Question

Finding a,x, and y

Answer 1

this is a rhombus
so we know it is a special parallelogram
in that all 4 sides are equal

Answer 2

so what does that mean about x an 3x-12?

Answer 3

and*

Answer 4

@iGreen

Answer 5

honestly idk

Answer 6

if all the sides are equal
and you have one side measurement is x
and another is 3x-12
and there is also another but we will look at that in a second once we solve for x
the side measurements are equal this is a given
that means x is equal to 3x-12

Answer 7

can you solve that equation for x?

Answer 8

you are solving x=3x-12 if you aren't sure still

Answer 9

would i subtract 3x from 1x

Answer 10

ok yep

Answer 11

1x-3x=-12 is what have now

Answer 12

wouldnt it be -2x since i just subtracted 3x from 1x

Answer 13

yep
so you have
-2x=-12

Answer 14

n divid -2 from -12 to get 6

Answer 15

:)

Answer 16

so x is 6

Answer 17

now you have to solve for y
and you know again the side measurements of a rhombus are all equal

Answer 18

so you could solve 8-y=x for y
where you just found x to be 6

so you actually have 8-y=6

Answer 19

i don't know if openstudy will do that thing it has been doing where it like refreshes over and over or seems to. But for the equation involving a, just know that the adjacent angles in a rhombus have sum 180 deg.

Answer 20

yes it keeps doing that to me!, and subtract 6 from both sides to get y = 2?

Answer 21

yep y=2
:)

Answer 22

Again since we have a rhombus adjacent angles (angles that share a common side) add up to be 180 deg

Answer 23

so you know that a+2a=180

Answer 24

subtract 2a from 1a to get -1a = 180 n divid by -1 to get -180

Answer 25

we know that 1+2=3
so 1a+2a=3a

Answer 26

so
the equation a+2a=180
is equivalent to saying 3a=180

Answer 27

wouldnt i be subtracted 2 though?

Answer 28

well the operation between a and 2a is addition
so that means you add a and 2a

Answer 29

\[a+2a=180 \\ 1a+2a=180 \\ (1+2)a=180 \\ (3)a=180 \\ 3a=180\]

Answer 30

so theyd youd dived by 3

Answer 31

yep

Answer 32

A would be 60

Answer 33

a would be 60 yes

Answer 34

congratulations you did it! :)

Answer 35

Thanks! would you mind helping em wiht a few more?

Answer 36

I might be able to help with one more.

Answer 37

Alright thank you! its not as long as that one haha

Answer 38

in a parallelogram opposite sides are equal (not all sides just opposite sides)
so what equations can you set up from that?

Answer 39

also this is a trick
they give you 3 expressions to choose from
you will only need 2 of those expressions
2 of the given are equal (1 you will not use at all)

Answer 40

hmmm

Answer 41

which sides are opposite?

Answer 42

Ab and CD

Answer 43

right! :)

Answer 44

so the side measurements given for those are equal

Answer 45

3x + 11 = 7x - 17 and then combine like terms?

Answer 46

yep and you would have to do that by either subtracting or adding items over to the other side

Answer 47

would i add 17 to 11

Answer 48

yes so you would have
3x+11+17=7x

Answer 49

so 3x + 28 = 7x then subtract 7x?

Answer 50

how about you choose to subtract 3x on both sides


if you did subtract 7x on both sides you would have 3x-7x+28=0
and you would have then created another step to perform to isolate x

Answer 51

it isn't wrong to do what you suggested
it just makes the problem a tad bit longer to solve

Answer 52

oh okay haha
so 28 = 4x then divide by 4 to get 7? ha

Answer 53

yeah

Answer 54

I think I see what problem you were having earlier
with the a+2a=180
I think you were thinking of a and 2a being on opposing sides
like what I mean is
since we had a and +2a on the same side
we just add them 3a=180


but if you had
a=2a+180
then yes you would subtract 2a on both sides
and have a-2a=180
which is -a=180

Answer 55

ohhhh yeah that makes sense

Answer 56

but yeah I'm not trying to confuse
the equation was
a+2a=180
which is
3a=180
which
means x=60 :)

Answer 57

okay!(:

Answer 58

anyways have a lovely day @jaybear97

Answer 59

Thanks you too and thank you fro the help

Answer 60

np