The graph of the parent function p( x) = x 2 passes through the point R(13, 169). The graph of p is transformed such that the new graph represents the function f( x) = ( x + 6) 2 − 10. If this transformation translates point R to a new location R', what is the x-coordinate of R'?

The  x-coordinate of R' is 7

Step-by-step explanation:

we have

This is the equation of a vertical parabola, open upward

The vertex is the point (0,0)

This is the equation of a vertical parabola, open upward

The vertex is the point (-6,-10)

so

The transformation of

p(x) -----> f(x)

(0,0) -----> (-6,-10)

The rule of the transformation is

(x,y) -----> (x-6,y-10)

That means ----> The translation is 6 units at left and 10 units down

Applying the rule of the translation to point R

R(13, 169) ------> R'(13-6, 169-10)

R(13, 169) ------> R'(7, 159)

therefore

The  x-coordinate of R' is 7

d. millimeters per hour.

step-by-step explanation:

we are given that,

carlo used a rain gauge to measure the amount of water his lawn is receiving from the sprinklers.

since, according to the options, we see that,

water cannot be measured by 'miles per hour', 'meters per second' and 'grams per seconds'.

we get that, the water can be measured by 'millimeters per hour'.

hence, the appropriate rate for describing the amount of water is 'millimeters per hour'.