

10 months ago
AnimeGhoul8863:

because they are whole numbers not decimals

10 months ago
dude:

No, you can rewrite some decimals as fractions $2.5=\frac{3}{2}$

10 months ago
AnimeGhoul8863:

oh let me think then

10 months ago
dude:

$$\color{#0cbb34}{\text{Originally Posted by}}$$ @dude No, you can rewrite some decimals as fractions $2.5=\frac{3}{2}$ $$\color{#0cbb34}{\text{End of Quote}}$$ ***meant to write 1.5, not 2.5***

10 months ago
AnimeGhoul8863:

ok i got nothing can you explain

10 months ago
dude:

Lets say you get 3 pies for Christmas|dw:1513379181468:dw| Each pie is 1 whole, right?

10 months ago
AnimeGhoul8863:

ok

10 months ago
dude:

|dw:1513379255487:dw| Each pie is 1 whole, represented by 1 in the denominator, but because you have 3 of those you have 3 in the numerator representing the number of full pies

10 months ago
AnimeGhoul8863:

ohhhh so all whole numbers can be a fraction and if the decimal is right it can be a fraction to

10 months ago
AnimeGhoul8863:

next question

10 months ago
dude:

That was a big oversimplification, all whole numbers can be rewritten as fractions but decimals with more than 1 decimal can also be rewritten $1.01=\frac{101}{100}$

10 months ago
AnimeGhoul8863:

ok so if it was .15 it wouldnt be a fraction but it i has a number in front to the decimal its a fraction

10 months ago
AnimeGhoul8863:

ok since we got that covered can we go on to the next question

10 months ago
dude:

No, I will explain later $0.15=\frac{3}{20}$

10 months ago
dude:

For question 2, would you like to solve by elimination or substitution?

10 months ago
AnimeGhoul8863:

elimination

10 months ago
dude:

So we want to get rid of one variable Let's get rid of y, do you have an idea on how to do this?

10 months ago
AnimeGhoul8863:

Kinda .................Not really

10 months ago
dude:

$Hint: What~is~-3y~+3y?$

10 months ago
AnimeGhoul8863:

i did it on calculator and it said 0

10 months ago
dude:

Yes, how do we turn y into -3y?

10 months ago
AnimeGhoul8863:

by subtracting 3

10 months ago
dude:

$Problem:\\ 2x+y=−4\\ 5x+3y=−6$ $-3 (2x+y=−4)\\ 5x+3y=−6\\~\\ \color{blue}{-6x-3y=+12\\ 5x+3y=−6}~~Add~both ~equations\\~\\ \color{red}{{-1x=6}}~Divide~by~-1~on~both~sides\\~\\ \color{purple}{x=-6}\\Part~1$

10 months ago
dude:

We then substitute back into any equation to find y $2x+y=-4~~~~~~~~~~~~~~\color{purple}{x=-6}\\ \color{green}{2(-6)+y=-4}~Simplify\\~\\ \color{cyan}{-12+y=-4}~Add~12~to~both~sides\\~\\ \color{orange}{\boxed{y=8}}$

10 months ago
AnimeGhoul8863:

so the answer is x=-6 and y=8

10 months ago
dude:

Well it only asks for the y-value

10 months ago
AnimeGhoul8863:

so the answer is y=8

10 months ago
dude:

Yes, but look at the work to see why it is 8!

10 months ago
AnimeGhoul8863:

i wrote it down thank you if i post it in another post can you check my answers from the written questions

10 months ago
dude:

Sure

10 months ago
AnimeGhoul8863:

thx

10 months ago