Abillboard is 2.5 times as long as it is wide. the area of the billboard is 2,250 ft. a scale drawing is made of the billboard, and the area of the scale drawing is 160 in. what is the scale used in the scale drawing? (explain)

1 inch : 14.08 feet

Step-by-step explanation:

First we need to find to find the length and the width of the billboard.

The area of a rectangle is given by A= length x width

Let's call w the width of the billboard ⇒The length of the billboard will be 2.5w

Area = w (2.5w)

2,250 = 2.5w²

2250/2.5 = w²

900 = w²

30 = w

Now, to find the scale in the drawing we are going to use a ratio.

Therefore, the width of the scale drawing is 2.13.

To find the scale used we can use a rule of three:

2.13 inches ------- 30 feet

1 inches --------------  x feet

x = 30/2.13 = 14.08 feet

Therefore, the scale used is 1 inch: 14.08 feet

multiply then divide

step-by-step explanation:

(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