Line g is dilated by a scale factor of one half from the origin to create line g'. Where are points E' and F' located after dilation, and how are lines g and g' related?

A. The locations of E' and F' are E' (−8, 0) and F' (0, 4), and lines g and g' intersect at point F.
B. The locations of E' and F' are E' (−4, 0) and F' (0, 2), and lines g and g' are the same line.
C. The locations of E' and F' are E' (−2, 0) and F' (0, 1), and lines g and g' are parallel.
D. The locations of E' and F' are E' (−1, 0) and F' (0, 0), and lines g and g' are not related.

The locations of E' and F' are E' (−2, 0) and F' (0, 1), and lines g and g' are parallel.

Step-by-step explanation:

If we have the graph of the equation y = f(x)

A dilation from the origin by a given factor, means that we multilpicate the function by that factor, so our new graph is:

y' = a*f(x)

where a is the scale factor, here a = 1/2.

so g' = (1/2)*g

then if E = (-4, 0)

          E' = (1/2)*E = (-2, 0)

          F = (0, 2)

          F' = (1/2)*F = (1, 0)

Then the correct option is C The locations of E' and F' are E' (−2, 0) and F' (0, 1), and lines g and g' are parallel.

b. 6

step-by-step explanation:

we are given the table representing an exponential function.

we can see from the table that, as x is increasing, the value of y is increasing in the power of 6.

i.e. the following relation is obtained,

x = 1, y = 6

x = 2, y = 36 =

x = 3, y = 216 =

x = 4, y = 1296 =

x = 5, y = 7776 =

so, the geometric series obtained is .

thus, the common ratio is given by = = 6.

hence, the common ratio is 6.

answer:   28.56 feet (approx)

step-by-step explanation:

since, triangle abc has measure of angle c equal to 55 degrees, measure of angle abc equal to 90 degrees, and length of bc equal to 20 feet.

we have to find out the measurement of segment ab.

therefore, tan 55° =

but bc = 20 feet.

⇒ tan 55 ° =  

⇒ ab = 20 × tan 55 °

⇒ ab = 20 × 1.42814800674

⇒ ab = 28.5629601348   ≈ 28.56 feet