20. a linear function is shown.

f(x) = (-5/2)x - 3

a. create a linear function g(x) such that f(x) = g(x) has exactly one solution.

b. what is the exact solution to f(x) = g(x)?

answer a:
answer b:

g(x) = (1/2)x + 3

f(x) = g(x) at (-1/2 , 13/4)

Step-by-step explanation:

g(x) and f(x) will have exactly one solution when they are not parallel (same slope) and when they are not equivalent functions (like doubling or halving all terms).

f(x) = (-5/2)x - 3

g(x) = (1/2)x + 3    <= choose an easy equation.

To find the solution, equate the two functions:

f(x) = g(x)

(-5/2)x - 3   =  (1/2)x + 3

(-5/2)x - (1/2)x = 3 + 3    <= move variables to one side, constants to other

(-6/2)x = 6   <= simplify

x = 6 / (-6/2)    <=isolate x

x = -6/12

x = -1/2

Substitute x = -1/2 into any equation to find y

g(x) = (1/2)x + 3

g(1/2) = (1/2)(1/2) + 3

g(1/2) = (1/4) + 3

g(1/2) = (1/4) + (12/4)   <= find common denominator to add

y = (13/4)   <= the function symbol can be replaced by y

The coordinates are (-1/2 , 13/4).

answer:  

step-by-step explanation:

odd numbers are only divisible by 1 and itself.

even numbers are divisible by more than 1 and itself.

for example 6 is even because it is divisible by more than 1 and its self. 1 x 6= 6 ; 2 x 3= 6

and 7 is odd because only 7 x 1 equals seveb