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ella [17]
3 years ago
6

How to complete the square with a leading coefficient?

Mathematics
1 answer:
Kamila [148]3 years ago
8 0
Factor out the leading coefficient:

ax^2+bx+c=a\left(x^2+\dfrac bax+\dfrac ca\right)

Now complete the square:

x^2+\dfrac bax+\dfrac ca=x^2+\dfrac bax+\dfrac{b^2}{4a^2}-\dfrac{b^2}{4a^2}+\dfrac ca=\left(x+\dfrac b{2a}\right)^2-\dfrac{b^2}{4a^2}+\dfrac{4ac}{4a^2}=\left(x+\dfrac b{2a}\right)^2-\dfrac{b^2-4ac}{4a^2}

Now, redistributing the leading a gives

a\left(x+\dfrac b{2a}\right)^2-\dfrac{b^2-4ac}{4a}
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If the ratio of purple marbles to orange marbles is 3 to 8, how many orange marbles will I have if I have 48 purple marbles?
sveticcg [70]

Answer:

You will have 128 orange marbles

Step-by-step explanation:

Set this up as an equation

Variable x = number of orange marbles

3/8 = 48/x

Cross multiply

3 × x = 8 × 48

3x = 384

Divide both sides by 3 to isolate the variable

3x ÷ 3 = 384 ÷ 3

1x = 128

x = 128

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Check work:

Substitute the variable x for the answer

3/8 = 48/128

Cross multiply

3 × 128 = 8 × 48

384 = 384

If the numbers equal, the answer is correct

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3 years ago
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Triangle A(-2,7) B(-2,3) and C(-5,3) is reflected in the line X=0. Find A' , B' and C' the image co ordinates of triangle ABC.​
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255290.4Aacdn

Step-by-step explanation:

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A flying disc in the shape of a circle has a circumference of 8 inches. What is the radius of the flying disc.
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A.

Step-by-step explanation:

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