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patriot [66]
3 years ago
9

Re-write the equation without the h component.

Mathematics
1 answer:
levacccp [35]3 years ago
3 0

Answer:

f(x) = 2[\frac{3^x}{9}] + 2

f(x) = 8(4)^x

Step-by-step explanation:

Given

f(x) = 2(3)^{x-2} + 2

f(x) = \frac{1}{2}(4)^{x+2}

Required

Remove the h component

In a function, the h component is highlighted as:

f(x) = a^{x+h}

So, we have:

f(x) = 2(3)^{x-2} + 2

Split the exponents using the following law of indices:

a^m/a^n = a^{m-n}

f(x) = 2*\frac{3^x}{3^2} + 2

f(x) = 2*\frac{3^x}{9} + 2

f(x) = 2[\frac{3^x}{9}] + 2

<em>The h component has been removed</em>

f(x) = \frac{1}{2}(4)^{x+2}

Split the exponent using the following law of indices

a^{m+n} =a^m * a^n

So, we have:

f(x) = \frac{1}{2}(4)^x * 4^2

Express 4^2 as 16

f(x) = \frac{1}{2}(4)^x * 16

Divide 16 by 2

f(x) = 8(4)^x

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Answer:

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Step-by-step explanation:

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In the diagram shown of circle A, tangent MB is drawn along with chords BAC and BF . Secant MFE intersects BAC at G. It is known
mote1985 [20]

Answer:

  • arc BF = 76°
  • ∠M = 31°
  • ∠BGE = 121°
  • ∠MFB = 111°

Step-by-step explanation:

(a) ∠FBM is the complement of ∠FBC, so is ...

  ∠FBM = 90° -52° = 38°

The measure of arc BF is twice this angle, so is ...

  arc BF = 2∠FBM = 2(38°)

  arc BF = 76°

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(b) ∠M is half the difference between the measures of arcs BE and BF, so is ...

  ∠M = (1/2)(138° -76°) = 62°/2

  ∠M = 31°

__

(c) arc FC is the supplement to arc BF, so has measure ...

  arc FC = 180° -arc BF = 180° -76° = 104°

∠BGE is half the sum of arcs BE and FC, so is ...

  ∠BGE = (1/2)(arc BE +arc FC) = (138° +104°)/2

  ∠BGE = 121°

__

(d) ∠MFB is the remaining angle in ∆MFB, so has measure ...

  ∠MFB = 180° -∠M -∠FBM = 180° -31° -38°

  ∠MFB = 111°

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3 years ago
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