Choose the correct transformation of the graph f(x) = |x - 8| +3 .
the graph of f(x) =x| is shifted to the left 8 units, down 3 units.
the graph of f(x) =x| is shifted to the right 8 units, down 3 units.
the graph of f(x) =x| is shifted to the left 8 units, up 3 units.
the graph of f(x) =x| is shifted to the right 8 units, up 3 units.

Step-by-step explanation:

f(x) + n - shift the graph of f(x) n units up

f(x) - n - shift the graph of f(x) n units down

f(x - n) - shift the graph of f(x) n units to the right

f(x + n) - shift the graph of f(x) n units to the left

We have g(x) = |x - 8| + 3

f(x) = |x| → f(x - 8) = |x - 8|     shift the graph 8 units to the right

f(x - 8) + 3 → |x - 8| + 3         shift the graph 3 unit up

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions

2.56 is the width of the garden

step-by-step explanation: