Determine whether each table or rule represents a linear or an exponential function. explain why or why not.
1. y = 4 * 5^x
2. y = 12 * x
3. y = -5 * 0.25^x
4. y = 7x + 3

From the list, the linear functions are  y=12x and y=7x+3. The exponentials functions are 4*5^x and -5*0.25^x.

Step-by-step explanation:

Any linear function can be expressed as:

y=mx+b  

Where b and m are constants (Real numbers) and x is the variable of the function.

For option 2, we have:

m=12 and b=0

For option 4, we have:

m=7 and b=3

The exponential functions are functions that can be written as:

y=a.b^x  

Here a and b represent the coefficient and the base of the exponential, both reals numbers, and x is the variable of the function.

For option 1, we have:

a= 4 and b=5

For option 3, we have:

a=-5 and b=0.25

37/3

step-by-step explanation:

step 1: simplify both sides of the equation.

7x+8(x+

1

4

)=3(6x−9)−8

7x+(8)(x)+(8)(

1

4

)=(3)(6x)+(3)(−9)+−8(distribute)

7x+8x+2=18x+−27+−8

(7x+8x)+(2)=(18x)+(−27+−8)(combine like terms)

15x+2=18x+−35

15x+2=18x−35

tep 2: subtract 18x from both sides.

15x+2−18x=18x−35−18x

−3x+2=−35

step 3: subtract 2 from both sides.

−3x+2−2=−35−2

−3x=−37

step 4: divide both sides by -3.

−3x

−3

=

−37

−3

x=

37

3