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2 years ago

8

Write 12/root2 + root18 in the form broot2 where b is an interger

1 answer:

katrin2010 [14]2 years ago

5 0

$\dfrac{12}{\sqrt 2} + \sqrt{18}\\\\\\=\dfrac{12 + \sqrt{18 \times 2}}{\sqrt 2}\\\\\\=\dfrac{12+\sqrt{9 \times 4}}{\sqrt 2}\\\\\\=\dfrac{12+3 \times 2}{\sqrt 2}\\\\\\=\dfrac{18}{\sqrt 2}\\\\\\=\dfrac{18\sqrt 2}{\left(\sqrt 2\right)^2}\\\\\\=\dfrac{18\sqrt 2}2\\\\\\=9\sqrt 2$

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lara31 [8.8K]

Answer:

(x + 1)² + (y + 1)² = (√6)²

Step-by-step explanation:

Group the x- and y- terms together:

9x^2 + 18x + 9y^2 + 9y = 36

Factor out the coefficient 9:

x^2 + 2x + y^2 + y = 4

Complete the square of x^2 + 2x and then do the same for y^2 + 2y:

x^2 + 2x + 1 - 1 + y^2 + 2y + 1 - 1 = 4

Rewrite x^2 + 2x + 1 as the square of the binomial x + 1:

(x + 1)^2 + (y + 1)^2 - 2 = 4

Collect the constant terms on the right side:

(x + 1)^2 + (y + 1)^2 = 6

Rewrite 6 as (√6)^2:

(x + 1)² + (y + 1)² = (√6)² is the equation in standard form (x - h)² + (y - k)² = r²

Completing the square is done as follows: x^2 + 2x

Start with x^2 + 2x

1. Take half of the coefficient of x, which results in 2/2, or 1

2. Square this result and add it to, and subtract it from x^2 + 2x

x^2 + 2x + 1 - 1

3. Rewrite the first three terms as the square of a binomial:

x^2 + 2x + 1 - 1 = (x + 1)² - 1.

Do the same for y² + 2y.

7 0

3 years ago

Help! What is the average rate of change of f(x)=x^2+3x+6 over the interval -3 less-than-or-equal-to x less-than-or-equal-to 3?

Makovka662 [10]

Answer:

The average rate of change of the function over the interval is 5.

Step-by-step explanation:

Average rate of change of a function:

The average rate of change of a function f(x) over an interval [a,b] is given by:

$A = \frac{f(b)-f(a)}{b-a}$

Interval -3 less-than-or-equal-to x less-than-or-equal-to 3

This means that $a = -3, b = 3$

$f(x) = x^2 + 3x + 6$

So

$f(b) = f(3) = (3)^2 + 3(3) + 6 = 9 + 9 + 6 = 24$

$f(a) = f(-3) = (-3)^2 + 3(-3) + 6 = 9 - 9 + 6 = 6$

Average rate of change

$A = \frac{f(b)-f(a)}{b-a} = \frac{24+6}{3-(-3)} = \frac{30}{6} = 5$

The average rate of change of the function over the interval is 5.

8 0

3 years ago

Did you hear about the two punsters who told a lot of jokes about cats

Rudik [331]

Cool. and. gooooooooood.

6 0

3 years ago

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Evaluate 5! + 2!.<br> Idk what is it

Sedbober [7]

Answer:

122

Step-by-step explanation:

If a number has an explanation point on the side of it, you should multiply all numbers that are equal to are less than that number.

$5!=5*4*3*2*1=120\\2!=2*1=2\\120+2=122$

4 0

3 years ago

Plz help pretty easy

cricket20 [7]

a and d b and c that's the answer

4 0

3 years ago

Read 2 more answers