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3 years ago

Complete the square

Mathematics

1 answer:

Nesterboy [21]3 years ago

4 0

Answer:

vertex at (1, -3)

Step-by-step explanation:

When x = 0

y² + 6y + 1 = 0

y² + 6y + = -1

y² + 6y + 9 = -1 + 9

(y + 3)² = 8 or (-y - 3)² = 8

y + 3 = √8 or -y - 3 = √8

y = - 3 +√8 or y = -3 - √8

(0, - 3 +√8) and (0, -3 - √8)

The mid point between these two is the average

y = ( - 3 + √8 + -3 - √8) / 2 = - 3

y² + 6y + 8x + 1 = 0

(-3)² + 6(-3) + 8x + 1 = 0

9 - 18 + 1 = -8x

- 8 = -8x

x = 1

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Factorize x^2/16+xy+4y^2

lisov135 [29]

Answer:

$\frac{x^2}{16} +xy+4y^2$ can be factored out as: $(\frac{x}{4} +2\,y)^2$

Step-by-step explanation:

Recall the formula for the perfect square of a binomial :

$(a+b)^2=a^2+2ab+b^2$

Now, let's try to identify the values of $a$ and $b$ in the given trinomial.

Notice that the first term and the last term are perfect squares:

$\frac{x^2}{16} = (\frac{x}{4} )^2\\4y^2=(2y)^2$

so, we can investigate what the middle term would be considering our $a=\frac{x}{4}$ , and $b=2y$ :

$2\,a\,b=2\,(\frac{x}{4}) \,(2\,y)=x\,y$

Therefore, the calculated middle term agrees with the given middle term, so we can conclude that this trinomial is the perfect square of the binomial:

$(\frac{x}{4} +2\,y)^2$

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3 years ago

If 0.22... < x <33 , which of the following could be the value of x?

masha68 [24]

Answer:

Step-by-step explanation:

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3 years ago

What is the mean of 20, 37, 43, 54, 83, 102, 117, 160, 208?

Alekssandra [29.7K]

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3 years ago

Q. A customer wants to re-carpet a living room andhallway. You charge $5.99 per square yard toremove old carpet and $4.50 per sq

Tanzania [10]

Living Room Area = 17.5 x 20 = 350 sq ft

Hall Area = 4 x 12 = 48 sq. ft.

Total area of carpeting: 340 + 48 = 398 sq. ft.

We need to convert total area in sq ft to sq yd. The conversion ratio is

1 sq ft = 0.11 sq yd

So, 398 sq ft would be:

398 * 0.11 = 44.22 sq yd.

Carpet removing rate is 5.99 per sq yd.

Removing rate would be:

44.22 * 5.99 = $264.88

Assuming you gotta install both carpet and pad,

Carpet + pad = 16.99 + 3 = 19.99 per sq yd.

You gotta buy for 44.22 sq yd.

So, it will cost (carpet):

44.22 * 19.99 = $883.96

Installing rate 4.50 per sq yrd, so to carpet 44.22 sq yd, would need:

4.50*44.22 = $198.99

Assuming carpet is provided by installation guys, total charge:

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1 year ago

What is the probability of rolling an odd number on one roll of dice

Tresset [83]

Answer: 1/2 or 50%

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Image is provided.

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3 years ago