Which is an equation of a direct proportion? y=−2x y=12x−2 y=−2x+3 y=4x

First option and last option.

Step-by-step explanation:

By definition, an equation of direct proportion has the following form:

Where k is the constant of proportionality.

The equation of the line , where m is the slope and b the y-intercept.

When b=0, means that the line passes through the origin. Therefore, it would be:

(which is similar to  )

Then, the slope of the line would be the constant of proportionality.

By definition, the slope can be positive or negative.

Keeping on mind the information above, you can see that the equation that have that form are:

geometric series converge the common ratio r has magnitude less than one.

which is equivalent to

for the example we need

|2-x| < 1

-1 < 2-x   and 2-x < 1

x < 3 and x > 1

we can write that

answer: 1 < x < 3

1a. common ratio r=250/25=10 > 1     diverges

1b.   r=50/100=1/2 converges

when these converge they converge to

where a is the first term.

answer: 200

1c. r=-1   so it's not the case that |r| < 1.     diverges

2a. x is the common ratio so we converge when |x|< 1

2b.   r=-10x / -2 = 5x.

we converge when

|5x| < 1

|x| < 1/5

2c.   r=3-2x

-1 < 3-2x and 3-2x < 1

-4 < -2x and 2 < 2x

x < 2 and 1 < x

1 < x < 2

2d. [/tex] r=-48x^3/12 = 4x^3[/tex]

|4x^3| < 1

|x^3| < \frac 1 4

|x| < 4^{-1/3}

18.75 gallons

step-by-step explanation: