algebra word problems?

Question

Solve the following problems involving applications of polynomials.
Please show how to do these.

1.Three consecutive even integers are such that the square of the third is 76 more than the square of the second. Find the three integers.

2. A rectangular parking lot is 50 ft longer than it is wide. Determine the dimensions of the parking lot if it measures 250 ft diagonally.

Answer 1

Problem 1. Let n be the middle integer. (It makes the algebra a little easier.) Then the three integers are n-2, n, and n+2. From the problem, we have:

(n+2)^2 = n^2 + 76
n^2 + 4n + 4 = n^2 + 76
4n = 72
n = 18

The integers are 16, 18, and 20 (Answer). 20^2 = 400 and 18^2 is 324. The difference is 76.


Problem 2. Let x be the width, so x+50 is the length. From the Pythagorean Theorem,

x^2 + (x+50)^2 = 250^2
x^2 + x^2 + 100x + 2500 = 62500
2x^2 + 100x = 62500 - 2500 = 60000
x^2 + 50x = 30000 (Equation 1)

Complete the square:

x^2 + 50x + 25^2 = 30000 + 25^2 = 30625
(x + 25)^2 = 30625 = 175^2

x can't be negative, so

x = -25 + 175 = 150 feet

The parking lot measures 200 ft by 150 ft (Answer).

[Note: Although I completed the square because I was lazy, Equation 1 can be factored; it's a 3-4-5 right triangle.]

x^2 + 50x = 30000 (Equation 1)
x^2 + 50x - 30000 = 0
(x + 200) (x - 150) = 0

So you also get x=150 this way, by factoring.

Answer 2

Q1.
c=(b+1)=(a+2) that is c is 1 larger than b and 2 larger than a (ie consequetive)
c(squared)=(b+1)squared
cxc = (b+1)x(b+1)
therefore :
csquared = bsquared +1b +1
if cSquared is 76 more than bsquared:
csquared = bsquared +76
therefore form 2 above equations 76 = 1b +1
therefore b=75
so a = 74, b =75, c = 76

Answer 3

If the students present day grade is a ninety% then we’re for sure assuming it’s out of one hundred% ninety/one hundred Now because the students grade stronger 20% from the merely correct grading era then you surely upload that to the previous one hundred% supplying you with ninety/ 120 = .seventy 5 and on the grounds that grades are in opportunities you multiply .seventy 5 by technique of one hundred supplying you with seventy 5% because the students previous grade