The equation for line f can be written as y=4/3x-5. line g, which is parallel to line f, includes point (4,5). what is the equation of line g?

Explanation:

When you know the slope and one point of a  line, you can deterrmine the equation of the line using the point-slope form of the equation, whose general general form is:

The point (x₁, y₁) is (4, 5).

For the slope, you use the fact that your line is perpedicular to the line y = 4/3x - 5.

The equation y = 4/3x - 5 is a slope-intercept equation. The coefficient of x, i.e. 4/3, is the slope of such line.

Since your line is parallel to this, you know that the slope is the same (paralllel lines have equal slope).

Now, you that you have the point (4,5) and the slope 4/3, you can write the equation of your line:

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}