Construct a difference table to predict the next term of the sequence -1,3,18,47,93,159,248

362

Step-by-step explanation:

-1,3,18,47,93,159,248

First difference (just do term minus previous term):

4, 15, 29, 46, 66 ,89

The first differences are not common.

Second difference (doing term minus previous term)

11,  14,  17, 20, 23

Third difference:

3 ,3 ,3, 3

So it is a cubic because the third differences are the same.

Anyways we don't have to find the explicit form of this sequence.  We just have to find the next term.

Let's go back through starting with second difference:

11 , 14, 17, 20, 23 , (25)

(25) would be next term here.

Let's go back to first difference:

4, 15, 29, 46, 66 ,89 , (89+25)

4, 15 ,29, 46, 66, 89 , (114)

Now let's go back to original sequence:

We want 114+248 to be the next term.

That equals 362.

let y equal to

the total fare and x is the mile of taxi ride. so the equation is

y = 0.55x + 1.75

since susie has

$10 to spend for a taxi cab, so he can have

10 = 0.55x +

1.75

x = 15 miles of

taxi ride

so the system of

inequality is

10 < 0.55x +

1.75

x > 2

a triangular prism is a 3 dimensional shape composed of triangles and rectangles. it is made from two triangular bases and three rectangular sides.