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2 years ago

Rotate the given triangle 180° counter-clockwise about the origin. [ 0 -3 5 ] [0 1 2]

Mathematics

2 answers:

Neporo4naja [7]2 years ago

4 0

The answers are : (alike the box order)
3 - 5
-1 -2

inysia [295]2 years ago

3 0

Answer:

$\left[\begin{array}{ccc}0&3&-5\\0&-1&-2\end{array}\right]$

Step-by-step explanation:

Rotation 180° (in either direction) about the origin causes each coordinate to have its sign changed. Effectively, the coordinate matrix is multiplied by -1.

<em>Additional comment</em>

This is equivalent to reflection across the origin.

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2 years ago

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3 years ago

Read 2 more answers

Find the area of the shaded region round to the nearest tenth

Alenkinab [10]

Answer: 818.4

Step-by-step explanation:

Using the area of a sector formula, we get the area of the entire sector is $(\pi)(27.8^{2})\left(\frac{150}{360} \right)$ .

Using the formula $A=\frac{1}{2} ab \sin C$ , we get the area of the triangle is $\frac{1}{2}(27.8)(27.8)(\sin 150^{\circ})$ .

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1 year ago

Are the equations lxl – 3 = 7 and [x] = 10 equivalent?

zvonat [6]

They're not equivalent.

$|x|$ (vertical bars) represents the absolute value of x. How it works is that it turns negative numbers positive but leaves 0 and positive numbers alone (hence it gets a number's distance from 0 on the number line).

$[x]$ (square brackets) usually represents the floor function, which returns the largest integer that is less than or equal to x. (The floor of x can also be written as $\lfloor x \rfloor$ --- it depends on what your textbook/source says).

To solve $|x| - 3 = 7$ , you first transform it into the equivalent equation $|x| = 10$ . Then by definition of absolute value, there are only two solutions for the first equation: x = 10 or x = -10.

[x] = 10 has infinitely many solutions. For example, the floor of 10 is 10, so $[10] = 10$ , thus a solution for the second equation is x = 10

The floor of 10.1 is 10, so $[10.1] = 10$ , thus another solution for the second equation is x = 10.1.

The two equations do not have the same solution set (as x = 10.1 does not solve |x| - 3 = 7 but solves [x] = 10), so they're not equivalent.

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2 years ago

The volume of a cube depends on the length of its sides . This can be writtin in function notation as v(s) . What is the best in

Soloha48 [4]

Answer:

The volume of a cube with side length 2 is 8.

Step-by-step explanation:

The argument of the function is the side length. In v(2), the argument is 2, so the side length of the cube of interest is 2 units.

The value of the function is the volume of the cube. The value of v(2) is 8, so that is the volume of the cube whose side length is 2.

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3 years ago

Rotate the given triangle 180° counter-clockwise about the origin. [ 0 -3 5 ] [0 1 2]​

Rotate the given triangle 180° counter-clockwise about the origin. [ 0 -3 5 ] [0 1 2]