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Phoenix [80]
3 years ago
6

What is the solution to x4 - 12x2+10>0

Mathematics
1 answer:
alexira [117]3 years ago
5 0

Answer:

  (-√(6-√26) < x < √(6-√26)) ∪ (x < -√(6 +√26)) ∪ (√(6 +√26) < x)

Step-by-step explanation:

Using x^2 = z, the equation can be rewritten as ...

  z^2 -12z +10 > 0

  (z -6)^2 -26 > 0

  |z -6| > √26

This resolves to two equations.

This one ...

  x^2 -6 < -√26 . . . . substitute x^2 for z

  |x| < √(6-√26) . . . . add 6, take the square root; use √a^2 = |a|

  -√(6-√26) < x < √(6-√26)

__

and this one ...

  x^2 -6 > √26

  |x| > √(6 +√26)

  x < -√(6 +√26) ∪ √(6 +√26) < x

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For f(x) = 2x+1 and g(x) = 3x-7, find (f-g)(x)
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Answer:

(f - g)(x) = -x + 8

General Formulas and Concepts:

  • Order of Operations: BPEMDAS

Step-by-step explanation:

<u>Step 1: Define</u>

f(x) = 2x + 1

g(x) = 3x - 7

(f - g)(x) = f(x) - g(x)

<u>Step 2: Simplify</u>

  1. Set up:                              (f - g)(x) = (2x + 1) - (3x - 7)
  2. Distribute -1:                     (f - g)(x) = 2x + 1 - 3x + 7
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Which represents the inverse of the function f(x) = 4x?
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2 years ago
The Golden Years Senior Citizen Center uses a phone tree to announce when the center will be closed for poor weather. When each
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Answer:

50 Minutes.

Step-by-step explanation:

The function c approximates the total number of calls made after m minutes since the start of the phone tree.

c(m)=\frac{2}{3}\times (3^{\frac{m}{10}}-1)

We need to find the number of minutes after which the total number of calls will 363.

Substitute c(m)=363 in the given function.

363=\frac{2}{3}\times (3^{\frac{m}{10}}-1)

Multiply 3/2 both sides.

363\times \frac{3}{2}=(3^{\frac{m}{10}}-1)

242=3^{\frac{m}{10}}-1

Add 1 on both sides.

243=3^{\frac{m}{10}}

3^5=3^{\frac{m}{10}}

On comparing both sides we get

5=\frac{m}{10}

Multiply both sides by 10.

50=m

Therefore, the total number of calls will 363 after 50 minutes since the start of the phone tree.

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Show work please!!! Solve the equation by completing the square. If necessary, round to the nearest hundredth.
weeeeeb [17]

Answer:

1. B 2. C

Step-by-step explanation:

1. x^2-18x+(18/2)^2=19+(18/2)^2

(x-18/2)^2=100

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Find the center, vertices, and foci for the ellipse 25x^2+64y^2=1600
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Answer:

Step-by-step explanation:

Answer:

Data

Equation               25x² + 64y² = 1600

Process

1.- Divide all the equation by 1600

                            25x²/1600 + 64y²/ 1600 = 1600/1600

-Simplify

                             x²/64 + y²/ 25 = 1

2.- Equation of a horizontal ellipse

                            

3.- Find a, b and c

   a² = 64             a = 8

   b² = 25             b = 5

-Calculate c with the Pythagorean theorem

                  a² = b² + c²

-Solve for c

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-Substitution

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-Simplification

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-Result

                 c = √13

4.- Find the center

         C = (0, 0)

5.- Find the vertices

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6.- Find the foci

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