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boyakko [2]
3 years ago
6

Simplify each expression below.

Mathematics
1 answer:
MatroZZZ [7]3 years ago
7 0

Answer:

Step-by-step explanation:

A: 2/3 - 1/8 = 16/24 - 3/24 = 13/24  which is greater than 1/3. 8/24 = 1/3

B: 5/6 - 1/4 = 20/24 - 6/24 = 14/24 which is greater than 1/3. 8/24 = 1/3

C: 10/15 - 6/15 = 4/15. 5/15 = 1/3. This is smaller than 1/3

D: 1 1/4 - 1 1/8 = 1/8 which is less than 1/3

Answer: A and B

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Is 5 equal to -5 in math
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What is the center of the data?
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Median = 13

Step-by-step explanation:

Given

See attachment for dot plot

Required

The center of data

This implies that, we calculate the median

From the attached plot,

n = 13 --- number of observation

So, the median is:

Median = \frac{n + 1}{2}

Median = \frac{13 + 1}{2}

Median = \frac{14}{2}

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Find cos(2*ABC) 100POINTS
juin [17]

Answer:

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Step-by-step explanation:

<u>Trigonometric Identities</u>

\cos(A \pm B)=\cos A \cos B \mp \sin A \sin B

<u>Trigonometric ratios</u>

\sf \sin(\theta)=\dfrac{O}{H}\quad\cos(\theta)=\dfrac{A}{H}\quad\tan(\theta)=\dfrac{O}{A}

where:

  • \theta is the angle
  • O is the side opposite the angle
  • A is the side adjacent the angle
  • H is the hypotenuse (the side opposite the right angle)

Using the trig ratio formulas for cosine and sine:

  • \cos(\angle ABC)=\dfrac{3}{5}
  • \sin(\angle ABC)=\dfrac{4}{5}

Therefore, using the trig identities and ratios:

\begin{aligned}\implies \cos(2 \cdot \angle ABC) & = \cos(\angle ABC + \angle ABC)\\\\& = \cos (\angle ABC) \cos (\angle ABC) - \sin(\angle ABC) \sin (\angle ABC)\\\\& = \cos^2(\angle ABC)-\sin^2(\angle ABC)\\\\& = \left(\dfrac{3}{5}\right)^2-\left(\dfrac{4}{5}\right)^2\\\\& = \dfrac{3^2}{5^2}-\dfrac{4^2}{5^2}\\\\& = \dfrac{9}{25}-\dfrac{16}{25}\\\\& = \dfrac{9-16}{25}\\\\& = -\dfrac{7}{25} \end{aligned}

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2 years ago
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