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1 year ago

Rewrite the function by completing the square.

Mathematics

1 answer:

ddd [48]1 year ago

6 0

Answer:

f(x) = (x -6)² +14

Step-by-step explanation:

Completing the square involves writing part of the function as a perfect square trinomial.

<h3>Perfect square trinomial</h3>

The square of a binomial results in a perfect square trinomial:

(x -h)² = x² -2hx +h²

The constant term (h²) in this trinomial is the square of half the coefficient of the linear term: h² = ((-2h)/2)².

<h3>Completing the square</h3>

One way to "complete the square" is to add and subtract the constant necessary to make a perfect square trinomial from the variable terms.

Here, we recognize the coefficient of the linear term is -12, so the necessary constant is (-12/2)² = 36. Adding and subtracting this, we have ...

f(x) = x² -12x +36 +50 -36

Rearranging into the desired form, this is ...

f(x) = (x -6)² +14

<em>Additional comment</em>

Another way to achieve the same effect is to split the given constant into two parts, one of which is the constant necessary to complete the square.

f(x) = x² -12x +(36 +14)

f(x) = (x² -12x +36) +14

f(x) = (x -6)² +14

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Find the shortest distance, d, from the point (5, 0, −6) to the plane x + y + z = 6.

DENIUS [597]

Answer:

$\frac{7}{\sqrt{3}}$

Step-by-step explanation:

The shortest distance d, of a point (a, b, c) from a plane mx + ny + tz = r is given by:

$d = |\frac{(ma + nb + tc - r)}{\sqrt{m^2 + n^2 + t^2}} |$ --------------------(i)

From the question,

the point is (5, 0, -6)

the plane is x + y + z = 6

Therefore,

a = 5

b = 0

c = -6

m = 1

n = 1

t = 1

r = 6

Substitute these values into equation (i) as follows;

$d = |\frac{((1*5) + (1*0) + (1 * (-6)) - 6)}{\sqrt{1^2 + 1^2 + 1^2}} |$

$d = |\frac{((5) + (0) + (-6) - 6)}{\sqrt{1 + 1 + 1}} |$

$d = |\frac{(-7)}{\sqrt{3}} |$

$d = \frac{7}{\sqrt{3}}$

Therefore, the shortest distance from the point to the plane is $d = \frac{7}{\sqrt{3}}$

5 0

3 years ago

40 POINTS IF YOU ANSWER CORRECTLY!

noname [10]

Answer:

Step-by-step explanation:

y is 15.49

Formula is b = √c^2-a^2

You could use sine [ opposite/hypotenuse ],

Cosine [adjacent/hypotenuse]

or Tangent [ opposite/adjacent ]

to find theta

Theta is 75.522

6 0

2 years ago

What is 1/2 to 1/4 equals

sergey [27]

Do you mean 1/2 of 1/4 if so it’s just timsing the numerator by the numerator and the denominator by the denominator. So, 1 x 1 = 1 and 2 x 4 = 8

Therefore it’s 1/8!

If you didn’t understand I’ll gladly elaborate!

4 0

2 years ago

PLEASE HELP !!!!!!! For what value of x is line m parallel to line n? Enter your answer in the box. x = Line m is parallel to li

Sonja [21]

Answer:

$x=10$

Step-by-step explanation:

we know that

When two lines are crossed by another line (transversal), the angles in matching corners are called Corresponding Angles.

When the line are parallel the corresponding angles are equal in measurement.

In this problem

$(8x+50)\°=130\°$ -----> by corresponding angles

see the attached figure to better understand the problem

Solve for x

Subtract 50 both sides

$8x=130-50$

$8x=80$

Divide by 8 both sides

$x=80/8$

$x=10$

7 0

2 years ago

Please help!! The slope of the line passing through the points (-3, 4) and (4, -1) is ___.

oksano4ka [1.4K]

I hope this helps you

slope=m

(-3,4) x'=-3 y'=4

(4,-1) x"=4 y"=-1

slope formula :

m. (x'-x")=y'-y"

m. (-3-4)=4-(-1)

m.-7=4+1

m=-5/7

4 0

2 years ago