The length and width of a rectangle are consecutive even integers. the area of the rectangle is 80 square units. what are the length and width of the rectangle?

10 and 8

Step-by-step explanation:

consecutive even numbers have a difference of 2 between them.

let the width be n then the length is n + 2

Area = n(n + 2) = 80, thus

n² + 2n = 80 ( subtract 80 from both sides )

n² + 2n - 80 = 0 ← in standard form

(n + 10)(n - 8) = 0 ← in factored form

Equate each factor to zero and solve for n

n + 10 = 0 ⇒ n = - 10

n - 8 = 0 ⇒ n = 8

But n > 0 ⇒ n = 8

width = n = 8 and length = n + 2 = 8 + 2 = 10

i believe it is d.) buddhism and e.) hinduism

(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