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adelina 88 [10]
2 years ago
5

Please help!!! i'll give brainliest and offering 20 pts each!!!

Mathematics
1 answer:
Aleks04 [339]2 years ago
8 0

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.

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20 points!~ And thanks if you help me.
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3 years ago
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Sophie [7]

Answer:

1

Step-by-step explanation:

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3 years ago
Is the line through points P(0, –9) and Q(2, –8) perpendicular to the line through points R(1, 4) and S(3, 3)? Explain
Serjik [45]
The quickest way to tell if a line is perpendicular is to find the slope, so you'll need to get the slope for both lines

PQ = ((-8) - (-9))/(2 - 0) = 1/2

and, for reference, a perpendicular slope is the negative reciprocal of the original (so we're looking for -2)

RS = (3 - 4)/(3 - 1) = -1/2

so, no, these two lines aren't perpendicular because the slope of RS is only the negative of PQ, not the negative <em>reciprocal</em>.
3 0
3 years ago
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