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
Hey Dude you think you can help me
for one please explain it for me
Well what is \[\sqrt{4}+\sqrt{25}?\]
Do you have to show work for each question?
no but i have 4 after this that do
7
Well \[\sqrt{4}+\sqrt{9}?\]
5
Are 5 and 7 rational or irrational numbers?
i think irrational
Oh, define irrational
An irrational number is a number that cannot be expressed as a fraction
Right, can you rewrite 5 and 7 as a fraction?
omg i think i was thinking irrational numbers were odd numbers
No no lol
5/7 right so yes
No \[5=\frac{5}{1}\\ ~\\ 7=\frac{7}{1}\] Do you understand this?
i think so
so the answer would be A
Yes but do you understand why I can rewrite those numbers as fractions?
because they are whole numbers not decimals
No, you can rewrite some decimals as fractions \[2.5=\frac{3}{2}\]
oh let me think then
\(\color{#0cbb34}{\text{Originally Posted by}}\) @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***
ok i got nothing can you explain
Lets say you get 3 pies for Christmas|dw:1513379181468:dw| Each pie is 1 whole, right?
ok
|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
ohhhh so all whole numbers can be a fraction and if the decimal is right it can be a fraction to
next question
That was a big oversimplification, all whole numbers can be rewritten as fractions but decimals with more than 1 decimal can also be rewritten \[1.01=\frac{101}{100}\]
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
ok since we got that covered can we go on to the next question
No, I will explain later \[0.15=\frac{3}{20}\]
For question 2, would you like to solve by elimination or substitution?
elimination
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?
Kinda .................Not really
\[Hint: What~is~-3y~+3y?\]
i did it on calculator and it said 0
Yes, how do we turn y into -3y?
by subtracting 3
\[Problem:\\ 2x+y=−4\\ 5x+3y=−6\] \[-3 (2x+y=−4)\\ 5x+3y=−6\\~\\ \color{blue}{-6x-3y=+12\\ 5x+3y=−6}~~Add~both ~equations\\~\\ \color{red}{{-1x=6}}~Divide~by~-1~on~both~sides\\~\\ \color{purple}{x=-6}\\Part~1\]
We then substitute back into any equation to find y \[2x+y=-4~~~~~~~~~~~~~~\color{purple}{x=-6}\\ \color{green}{2(-6)+y=-4}~Simplify\\~\\ \color{cyan}{-12+y=-4}~Add~12~to~both~sides\\~\\ \color{orange}{\boxed{y=8}}\]
so the answer is x=-6 and y=8
Well it only asks for the y-value
so the answer is y=8
Yes, but look at the work to see why it is 8!
i wrote it down thank you if i post it in another post can you check my answers from the written questions
Sure
thx
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