Question

Help me with these math questions.

Answer 1

graph A

no x-intercept

no y-intercept

H.A is y = 5

V. A. is x = 0

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Answer: $\frac{150}{31}$

Step by step explanation:

log₆(5x + 6) - log₆(x - 4) = 2

log₆$(\frac{5x+6}{x-4})$ = 2

$(\frac{5x+6}{x-4})$ = 6²

$(\frac{5x+6}{x-4})$ = 36

5x + 6 = 36(x - 4)

5x + 6 = 36x - 144

       6 = 31x - 144

    150 = 31x

     $\frac{150}{31}$ = x

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Answers:

• a. (-1, -5)
• b. up
• c. x = -1
• d. $\frac{-2+\sqrt{15}}{3} and\frac{-2-\sqrt{15}}{3}$
• e. -2
• f. see attachment
• g. domain (-∞, ∞)  range [-5, ∞)

Explanation:

f(x) = 3x² + 6x - 2

      a=3  b=6 c=-2

x = $\frac{-b}{2a} =\frac{-6}{2(3)} = \frac{-6}{6} = -1$

Axis Of Symmetry: x = -1

f(-1) = 3(-1)² + 6(-1) - 2

       = 3 - 6 - 2

       = -5

Vertex: (-1, -5)

x = $\frac{-b+/-\sqrt{b^{2}-4ac}}{2a}$

  = $\frac{-6+/-\sqrt{6^{2}-4(3)(-2)}}{2(3)}$

  = $\frac{-6+/-\sqrt{36+24}}{6}$

  = $\frac{-6+/-\sqrt{60}}{6}$

  = $\frac{-6+/-2\sqrt{15}}{6}$

  = $\frac{-2+/-\sqrt{15}}{3}$

x-intercepts: $\frac{-2+/-\sqrt{15}}{3}$