Factor each completely 5n^2-8n-21 6r^2+53r-79 4n^2-25

5n² - 8n - 21    →    (5)(- 21) = -105    (find 2 numbers whose product is 105 and sum is -8)

= 5n² - 15n  + 7n - 21

= 5n(n - 3)  + 7(n - 3)

= (5n + 7)(n - 3)

6n² + 53n - 79 → (6)( -79) = -474 (find 2 numbers whose product is -474 and sum is 53)  DOES NOT EXIST! only factors are: (1, 474) (2, 237) (3, 158) (6, 79)

= Prime

4n² - 25   (this is the difference of two squares)

= √(4n²) +/- √(25)

= 2n +/- 5

= (2n + 5)(2n - 5)

the smallest possible measurement of the width is 14 feet

step-by-step explanation:

let's assume length of parallelogram is 'l'

width of parallelogram is 'w'

the perimeter of a parallelogram must be no less than 40 feet

so, we get

we are given

length of parallelogram is 6 feet

so,

l=6

we can plug it

now, we can solve for w

subtract both sides by 12

divide both sides by 2

and we get

so,

the smallest possible measurement of the width is 14 feet

let x be the money she spent so that she can earn the free t-shirt.

since, she already spent $112.49

⇒

also, as per the statement: jennifer must spend $250 or more in order to qualify for a free t-shirt at the store.

then,

we have an inequality i.,e

subtract 112.49 from both sides we get;

therefore, $137. 51 more money does jennifer need to spend so that she can earn the free t-shirt