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
_____
<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:
x=-15, y=25. (-15, 25).
Step-by-step explanation:
2x+3y=45
x+y=10
--------------
x=10-y
2(10-y)+3y=45
20-2y+3y=45
20+y=45
y=45-20
y=25
x+25=10
x=10-25
x=-15
Answer:
9.264817823
Step-by-step explanation:
If you use your calculator, press the log function button. Then type this (10 x 184,000,000). It will now give you your final answer.
Answer:
2 years
Step-by-step explanation:
$400 x 14% = $56
$56 x 2 = $112
Answer: 29/139
Explanation:
Total student: 139 (66 boys/73 girls)
Football: 56 student (28 boy/28 girl)
Tennis: 54 student (27 boy/ 27 girl)
Running: 29 student (18 girls/11 boys)
The probability that a student chose running is 29/139
