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3 years ago

Evaluate the expression.

Mathematics

2 answers:

Masja [62]3 years ago

5 0

Answer:

-20x

Step-by-step explanation:

4x - 11 × (14 - 10)

-5x (4)

-20x

aivan3 [116]3 years ago

5 0

Let's simplify step-by-step.
4x−11x(14−10)
=4x+−44x
Combine Like Terms:
=4x+−44x
=(4x+−44x)
=−40x

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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?

AleksAgata [21]

Answer:

$\large \boxed{2}$

Step-by-step explanation:

The formula for the nth term of a geometric sequence is

aₙ = a₁rⁿ⁻¹

In your geometric sequence, a₁ = 4 and a₁₃ = 16 384.

$\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 $\large \boxed{\mathbf{2}}$}$

Check:

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

It checks.

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