The number of seats in the first five rows of an amphitheater is shown in the table below.

F(n)=an+b
We need to find "a" and "b"

when n=1→f(n)=f(1)=18 (see the table), replacing n=1 and f(n)=18 in the equation above, we have:
n=1→f(1)=a(1)+b→a+b=18   (1)

when n=2→f(n)=f(2)=24 (see the table), replacing n=2 and f(n)=24 in the equation above, we have:
n=2→f(2)=a(2)+b→2a+b=24   (2)

We have a system of 2 equations and 2 unknwons:
(1) a+b=18
(2) 2a+b=24

Subtractict equation (1) from equation (2):
Equation (2) - Equation (1):
2a+b-(a+b)=24-18→2a+b-a-b=6→a=6

Replacing "a" by 6 in equation (1):
(1) a+b=18→a=6→6+b=18→6+b-6=18-6→b=12

Then the equation is:
f(n)=an+b; a=6, b=12
f(n)=6n+12

f(n)=6n+12

Answer: d. 39 cmin the diagram, the approximate length of the minor arc de is 39 centimetres.step-by-step explanation: the formula for the length of an arc in a circle is as displayed below.let the length of the minor arc de = xx = 2( pi )r × angle of sector / 360°from this, we will substitute the values given from the problem into the formula to obtain the length of the minor arc de.x = 2( pi )r × angle of sector / 360°r = radius = 25cmpi as an approximate value = 3.14angle of sector = 120°x = 2( 3.14 )( 25 ) × 120° / 360°x = 157 × 1 / 4x = 39.25x = 39 ( rounded to the nearest whole number as an approximate value )

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