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:
`(150)/(31)`

Step by step explanation:

log₆(5x + 6) - log₆(x - 4) = 2

log₆
`((5x+6)/(x-4))` = 2

`((5x+6)/(x-4))` = 6²

`((5x+6)/(x-4))` = 36

5x + 6 = 36(x - 4)

5x + 6 = 36x - 144

6 = 31x - 144

150 = 31x

`(150)/(31)` = x

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Answers:

• a. (-1, -5)
• b. up
• c. x = -1
• d.
  `(-2+√(15))/(3) and(-2-√(15))/(3)`
• e. -2
• f. see attachment
• g. domain (-∞, ∞) range [-5, ∞)

Step-by-step explanation:

f(x) = 3x² + 6x - 2

a=3 b=6 c=-2

x =
`(-b)/(2a) =(-6)/(2(3)) = (-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)}`

=
`(-6+/-√(36+24))/(6)`

=
`(-6+/-√(60))/(6)`

=
`(-6+/-2√(15))/(6)`

=
`(-2+/-√(15))/(3)`

x-intercepts:
`(-2+/-√(15))/(3)`