The vertices of her garden are located at the points (−1,5), (4,2) and (9,−4) on a coordinate grid. If each unit on the grid represents a foot and the material costs $8 per foot, how much will she pay for the material on the side between points (−1,5) and (4,2)?

Given:

The vertices of the garden on a coordinate grid are (−1,5), (4,2) and (9,−4).

Each unit on the grid represents a foot and the material costs $8 per foot.

To find:

The cost for the material on the side between points (−1,5) and (4,2).

Solution:

Distance formula:

Using the above formula, the distance between points (−1,5) and (4,2) is

On further simplification, we get

Now,

1 unit = 1 foot and 1 foot material costs is $8.

So, 1 unit material cost is $8.

Cost of material for 5.83 units is

Therefore, the cost for the material on the side between points (−1,5) and (4,2) is $46.64.

(a) common ratio in the given sequence is, 3

(b) push ups will do kendall do on the 20th week

step-by-step explanation:

geometric sequence is a sequence of numbers that follows a pattern were the next term is found by multiplying by a constant called the common ratio(r)

(a)

given the sequence: 6 , 18 , 54 , 162 ,

this sequence is geometric sequence where each term is 3 times the previous term.

therefore,

common ratio(r) = 3.

(b)

a formula for nth term of geometric sequence is given by;

,   where r is the common ratio between the successive terms and is the first term,

to find how many push ups will kendall do on the 20th week.

here. n = 20th term.

in the given sequence first term

then;

simplify:

therefore, push ups will do kendall do on the 20th week