A gardener is planting two types of trees: Type A is 3 feet tall and grows at a rate of 22 inches per year. Type B is 4 feet tall and grows at a rate of 20 inches per year. Algebraically determine exactly how many years it will take for these trees to be the same height.

  6 years

Step-by-step explanation:

The height of tree A can be modeled by ...

  A = 36 +22y . . . . . where y is the number of years, height is inches

The height of tree B can be modeled by ...

  B = 48 +20y . . . . . same deal

The two heights are the same when ...

  A = B

  36 +22y = 48 +20y

  2y = 12 . . . . . . subtract 36+20y

  y = 12/2 = 6

It will take 6 years for the trees to be the same height.

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Note that you can "cut to the chase" by recognizing that the taller tree is growing at the slower rate, so the 12-inch difference in height is being reduced by 2 inches per year. (That is the meaning of 2y=12, above.) From there, it is a simple step to get to the divide 12 by 2.

"image"

step-by-step explanation:

in most of these problems, the notation is that the point with a "prime" is the image of the point without. that is, b' is the image of b.

here, there is no dilation or reflection. there is simply translation (with no direction shown). which figure you call the "preimage" and which one you call the "image" is up to you. as a matter of convention, the naming is as described above.

the answer is 150.6

step-by-step explanation:

you multiply .02 by 30 and get .6.

and then you multiply 5.00 by 30 and get 150.

hope this !