Question

Will give medal.
1. Solve formula for indicated variable.
s=6r^3t , for t

2. the function F(x)=x^2 . translate 3 units to the right and 3 units down. what is the new function?

3. solve the system by substitution
2.25x -3y = -13
3.25x - y = -14

Answer 1

Hint for #1:

If x*y = z, then y = z/x. This happens after you divide both sides by x. The division happens to undo the multiplication.

For example,

2*x = 10 will turn into x = 10/2 = 5 after you divide both sides by 2 (to undo the multiplication of 2)

Answer 2

??

Answer 3

With \[\Large s=6r^3t\] you have \(\Large 6r^3\) times \(\Large t\) on the right side. Agreed?

Answer 4

yeah

Answer 5

so to isolate t, you undo that multiplication

Answer 6

divide both sides by 6r^3 to undo the multiplication of 6r^3

Answer 7

Divide both sides by 6r^3
\[\Large s=6r^3t\]
\[\Large \frac{s}{6r^3}=\frac{6r^3t}{6r^3}\]
\[\Large \frac{s}{6r^3}=\frac{6r^3}{6r^3}*t\]
\[\Large \frac{s}{6r^3}=\frac{\cancel{6r^3}}{\cancel{6r^3}}*t\]
\[\Large \frac{s}{6r^3}=t\]
\[\Large t=\frac{s}{6r^3}\]

Answer 8

oh i see.. okay thanks.

Answer 9

The reason why the cancellation occurs is because anything divided by itself is 1. Well anything but 0.

Answer 10

that i know.

Answer 11

do you know any of the other questions?

Answer 12

Show me how far you got with #2

Answer 13

i didn't get anywhere. i skipped it because i couldn't remember how thoes changes affect the equation.

Answer 14

I'll give a similar example

Let's say we want to shift f(x) = x^3 five units down and two units to the left

to go 2 units to the left, we replace every x with x+2 to get f(x) = (x+2)^3

to shift 5 units down, we just subtract 5 at the end, so f(x) = (x+2)^3 - 5

Answer 15

so if we move it 3 units to the right it would be F(x)=(x-3)^2 ?

Answer 16

then 3 units down would be f(x)= (x-3)^2 -3 ?

Answer 17

`so if we move it 3 units to the right it would be F(x)=(x-3)^2 ?`
correct

Answer 18

`then 3 units down would be f(x)= (x-3)^2 -3 ?`
also correct

Answer 19

okay. do you know the last question?

Answer 20

are you able to solve \(\Large 3.25x - y = -14\) for y? are you able to get y all by itself?

Answer 21

umm hang on.

Answer 22

that would be y=14+3.25x right?

Answer 23

very good

Answer 24

now move onto the first equation \(\Large 2.25x -3y = -13\)

Answer 25

i remember i had solved this but she said my asnwer was wrong. so. i must have missed something.

Answer 26

replace EVERY copy of 'y' with 14+3.25x

this works because y is equivalent to this expression (aka they're the same)
this is what substitution is all about. Think about your substitute teacher. The substitute teacher is a temporary replacement for your actual teacher. Ideally they would be identical but of course in the real world, they are not

Answer 27

anyways, we would go from this
\[\Large 2.25x -3y = -13\]
to this
\[\Large 2.25x -3(14+3.25x) = -13\]
take note how the y term is now gone. So from here you just solve for x

Answer 28

okay.

Answer 29

2.25x -42 + 9.75x = -13

Answer 30

12x - 42 = -13

Answer 31

am i doing this right?

Answer 32

you made a mistake when you did 2.25x -42 + 9.75x = -13

Answer 33

the negative distributes through

Answer 34

oh so 2.25X -42 -9.25X = -13

Answer 35

yes

Answer 36

then. -7.5x - 42 =-13

Answer 37

-7.5x =29

Answer 38

x==3.8?

Answer 39

-3.8

Answer 40

???

Answer 41

I'm getting -3.866666667 for x

Answer 42

yeah that is what i got. i siplified.

Answer 43

-3.9 if you round.

Answer 44

if you're going to round to the nearest tenth, then it would be -3.9

Answer 45

yes correct