True because 5(3)=15-1=14 and 14/2=7
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.
Area of the shaded region = area of big square minus area of little square.
Here is the set up:
Let A_s = area of shaded region.
A_s = (2x + 2)(3x - 4) - [(x - 3)(x - 6)]
Take it from here.
Answer:
StartFraction 50 miles Over 1 hour EndFraction = StartFraction 200 miles Over question mark hours EndFraction
Step-by-step explanation:
For constant speed, miles and hours are proportional. One possible equation is ...
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<em>Comment on the solution</em>
I personally like to put the unknown in the numerator, so the equation can be solved in one step. The equation above requires two steps: one to cross-multiply, and one to divide by 50.
I might write the equation as ...
(? hours)/(200 mi) = (1 hour)/(50 mi) . . . . multiply by 200 mi to solve
Another way to write the equation is matching the ratios of times to corresponding miles:
(? hours)/(1 hour) = (200 mi)/(50 mi)
This only requires simplification to solve it: ? = 4.
