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Mathematics 12 Online
OpenStudy (anonymous):

quick medal! help please ! check out the attachment in the comment box for the question. Is the answer 9, 6 & 8?

OpenStudy (anonymous):

OpenStudy (jdoe0001):

well... .what did you get for the value of "x"?

OpenStudy (anonymous):

replaced the x with the number(s)

OpenStudy (jdoe0001):

did you solve \(\bf x^2 \le 64 \quad ?\)

OpenStudy (jdoe0001):

that will give you what "x" is

OpenStudy (anonymous):

idk the steps in order to solve for it @jdoe0001

OpenStudy (jdoe0001):

\(\bf x^2\le 64\qquad \textit{taking square root to both sides}\\ \quad \\ \sqrt{x^2}=\sqrt{64}\implies x = \pm \sqrt{64} \) what's the square root of 64?

OpenStudy (jdoe0001):

lemme remove the = sign \(\bf x^2\le 64\qquad \textit{taking square root to both sides}\\ \quad \\ \sqrt{x^2}\le\sqrt{64}\implies x \le \pm \sqrt{64}\)

OpenStudy (jdoe0001):

anyhow, still though, what's the square root of 64?

OpenStudy (anonymous):

8!

OpenStudy (jdoe0001):

\(\large \bf \sqrt{x^2}\le\sqrt{64}\implies x \le \pm \sqrt{64}\implies x \le \pm 8 \)

OpenStudy (jdoe0001):

so that's what "x" is... now check which numbers are LESS THAN OR EQUALS to \(\bf \pm 8\)

OpenStudy (anonymous):

o i plug in 8x^2 √64?

OpenStudy (jdoe0001):

well... solving the inequality will just give you what values "x" would be.... so now we know that \(\bf x \le \pm 8\) so, from the list you're meant to check which numbers meet that

OpenStudy (jdoe0001):

let's try ..say 9, is 9 less than or equals to 8? no, so no that one 66... is 66 less than or equals to 8? no... so no that one either

OpenStudy (anonymous):

64 equals to 8

OpenStudy (jdoe0001):

64= 8? they look very different

OpenStudy (anonymous):

does 6 equal to 8? no right?

OpenStudy (jdoe0001):

so... say.. if we both go to the mall and you buy a $64 dress.. can I buy the same dress with $8? well

OpenStudy (jdoe0001):

if 64 = 8.. I guess I could

OpenStudy (anonymous):

so far its 64 & 8?

OpenStudy (jdoe0001):

well.. think about it... is 64 less than or equals to 8?

OpenStudy (jdoe0001):

or is it more than 8 ?

OpenStudy (anonymous):

im thinking 8x8=64! lol but its more than 8

OpenStudy (jdoe0001):

... well.. \(\bf 8^2 = 64\qquad 8\ne 64\) so you're right... 64 is more than 8, so it's not that one either

OpenStudy (jdoe0001):

what about 6? is 6 less than or equals to 8?

OpenStudy (anonymous):

less than 6!

OpenStudy (jdoe0001):

wel... less than 8, yes, so that one is one what about 8, is 8 less than or equals to 8?

OpenStudy (anonymous):

8 equals!

OpenStudy (jdoe0001):

yeap

OpenStudy (anonymous):

so overall the answers is 6 & 8! :)

OpenStudy (jdoe0001):

9 is more than 8.... so no dice 66 is more than 8, no dice 64 is more than 8, no dice 6 is less than 8, so ok 8 is equals to 8, so ok too

OpenStudy (anonymous):

thanks so much for being patient with me

OpenStudy (jdoe0001):

yw

OpenStudy (anonymous):

hey @jdoe0001 sorry to bother you again but isnt the answer for this 9 & 100? the square root of a 100 is 10 9 is less than 10!

OpenStudy (jdoe0001):

\(\large\bf x^2 < 100\implies x<10\) 9 is less than 100 is not less than 10, is actually much more

OpenStudy (anonymous):

what I'm doing wrong?

OpenStudy (jdoe0001):

well.. x < 10 means, "x" is LESS, not equals or greater, just LESS than 10

OpenStudy (anonymous):

6&9 is less than!

OpenStudy (jdoe0001):

yeap :)

OpenStudy (anonymous):

thank youuu :)

OpenStudy (jdoe0001):

yw

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