Which of the following is the result of the equation below after completing the square and factoring? x^2+3x+8=6
1 answer:
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Answer:
x = -4, 5/2
Step-by-step explanation:
A quadratic can be solved may ways, including graphing, factoring, and the quadratic formula. You can also check possible answers by making use of the relationships between solutions and the coefficients.
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A graph is attached. It shows the solutions to be -4 and 5/2.
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When factored, the equation becomes ...
(2x -5)(x +4) = 0 . . . . . has solutions x=-4, x=5/2 (these make the factors zero)
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Using the quadratic formula, the solutions of ax^2 +bx +c = 0 are found from ...
x = (-b±√(b²-4ac))/(2a)
x = (-3±√(3²-4(2)(-20))/(2(2)) = (-3±√169)/4 = {-16, +10}/4
x = {-4, 5/2}
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For ax^2 +bx +c = 0, the solutions must satisfy ...
product of solutions is c/a = -20/2 = -10
Only the first and last choices have this product.
sum of solutions is -b/a = -3/2
Only the first choice (-4, 5/2) has this sum.
Answer:
Number of pounds of dried mangoes Chloe bought = 3.5
Number of pounds of dried kiwi Chloe bought bough = 6.5
Step-by-step explanation:
Total number of pounds of dried fruit purchased = 10
Let number of pounds of dried mango purchased =
Let number of pounds of dried kiwi purchased be =
Total weight of dried fruits purchased =
So, we have a sum equation as:
Total cost of dried fruits = $40.34
Cost of a pound of dried mango = $2.11
Cost of pounds of dried mango in dollars can be given as =
Cost of a dried kiwi = $5.07
Cost of pounds of dried kiwi in dollars can be given as =
Total cost of dried fruits in dollars =
So, we have a cost equation as:
The system of equations is :
A)
B)
Solving by substitution.
Rearranging equation A, to solve for in terms of
Subtracting both sides by
Substituting value of we got from A into equation B.
Using distribution.
Simplifying.
Subtracting both sides by 50.7.
Dividing both sides by -2.96.
∴
We can plugin in the rearranged equation A to get value of
∴
So, number of pounds of dried mangoes Chloe bought = 3.5
Number of pounds of dried kiwi Chloe bought bough = 6.5