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Orlov [11]
2 years ago
8

Rewrite the function by completing the square.

Mathematics
1 answer:
ddd [48]2 years 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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KATRIN_1 [288]
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A number line going from negative 3 to positive 5. a closed circle is at negative 1.5. everything to the left of the circle is s
algol13

The inequalities which matches the graph are: x ≥ ₋1.5 and ₋1.5 ≤ x

Given, a number line is moving from ₋3 to ₊5 .

Next a mark is made at ₋1.5 and everything to its left is shaded which means not visible.

When we mark the point and shade the left part of it then we can start applying the inequality expressions.

And from that we can match the applicable inequalities while observing the graph.

  • For the first inequality ₋1.5 ≥ x.Here,x value ranges from ₋1.5 to ₊5, hence we take this as an inequality expression.
  • Next, if we consider x ≤ ₋1.5, then here x value will range from ₋1.5 to ₋3. where the region is shaded. Hence this expression doesn't satisfy the graph.
  • the next expression is ₋1.5 ≤ x. here the value will again range in the shaded area so it is not applicable.
  • ₋1.5 ≥ x, here the values will satisfy the graph.
  • remaining inequality expressions does not support the graph.

Therefore the only inequalities the graph represents is  x ≥ ₋1.5 and ₋1.5 ≤ x

Learn more about "Linear Inequalities" here-

brainly.com/question/371134

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5 0
2 years ago
Can someone help with an explanation? This is finding Surface Area.​
Y_Kistochka [10]
The answer should be 95in^2

Explanation:

You’re essentially just finding the area of all the shapes on the triangle and adding them together.

Area of a triangle = 1/2•b•h
Area of a square = l•w or just s2

The area of the triangles given what we have in the diagram can be found with
1/2•5•7 = 17.5

There are 4 triangles so you multiply 17.5 by 4 which gives 70

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2 years ago
You have 108 seats, there are 12 times as many seats as rows, how many rows
nignag [31]
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If sin ⁡x=725, and 0 ∠ x ∠ pi/2, what is the tan (x - pi/4)
krok68 [10]

Tan(x-\frac{\pi }{4}) = \frac{-17}{31}

<u>Step-by-step explanation:</u>

Here we have ,  sin ⁡x=7/25( given sin x = 725 which is not possible ) , 0 . Let's find tan (x - pi/4):

⇒ Tanx = \frac{sinx}{cosx}

⇒ Tanx = \frac{sinx}{\sqrt{1-(sinx)^{2}}}

⇒ Tanx = \frac{\frac{7}{25}}{\sqrt{1-(\frac{7}{25})^{2}}}

⇒ Tanx = {\frac{7}{25}}{\sqrt{(\frac{625}{625-49})^{}}}

⇒ Tanx = {\frac{7}{25}}(\frac{25}{24} )

⇒ Tanx = {\frac{7}{24}}

Now , Tan(x-\frac{\pi }{4}) = \frac{Tanx - Tan(\frac{\pi }{4} )}{1+ Tanx(Tan(\frac{\pi }{4} )}

⇒ Tan(x-\frac{\pi }{4}) = \frac{Tanx -1}{1+ Tanx(1)}

⇒ Tan(x-\frac{\pi }{4}) = \frac{\frac{7}{24}  -1}{1+\frac{7}{24} }

⇒ Tan(x-\frac{\pi }{4}) = \frac{\frac{7-24}{24} }{\frac{7+24}{24} }

⇒ Tan(x-\frac{\pi }{4}) = \frac{-17}{24} (\frac{24}{31} )

⇒ Tan(x-\frac{\pi }{4}) = \frac{-17}{31}

7 0
3 years ago
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