Based on the table of values below, find the slope between points where x = 1 and where x = 4.

x: 1 , 3 , 4
y: 8, 6, -1

answer choices:
a. −3
b. negative two thirds
c. three over two
d. 3

The slope between the points where x=1 and where x=4 is :

-3

i.e. option: A is the correct answer.

Step-by-step explanation:

Let Y=f(X)

We are given a table of values as:

X: 1 , 3 , 4

Y: 8, 6, -1

Let m represents the slope .

We know that the slope between the points x=a and x=b is give by:

Here we are asked to find the slope between x=1 and x=4

i.e. we have:

a=1     and   b=4

f(a)=8   and    f(b)= -1

Hence, the slope between x=1 and x=4 is calculated as:

Hence, the slope is:

-3

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}

24

step-by-step explanation: