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3 years ago

Which statement best explains whether the table represents a linear or nonlinear function? (4 points)

Mathematics

1 answer:

stich3 [128]3 years ago

4 0

Answer:

Step-by-step explanation:

Nonlinear, because the slope is not constant - it keeps changing.

Slope between (1,1) and (1,2) is (1/1) or 1

Slope between (2,4) and (16,3) is:

Rise = (3-4) = -1

Run = (16-2) = 14

Slope = 14/-1 or -14

Definitely not linear. The slope changes dramatically very quickly. A straight line would disapprove.

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Which equation has x = –6 as the solution?

olya-2409 [2.1K]

Answer:

The equation 'log Subscript 3 Baseline (negative 2 x minus 3) = 2' i.e. $\log _3\left(-2x-3\right)=2$ has x = –6 as the solution.

Step-by-step explanation:

<u>Checking the equation</u>

log Subscript 3 Baseline (negative 2 x minus 3) = 2

Writing in algebraic expression

$\log _3\left(-2x-3\right)=2$

Use the logarithmic definition

$\mathrm{If}\:\log _a\left(b\right)=c\:\mathrm{then}\:b=a^c$

$\log _3\left(-2x-3\right)=2\quad \Rightarrow \quad \:-2x-3=3^2$

$-2x-3=3^2$

$-2x-3=9$

$-2x=12$

$\mathrm{Divide\:both\:sides\:by\:}-2$

$\frac{-2x}{-2}=\frac{12}{-2}$

$x=-6$

Therefore, the equation 'log Subscript 3 Baseline (negative 2 x minus 3) = 2' i.e. $\log _3\left(-2x-3\right)=2$ has x = –6 as the solution.

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