A gardener is planting two types of trees:
Type A is 10 feet tall and grows at a rate of 21 inches per year.
Type B is 7 feet tall and grows at a rate of 25 inches per year.
Algebraically determine exactly how many years it will take for these trees to be the
same height.

9 years will take foe these trees to be the same height, If type A is 10 feet tall and grows at a rate of 21 inches per year and type B is 7 feet tall and grows at a rate of 25 inches per year.

Step-by-step explanation:

The given is,

                Type A is 10 feet tall and grows at a rate of 21 inches per year

                Type B is 7 feet tall and grows at a rate of 25 inches per year

Step:1

             Convert the rate of grows of tree inch to feet,

             For Tree A,

                   Rate of grow, A = 21 inches per year

                                              = 21 × 0.0833333      ( 1 inch = 0.0833333 feet)

                                             = 1.75 feet per year

              For Tree B,

                   Rate of grow, B = 25 inches per year

                                              = 25 × 0.0833333     ( 1 inch = 0.0833333 feet)

                                             = 2.08333 feet per year

Step:2

           Difference in the tall of  Tree A & B,

                                               = 10 - 7

                                              = 3 feet

           Difference in the rate of grow of tree A & B,

                                                = 2.08333 - 1.75

                                               = 0.3333325 feet per year

Step:3

           Year take to both trees are same height,

                                               = 9 years

Step:4

            Check for solution,

            Height of tree = Height of Tree + (Rate of grow × Years)

            For A,

                                    = 10 + ( 1.75 × 9 )

                                   = 25.75 feet.........................................(1)

            For B,

                                   = 7 + ( 2.08333 × 9 )

                                    = 25.74999

                                   ≅ 25.75 feet.....................................(2)

          From Equation (1) and (2),

                  25.75 feet = 25.75 feet

Result:

          9 years will take foe these trees to be the same height, If type A is 10 feet tall and grows at a rate of 21 inches per year and type B is 7 feet tall and grows at a rate of 25 inches per year.

a reflection across the x-axis , followed by the by a reflection across the y-axis , and then a scale dilation of 0.5 .

you can first factor out the n to get n(1+5). we know that 1+5 is 6, so we just have 6n.