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.
Hello!
Let's write this as an equation below.
310/3+d=295/d
As you can see, we can cross-multiply this proportion giving us the equation below.
310d=295(3+d)
310d= 295d+885
Now, we subtract 295d from both sides.
15d=885
Now we divide both sides of the equation by 15.
d=59
Therefore, Dana travels 59 mph.
I hope this helps!
F(-3)=(-2)*(-3)-4=6-4=2
F(-2)=(-2)*(-2)-4=4-4=0
F(-1)=(-2)*(-1)-4=2-4=-2
Answer:
A=b(1/2b-1)
112ft^2
Step-by-step explanation:
-Write the equation in factored form: A= b (1/2 b -1 )
-Supposed the base of the flower bed is 16 feet. What will the area be:
b=16 feet
Formula is A=1/2(1/2b-1)
Replace the b with 16
A=1/2 (16)^2 - 16
A=1/2 (256)-16
A=256/2 - 16
A=128-16
A=112 ft^2
The area will be 112 ft^2
Answer:
He have to invest $527.777778 .
Step-by-step explanation:
X : 4.75% = $10,000 : 90
