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:
<em>4.5%</em>
Step-by-step explanation:
From the question, we are informed that Diego measured the length of a pen to be 22 cm while the actual length of the pen is 23 cm.
The percentage decrease:
= (23 - 22)/22 × 100
= 1/22 × 100
= <em>4.5%</em>
good luck :)
The answer is the number that 'x' must be in order for
that equation to be a true statement. Here's one way
to find out what the number is:
x + 36 = 4x
Subtract 'x' from each side: 36 = 3x
Divide each side by 3 : 12 = x
The probabilities of picking a red, blue, and yellow marble must be equal to 1. so
P(R)+P(Y)+P(B)=1
1/6+1/2+P(B)=1 making all terms have a common denominator of 6 we have:
1+3+6P(B)=6
4+6P(B)=6
6P(B)=2
P(B)=2/6
P(B)=1/3
I think its a but im not sure im sorry if im wrong its been awhile
