Jamal and dorothy were hiking and had a choice between two trails. one was 5 1/3 miles long, and other was 1 3/4 times as long. how long was the longer trail?

(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

the area of a triangle is determined by the formula: base x height * 1/2

you'll need to assign a base to the triangle. based on the vertices given, the simplest base would be the line segment from (-2,1) to (2,1). the distance between any two numbers is found by just subtracting them. here, you should subtract the x values to find the distance of this side.

2 - (-2) = 4.

so the distance (aka the length of the base) is 4. the height of the triangle is the distance between the base and the highest point on the triangle which is (3,4). we should subtract the y values this time to find the height/distance.

4 - 1 = 3

so the height is 3.

base = 4

height = 3

hope this if needed hmu