SOLUTION: 1.)The sum of the squares of 2 consecutive negative integers is 41. What are the numbers? Which of the following equations is the result of using the factoring method to solve th

Question 823269: 1.)The sum of the squares of 2 consecutive negative integers is 41. What are the numbers?
Which of the following equations is the result of using the factoring method to solve the problem?
(n - 5)(n - 4) = 0
(n - 5)(n + 4) = 0
(n + 5)(n - 4) = 0
(n + 5)(n + 4) = 0
2.) 1/5x^2=x-4/5
{-1, -4}
{1, -4}
{1, 4}
3.)Write the quadratic equation in factored form. Be sure to write the entire equation.
x 2 - 5x - 24 = 0
4.)Write a quadratic equation in factored form to model the given problem. Be sure to write the entire equation.
The height of a triangle is 4 more than the base, and the area of the triangle is 6 square units. Find the length of the base. Let x = the length of the base.
Answer by TimothyLamb(4379) (Show Source): You can put this solution on YOUR website!
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you have four different problems here!
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I will do the first two for you:
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problem 1:
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y = x + 1
xx + yy = 41
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xx + yy = 41
xx + (x + 1)(x + 1) = 41
xx + xx + 2x + 1 = 41
2xx + 2x - 40 = 0
xx + x - 20 = 0
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factoring:
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(x - 4)(x + 5)
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problem 2:
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1/5x^2 = x - 4/5
y = 1/5x^2 - x + 4/5 = 0
y = 0.2x^2 - x + 0.8 = 0
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the above quadratic equation is in standard form, with a=0.2, b=-1, and c=0.8
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to solve the quadratic equation, by using the quadratic formula, copy and paste this:
0.2 -1 0.8
into this solver: https://sooeet.com/math/quadratic-equation-solver.php
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this quadratic has two real roots (the x-intercepts), which are:
x = 4
x = 1
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answer:
x = 4
y = 1
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NOTE: since this answer doesn't match any of the answers given in the problem statement, the problem statement probably contains errors.
if this answer is not what you expected, check the problem statement, fix any errors, and resubmit the question.
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answer:
distance from the bottom of the ladder to building = 3 m
distance from the ground to the top of ladder = 4 m
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Solve and graph linear equations:
https://sooeet.com/math/linear-equation-solver.php
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Solve quadratic equations, quadratic formula:
https://sooeet.com/math/quadratic-formula-solver.php
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Solve systems of linear equations up to 6-equations 6-variables:
https://sooeet.com/math/system-of-linear-equations-solver.php
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