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3 years ago

Divide the following 81x⁷yz³ by -3x²y²z²

Mathematics

1 answer:

Readme [11.4K]3 years ago

4 0

Answer:

-27x^5y^-1 z

Step-by-step explanation:

-3x²y²z²

-27x^5y^-1 z

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The .............. from the regular selling price to the discounted sale price is 20%

11Alexandr11 [23.1K]

Answer:

80%

Step-by-step explanation:

regular price is 100%

so, after the discounted price is 20%

the discount is 80%

4 0

3 years ago

Karens batting average was 0.444. She was at bat 45 times. How many hitd did she get?

Igoryamba

Average of 0,444 in 45 battings can be wirtten as:

45 * 44,4% = 19,98

After rounding it up it'll give us 20 and that's exactly how many hits Karen got.

7 0

3 years ago

There are 3 islands A,B,C. Island B is east of island A, 8 miles away. Island C is northeast of A, 5 miles away and northwest of

Nostrana [21]

Answer:

The bearing needed to navigate from island B to island C is approximately 38.213º.

Step-by-step explanation:

The geometrical diagram representing the statement is introduced below as attachment, and from Trigonometry we determine that bearing needed to navigate from island B to C by the Cosine Law:

$AC^{2} = AB^{2}+BC^{2}-2\cdot AB\cdot BC\cdot \cos \theta$ (1)

Where:

$AC$ - The distance from A to C, measured in miles.

$AB$ - The distance from A to B, measured in miles.

$BC$ - The distance from B to C, measured in miles.

$\theta$ - Bearing from island B to island C, measured in sexagesimal degrees.

Then, we clear the bearing angle within the equation:

$AC^{2}-AB^{2}-BC^{2}=-2\cdot AB\cdot BC\cdot \cos \theta$

$\cos \theta = \frac{BC^{2}+AB^{2}-AC^{2}}{2\cdot AB\cdot BC}$

$\theta = \cos^{-1}\left(\frac{BC^{2}+AB^{2}-AC^{2}}{2\cdot AB\cdot BC} \right)$ (2)

If we know that $BC = 7\,mi$ , $AB = 8\,mi$ , $AC = 5\,mi$ , then the bearing from island B to island C:

$\theta = \cos^{-1}\left[\frac{(7\mi)^{2}+(8\,mi)^{2}-(5\,mi)^{2}}{2\cdot (8\,mi)\cdot (7\,mi)} \right]$

$\theta \approx 38.213^{\circ}$

The bearing needed to navigate from island B to island C is approximately 38.213º.

8 0

3 years ago

The sum of two consecutive natural numbers is 525.<br> Find the numbers.

Luda [366]

Answer:

262 and 263 are consecutive natural numbers whose sum is 525.

Step-by-step explanation:

Natural number are a subset of real numbers consisting in positive integers (i.e. 1, 2, 3, 525) and two natural numbers are consecutive when distance between each other is equal to 1. ( $|x-y| = 1$ , $\forall\,x,y \in \mathbb{N}$ ) We can interpret the statement mathematically by means of the following expression: