Create an equation that matches the table

The equation that matches the table is

Explanation:

From the table, we can see that this is a geometric progression because the common difference in the y-term is

Thus, and

To determine the equation, let us substitute the values of r and a in the general form of geometric progression.

The general form of geometric progression is given by

Now, substituting we have,

Simplifying by adding the powers of similar terms, we get,

Writing it in terms of x, we get,

Thus, the equation that matches the given table is

there are many solutions.

step-by-step explanation:

step 1: simplify both sides of the equation.

4x+6=4x^2+10x−4

step 2: subtract 4x^2+10x-4 from both sides.

4x+6−(4x^2+10x−4)=4x^2+10x−4−(4x^2+10x−4)

−4x^2−6x+10=0

step 3: factor left side of equation.

−2(2x+5)(x−1)=0

step 4: set factors equal to 0.

x=-5/2 or x=1

set each factor equal to 0

4x-3 = 0

2x-1 = 0

solve for x.

4x-3=0

4x=3

x= 3/4

solve for x. 

2x-1= 0

2x= 1

x= 1/2

your answer should be 1/2 is less than or equal to x and 3/4 is greater than or equal to x