Emma always learned that when you multiply by a power of ten, all you need to do is add a zero. She used that trick to solve the following problems: 345 x 10 = 3,450
4,789 x 100 = 478,900
5.6 x 10 = 5.60

Emma’s sister told her that her “trick” doesn’t work, and that 5.6 x 10 is NOT 5.60.
Which girl is correct? How do you know?

help meee plsss you smart people

Her sis is right

Step-by-step explanation:

She is correct because if you multiply a decimal by a power of 10 instead of adding a zero you bring numbers out of the decimal state.

answer: 0

step-by-step explanation: the positive, like 5, + its opposite, like -5 would be 0

5+(-5)=0, or 5-5=0

< xcy ≅ < xby

step-by-step explanation:

in δcax and δbax,

so, δcax ≅ δbax (side-angle-side or sas)

since δcax ≅ δbax, we can conclude < acx ≅ < abx

in δacy and δaby,

so, δacy ≅ δaby (side-angle-side or sas)

since δacy ≅ δaby, we can conclude < acy ≅ < aby

now,

< acy ≅ < aby

=> < acx + < xcy ≅ < abx + < xby

=> < acx + < xcy ≅ < acx + < xby   (since < acx ≅ < abx already proved above)

subtracting < acx from both sides, we get

< acx + < xcy -< acx ≅ < acx + < xby -< acx

cancelling out < acx and -< acx from both sides, we get

< xcy ≅ < xby (proved)