3 years ago

Solve the inequality. Explain all steps and identify the properties used. 3a−4≤5

Mathematics

1 answer:

kipiarov [429]3 years ago

4 0

Answer:

a≤3

Step-by-step explanation:

3a-4≤5

Move constant to the right hand side and change its sign

3a≤5+4

Add the numbers

3a≤9

Divide both sides of th inequality by 3

a≤3

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The 13th term of a geometric sequence is 16, 384 and the first term is 4. What is the common ratio?

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Answer:

$\large \boxed{2}$

Step-by-step explanation:

The formula for the nth term of a geometric sequence is

aₙ = a₁rⁿ⁻¹

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$\begin{array}{rcl}16384 & = & 4r^{(13 - 1)}}\\16384 & = & 4r^{12}\\4096 & = & r^{12}\\3.6124 & = & 12 \log r\\0.30102 & = & \log r\\r & = & 10^{0.30102}\\ & = & \mathbf{2}\\\end{array}\\\text{The common ratio is $\large \boxed{\mathbf{2}}$}$

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$\begin{array}{rcl}16384 & = & 4(2)^{12}\\16384 & = & 4(4096)\\16384 & = & 16384\\\end{array}$

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