Question

factoring y^2+2y-1

Answer 1

find two numbers that multiply to -1 (last term) and add to 2 (middle coefficient) at the same time

Answer 2

there is nothing that does that though

Answer 3

we do this by listing the factors of -1

-1 = -1*1

but these two factors don't add to 2 (since -1+1 = 0), so this means that y^2 + 2y - 1 is prime

Answer 4

if it were y^2+2y+1, then the two numbers would be 1 and 1 (since 1+1 =2 and 1*1 = 1)

so y^2+2y+1 factors to (y+1)(y+1)

Answer 5

the whole question is y^2+2y-1/2y^2+5y+2(and all of that divided by)y-1/y+2

Answer 6

and you're 100% sure it's y^2+2y-1 and not y^2+2y+1 or something else?

Answer 7

Yeahh the papers right in front of me. Unless it's a typo

Answer 8

hmm it might be a typo, but only the person who wrote it would know for sure

Answer 9

anyways, the idea is to factor each piece and cancel any common factors you can

Answer 10

so would i just leave the answer with that unfactored?

Answer 11

yeah you have to since y^2+2y-1 can't be factored

fortunately, 2y^2+5y+2 can be factored

Answer 12

Yeah so if the other one could be factored everything would cancel out perfectly

Answer 13

well everything doesn't have to cancel, but usually each piece would factor somehow

Answer 14

each trinomial that is

Answer 15

Can I ask you one more question?

Answer 16

sure

Answer 17

What values make the expression undefined?
7
-----------
x^2+2x-35

Answer 18

an expression is undefined when you're dividing by zero

Answer 19

example: 2/0 is undefined

Answer 20

so what makes the denominator zero?

Answer 21

so would it be cant equal 5 and cant equal -7

Answer 22

you nailed it perfectly

Answer 23

Yessss, thank you so much

Answer 24

x^2+2x-35

(x-5)(x+7) = 0

x-5=0 or x+7=0

x = 5 or x = -7

these two values make the denominator zero, so they make the expression undefined

you're welcome

Answer 25

If you're not busy could I check more of my problems with you?

Answer 26

sure what do you need checking?

Answer 27

3 -7
---- + -----
x-4 x+4

Answer 28

I got x-10
------
(x+4)(x-4)

Answer 29

let me check

Answer 30

3/(x-4) + (-7)/(x+4)


3(x+4)/((x-4)(x+4)) + (-7)/(x+4)


(3x+12)/((x-4)(x+4)) + (-7)/(x+4)


(3x+12)/((x-4)(x+4)) + (-7(x-4))/((x-4)(x+4))


(3x+12)/((x-4)(x+4)) + (-7x+28)/((x-4)(x+4))


(3x+12 + -7x+28)/((x-4)(x+4))


(-4x+40)/((x-4)(x+4)) ... note: you can stop here if you want


(-4(x-10))/((x-4)(x+4))

Answer 31

one sec, I'll write it out better

Answer 32

where did you get the -4 from?

Answer 33

okay thanks you're a life saver

Answer 34

\[\large \frac{3}{x-4} + \frac{-7}{x+4}\]


\[\large \frac{3(x+4)}{(x+4)(x-4)} + \frac{-7}{x+4}\]


\[\large \frac{3x+12}{(x+4)(x-4)} + \frac{-7}{x+4}\]


\[\large \frac{3x+12}{(x+4)(x-4)} + \frac{-7(x-4)}{(x-4)(x+4)}\]


\[\large \frac{3x+12}{(x+4)(x-4)} + \frac{-7x+28}{(x-4)(x+4)}\]


\[\large \frac{3x+12+(-7x+28)}{(x-4)(x+4)}\]


\[\large \frac{(3x-7x)+(12+28)}{(x-4)(x+4)}\]


\[\large \frac{-4x+40}{(x-4)(x+4)}\]


\[\large \frac{-4(x-10)}{(x-4)(x+4)}\]

Answer 35

hopefully that's a bit clearer

Answer 36

Yeah it is thank youu
another one?

Answer 37

sure

Answer 38

Find an equation of the line through (2,6) and (7,-4). Write the result in slope-intercept form.
I got y=-2x+10

Answer 39

getting the same thing

Answer 40

as a check, you can plug each point into the equation and you should get true equations

Answer 41

Okay can I just ask you two more than I'm done promise haha

Answer 42

lol sure go for it

Answer 43

Solve by either substitution or elimination
2x+y=7
3x+2y=13
I got 1

Answer 44

you got a single number?

Answer 45

Yeah

Answer 46

whenever you're solving a system of equations with 2 variables, you would get an ordered pair

not just a single number

Answer 47

the ordered pair is due to the fact you get a solution for x and a solution for y

Answer 48

Ohhh so I'd plug in 1 as x and get y?

Answer 49

yep

Answer 50

So y would be 5 (1,5)

Answer 51

perfect

Answer 52

visually, (1,5) is the point of intersection between the two lines 2x+y=7 and 3x+2y=13

Answer 53

Okay so next one is: Define the appropriate variables. Set up the appropriate equations and solve. How many gallons of 10% solution and of 20% solution must be mixed togehter to get 20 gallons of 18% solution?

Answer 54

I got x=4 gallons of 10% and y=16 gallons of 20%

Answer 55

good, here's how you check it

Answer 56

4+16 = 20

so the two amounts add to 20 gallons, that first part checks out

Answer 57

4 gallons of 10% solution ----> 4*0.10 = 0.4 gallons of pure substance
16 gallons of 20% solution ----> 16*0.20 = 3.2 gallons of pure substance
add them: 0.4+3.2 = 3.6 gallons of pure substance


20 gallons of 18% solution ----> 20*0.18 = 3.6 gallons of pure substance


so that next part checks out

Answer 58

Awesome!

Answer 59

Find f(-3) given f(x)= 2x
---------
x^2+7x+6

Answer 60

what did you get

Answer 61

I got 1

Answer 62

me too

Answer 63

Thank you so much!

Answer 64

you're welcome