Marianne has a scarf that is 5 inches longer than it is wide. if the area of her scarf is 84 square inches. what are the dimensions of her scarf?

The dimensions of Marianne scarf = 12  × 7  inches

The length of the scarf  =12inches

The width of the scarf = 7 inches

Step-by-step explanation:

Step(i):-

Let 'x' be the width of the scarf

Given that the length of the scarf = x+5

The area of the rectangle = length × width

Given that the area of the rectangle (scarf) = 84 square inches

Step(ii):-

   length × width = 84

    (x+5) × x = 84

    x² + 5x - 84 =0

   x² + 12 x - 7 x - 84 =0

   x(x+12) -7( x+12) =0

    (x-7)(x+12) =0

    x -7 =0  and x+12=0

     x =7   and x= -12

Step(iii):-

We have to choose x =7

The length of the scarf = x+5 = 7+5 =12inches

The width of the scarf = x = 7 inches

arithmetic sequence

step-by-step explanation:

given that a sequence has terms as

19, 15, 11,

this is represented on a graph

the pattern indicates that the sequence is an arithmetic sequence with i term

a=19 and common difference d =-4

any general term

thus the sequence is reduced by 4 for each successive term starting from 1 and nth term is

24-5n.

first negative term would start after 5th term

5th term =24-25< 0

from 5th term onwards the sequence would be negative.

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