The sum of the squares of two consecutive integers is 145. Find the two integers. Please help asap .

The two integers are 8 and 9.

Step-by-step explanation: Let n represent the number.

n^2 + (n + 1)^2 = 145

By foiling, this can be rearranged to:

n^2 + n^2 + 2n + 1 = 145

Subtract 145 from both sides:

2n^2 + 2n - 144 = 0

Divide both sides by 2:

n^2 + n - 72 = 0

Factor the polynomial:

(n + 9)(n - 8) = 0

Solve for n:

n = -9, n = 8

Since they need to be consecutive, make the 9 positive. It will be positive either way because it is being squared.

Now, n = 9 and n = 8.

These are your two integers. Hope this helps!

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step-by-step explanation:

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