We do completing the square as follows:
1. Put all terms with variable on one side and the constants on the other side.
<span>5x^2 - 3x = 25
2. Factor out the coefficient of the x^2 term.
</span>5(x^2 - 3x/5) = 25
3. Inside the parentheses, we add a number that would complete the square and also add this to the other side of the equation. In this case we add 9/100 and on the other side we add 9/20.
5(x^2 - 3x/5 + 9/100) = 25 + 9/20
4. We simplify as follows:
5(x^2 - 3x/5 + 9/100) = 25 + 9/20
5(x - 3/10)^2 = 509/20
(x - 3/10)^2 = 509/100
x1 = √(509) /100 + 3/10
x2 = -√(509) /100 + 3/10
F(1) = (1)^3 + 2(1)^2 - 5(1) - 6 = 1 + 2 - 5 - 6 = -8; x = 1 is not a solution to the polynomial.
f(-1) = (-1)^3 + 2(-1)^2 - 5(-1) - 6 = -1 + 2 + 5 - 6 = 0; x = -1 is a solution to polynomial.
From the options, a or c has x = -1, both has x = , so lets check for x = 3
f(3) = (3)^3 + 2(3)^2 - 5(3) - 6 = 27 + 18 - 15 - 6 = 24; x = 3 is not a solution to the polynomial.
Therefore the solutions to the polynomial are x = -3, x = -1, x = 2
According to the number of cups, 564 people can be invited to the party.
Step-by-step explanation:
This is a simple question of cross multiplication
<u>DATA:</u>
<em>1. Total number of cups of yogurt is 423 cups</em>
<em>2. 1 serving = th of a cup</em>
<em>3. Each guest gets of a cup or 1 serving</em>
<em>4. Find out how many guests can be invited to the party,</em>
Cups : People
: 1
423 : p
<em>5. Cross multiply</em>
p = 423 x 1
3p = 423 x 4
p =
p = 564
Therefore, according to the number of cups, 564 people can be invited to the party.
Key word: Multiplication
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