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ExtremeBDS [4]
3 years ago
7

18 points please help pic inserted

Mathematics
1 answer:
g100num [7]3 years ago
6 0

Answer:

1). \text{log}_4(5x^2+2)=\text{log}_4(x + 8)

2). log(x - 1) + log5x = 2

3). ln(x + 5) = ln(x - 1) + ln(x + 1)

4). e^{x^2}=e^{4x+5}

Step-by-step explanation:

1). ln(x + 5) = ln(x - 1) + ln(x + 1)

   ln(x + 5) = ln(x - 1)(x + 1)  [Since ln(a×b) = ln a + lnb]

   (x + 5) = (x- 1)(x + 1)

   x + 5 = x² - 1

   x² - x - 6 = 0

   x² - 3x + 2x - 6 = 0

   x(x - 3) + 2(x - 3) = 0

   (x + 2)(x - 3 ) = 0

   x = -2, 3

   But x = -2 is an extraneous solution.

  Therefore, x = 3 is the only solution.

2). e^{x^2}=e^{4x+5}

  x² = 4x +5

  x² - 4x - 5 = 0

  x² - 5x + x - 5 = 0

  x(x - 5) + 1(x - 5) = 0

  (x + 1)(x - 5) = 0

  x = -1, 5

  Therefore, solution set is (-1, 5)

3). \text{log}_4(5x^2+2)=\text{log}_4(x + 8)

   5x² + 2 = (x + 8)  

   5x² - x - 6 = 0

   5x² - 6x + 5x - 6 = 0

   x(5x - 6) + 1(5x - 6) = 0

   (x + 1)(5x - 6) = 0

   x = -1, \frac{6}{5}

4). log(x - 1) + log5x = 2

    log(x - 1)(5x) = 2

    5x(x - 1) = 10² [if loga = b, a=10^{b}]

    5x² - 5x - 100 = 0

    x² - x - 20 = 0

    x² - 5x + 4x - 20 = 0

    x(x - 5) + 4(x - 5) =0

    (x - 5)(x + 4) = 0

    x = -4, 5

But x = -4 is an extraneous solution.

Therefore, x = 5 is the only solution.

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11/ 42 Marks
amm1812

Answer:

(a)x=128 degrees

(b)\angle APD\neq 116^\circ

Step-by-step explanation:

\angle ABD+\angle CBD =180^\circ$ (Linear Postulate)\\\angle ABD+116^\circ =180^\circ\\\angle ABD=180^\circ-116^\circ\\\angle ABD=64^\circ

(a) Now:

\angle AOD=2 \times \angle ABD$ (Angle at the centre is twice the  angle at the circumference)\\x=2 \times 64^\circ\\x=128^\circ

(b)

\angle APD=2 \times \angle ABD$ (Inscribed Angle Theorem)\\\angle APD=2 \times 64^\circ\\ \angle APD=128^\circ

\angle APD\neq 116^\circ

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Answer:

C) 125°

Step-by-step explanation:

Supplementary angles add to 180 degrees.  Complementary angles add to 90

An angle's complement is 35°.

35+x =90

Subtract 35 from each side

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x = 55

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55+y = 180

Subtract 55 from each side

55-55+y = 180-55

y= 125

The angle is 55 so its supplement is 125

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Step-by-step explanation:

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s5 = 24×2 = 48

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s17 = 3 × 2¹⁶ = 3 × 65,536 = 196,608

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