SOLUTION: please solve the following: 1.find two numbers whose sum is 13 and whose product is 40 2.the area of a rectangle is 94sq. units and its perimeter is 38units. find the length a

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: please solve the following: 1.find two numbers whose sum is 13 and whose product is 40 2.the area of a rectangle is 94sq. units and its perimeter is 38units. find the length a      Log On


   

Question 874921: please solve the following:
1.find two numbers whose sum is 13 and whose product is 40
2.the area of a rectangle is 94sq. units and its perimeter is 38units.
find the length and width of the rectangle.
3.form an equation whose roots are the additive inverse of the roots
+10t%5E2-12=-7t+
Answer by josgarithmetic(39838) About Me  (Show Source):
You can put this solution on YOUR website!
Those are two very simple problems, and one interesting problem.

(1)
x and y.
x+y=13 and xy=40. Solve for x and y. You will use a quadratic equation.

(2)
x and y.
2x+2y=38 and xy=94. Solve for x and y. You will use a quadratic equation.

(3)
Very interesting.
10t%5E2%2B7t-12=0
t=%28-7%2B-+sqrt%2849%2B4%2A10%2A12%29%29%2F%282%2A10%29
t=%28-7%2B-+sqrt%28529%29%29%2F%282%2A10%29
t=%28-7%2B-+23%29%2F20
highlight_green%28t=-3%2F2%29 OR highlight_green%28t=16%2F20=4%2F5%29.
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Question asks for additive inverses of those roots to be roots in another equation, and to give that equation. "Form the equation...".
highlight%28%28y-3%2F2%29%28y%2B4%2F5%29=0%29, this will serve.
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Note, its roots are 3%2F2 and -4%2F5, which are the additive inverses of the given equation in the question.