Question

Simplify the expression

Answer 1

start by simplifying the denominator

Answer 2

and rewrite numerator in terms of \(\large i\)

Answer 3

The third answer is the correct one.

Answer 4

how do i simplify the denominator?

Answer 5

like would it be 4 + 3i?

Answer 6

Yes !

Answer 7

wat about numerator ?

Answer 8

-3?

Answer 9

\(\large \sqrt{-9} = ?\)

Answer 10

nope, use this :

\(\large \sqrt{-1} = i\)

Answer 11

hmmmm so 3?

Answer 12

\(\large \sqrt{-9} = \sqrt{-1} \times \sqrt{9} = i \times 3 = 3i \)

Answer 13

So, the simplified(not so) expression is :

\(\huge \frac{3i}{4+3i}\)

Answer 14

Multiply top and bottom by the conjugate of denominator : 4 - 3i

Answer 15

but that's not one of my options. do i have to do more work?

Answer 16

hahah yes more work :)

Answer 17

OHHHH I GET IT NOW

Answer 18

THANK YOU SO MUCH

Answer 19

what did u get ?

Answer 20

12 + 9i/7?

Answer 21

or is it 9 + 12i/25?

Answer 22

It's 9 + 12i/25

Answer 23

Oh okay thanks!

Answer 24

\(\huge \frac{3i}{4+3i}\)



\(\huge \frac{3i}{4+3i} \times \frac{4-3i}{4-3i}\)


\(\huge \frac{12i-9i^2}{(4+3i)(4-3i)}\)


\(\huge \frac{12i-9(-1)}{4^2 - (3i)^2}\)


\(\huge \frac{12i+9}{16 - 9(-1)}\)


\(\huge \frac{12i+9}{25}\)

Answer 25

thaaaankkkk youuu so much for all your help! You're wonderful!

Answer 26

np :) u wlc !!

Answer 27

are you busy? could you help me with a few more or no?

Answer 28

sure :) shoot...

Answer 29

one question at a time

Answer 30

what?

Answer 31

\(\huge 4 ~\sqrt[4]{48}\)

Answer 32

prime factorize the inside 48 :

48 = 2 x 24
= 2 x 2 x 12
= 2 x 2 x 2 x 6
= 2 x 2 x 2 x 2 x 3
= 2^4 x 3

Answer 33

right ?

Answer 34

Yep, okay so what do i do next?

Answer 35

\(\huge 4 ~\sqrt[4]{48}\)


\(\huge 4 ~\sqrt[4]{2^4 \times 3}\)

Answer 36

when u pull out 2^4 out of radical, it becomes 2

Answer 37

\(\huge 4 ~\sqrt[4]{48}\)


\(\huge 4 ~\sqrt[4]{2^4 \times 3}\)


\(\huge 4\times 2~\sqrt[4]{3}\)

Answer 38

so it's the first option?

Answer 39

Correct !

Answer 40

Thanks!

Answer 41

Can you help me with that one?

Answer 42

The graph is opening UP, eh ?

Answer 43

so it will have a positive leading coefficient

Answer 44

having that information,
which two options u can strike off ?

Answer 45

the first two

Answer 46

Yes !!

Answer 47

answer must be between last two options,
lets see

Answer 48

u should know the vertex form of parabola :

\(\large y = a(x-h)^2 + k\)

Answer 49

where, \((h,k)\) is the vertex

Answer 50

True

Answer 51

Look at the graph, and can u identify the vertex coordinates ?

Answer 52

-2, 3?

Answer 53

first comes the x coordinate...

Answer 54

3, -2

Answer 55

so vertex = (3, -2)

okay ?

Answer 56

yes :)

Answer 57

OHHH SO IT'S THE THIRD ONE

Answer 58

wooohoooo yayy

Answer 59

you got it !! good job :)

Answer 60

thanks! okay i have another one

Answer 61

Edgar started with 2 poems in his journal. Then he started writing 3 poems each day. Which of the following graphs represents Edgar's poem writing?

Answer 62

start value = 2
that means, the line will cut the y axis at 2

Answer 63

^^from that info,
which two options we can strike off ?

Answer 64

the last two?

Answer 65

Correct, last two options are cutting y axis at 3. so they're wrong.

Answer 66

that leaves the correct answer to be between first two

Answer 67

how to figure out which one is right ?

Answer 68

yeah i dont know.

Answer 69

use the remaining info in quesiton

Answer 70

Then he started writing 3 poems each day.

Answer 71

Ohh it's the second option.

Answer 72

that means,
as u each day, the graph rises UP by 3

Answer 73

right?

Answer 74

Excellent !!

Answer 75

thank you.

Answer 76

I only have like one more then I'm done hahaha

Answer 77

first step : prime factorize the stuff inside radicals

Answer 78

how?

Answer 79

\(\huge 4~\sqrt{24} - 4~\sqrt{8} + \sqrt{98}\)


\(\huge 4~\sqrt{4 \times 6} - 4~\sqrt{4 \times 2} + \sqrt{49\times 2}\)


\(\huge 8~\sqrt{ 6} - 8~\sqrt{2} + 7\sqrt{ 2}\)

Answer 80

combine like terms and simplify

Answer 81

okay!

Answer 82

7 square root of 2?