The tables represent the functions f(x) and g(x). A table showing g(x) equals 2 x plus 15 with 2 columns and 7 rows. The first column, x, has the entries, negative 15, negative 12, negative 9, negative 6, negative 3, 0. The second column, g(x), has the entries, negative 15, blank, blank, blank, blank, 15. Which input value produces the same output value for the two functions? x = –12 x = –9 x = –6 x = –3The simple interest formula is I = Prt, where I represents simple interest on an amount, P, for t years at a rate of r, where r is expressed as a decimal. What is the amount of money, P, that will generate $40 in interest at a 10% interest rate over 5 years? $60 $80 $90 $100

(1) For x = –12, g (x) = -9

   For x = –9, g (x) = -3

   For x = –6, g (x) = 3

   For x = –3, g (x) = 9

(2) The principal amount of money is $80.

Step-by-step explanation:

(1)

The expression of g (x) is,

The complete table is:

x                    g (x)

-15        

-12        

-9        

-6        

-3        

0        

(2)

The formula for simple interest is:

Given:

I = $40

r = 10%

t = 5 years.

Compute the value of P as follows:

Thus, the principal amount of money is $80.

- "runner b is moving at a slower rate."

- "the graphs shown are graphs of distance(km) against time(min).

the slopes of this graphs are are given by:

slope = (change in y)/(change in x)

= (change in distance)/(change in time)

this is the formula for finding the speed. so, the slope of these graphs represent the speed of the runner.

taking each division in the graph to represent 1 on both axis:

runner a ⇒ speed = (2-0)/(1-0)

= 2/1

= 2 km/min

runner b ⇒ speed = (3-0)/(3-0)

= 3/3

= 1 km/min

this shows that   runner b is moving at a slower rate."