Answer:
- 5(x +1.5)^2
- 10(x +1)^2
- 1/4(x +2)^2
- 3(x +5/6)^2
Step-by-step explanation:
When your desired form is expanded, it becomes ...
a(x +b)^2 = a(x^2 +2bx +b^2) = ax^2 +2abx +ab^2
This tells you the overall factor (a) is the leading coefficient of the given trinomial. Factoring that out, you can find b as the root of the remaining constant.
a) 5x^2 +15x +11.25 = 5(x^2 +3x +2.25) = 5(x +1.5)^2
b) 10x^2 +20x +10 = 10(x^2 +2x +1) = 10(x +1)^2
c) 1/4x^2 +x +1 = 1/4(x^2 +4x +4) = 1/4(x +2)^2
d) 3x^2 +5x +25/12 = 3(x^2 +5/3x +25/36) = 3(x +5/6)^2
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<em>Additional comment</em>
If you know beforehand that the expressions can be factored this way, finding the two constants (a, b) is an almost trivial exercise. It gets trickier when you're trying to write a general expression in vertex form (this form with an added constant). For that, you must develop the value of b from the coefficient of the linear term inside parentheses.
Answer:
72 signs
Step-by-step explanation:
90 min = 1.5 hour
6 hours hangs 6/1.5 * 18 signs = 72
Answer:
20 dollars
Step-by-step explanation:
15 dollars times 12 people to see how much money she got/has right now is 180 dollars
then take 200-180 to get <u>20</u>
Answer:
3/-1
Step-by-step explanation:
the equation for slope is y2-y1/x2-x1
I chose the two points (4,2) and (0,-2) because that's where the line meets up
then I put them in the equation getting 4--2/0-2
simplifying getting you 6/-2
you can simplify more giving you 3/-1
