Aplasmid contains the gene for tetracycline resistance and a lacz gene that has a restriction site in it. foreign dna has the same restriction site at its ends. a mixture of foreign dna and plasmid dna cut with the same restriction enzyme is used to transform host bacteria that are then grown on medium with tetracycline and x-gal. colonies that are producing β-galactosidase and are tetracycline resistant are carrying

The colonies are carrying the resistance genes from plasmids

Explanation:

Bacteria can acquire beneficial characteristics that they didn’t have. One way for these is through plasmids, which ones are little fragments of DNA that usually contains resistance genes (for antibiotics, disinfectants, heavy metals, etc.) or other capacities, like the ability to use some substances (for example sugars).

In this specific situation, we already know that the plasmid carrying genes for tetracycline resistance and the lacZ gene.  

A little explanation:

Tetracycline is an antibiotic that inhibits bacterial growth and kills the bacteria.  The bacteria can “fight” to this antibiotic if it has a resistant gene, the result is that the antibiotic can’t affect the bacteria and survive.  An analogy is like a Police Officer (bacteria) that have a bulletproof vest (tetracycline-resistant gene) so the bullets (tetracycline) didn’t affect the police.

In the case of X-gal, is a compound consisting primarily in one sugar called galactose. Not all bacteria can eat galactose, they need an enzyme called β- galactosidase (comes from lacZ gene) that helps the bacteria “eat” the sugar (cuts the sugar in little pieces so the bacteria can eat).  

Then, as the bacterial colonies can grow in the medium with tetracycline and X-gal,  we know that those bacteria are carrying the resistance genes for tetracycline (does not affect the bacteria) and the lacZ gene (bacteria produce β- galactosidase that cuts galactose). These genes are coming from the plasmids because we already know that the plasmid carries these genes and not from the exogenous DNA.  

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