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Math and Arithmetic

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Nikko Gleichner

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Cards in this guide (24)
When a figure can be rotated 180 degrees and still looke the same

When u rotated a figure 180 is the reflection the same

Is Multiplication of 2 X 2 matrices associative

All matrix multiplications are associative

Always .. .A+

Multiplication of 2 X 2 matrices is commutative

Sometimes . . A+

Is rotation scalar or vector

Rotation is a vector having a direction and magnitude.

If in ABC B is equal to C what kind of triangle is ABC

Triangle ABC would be an isosceles. An isosceles triangle is defined as having two sides of equal length. This would also mean, then, that two angles in the triangle are also the same.

In triangle ABC what is the length of line C if A equals 5 and B equals 10

We cannot know.

What are the coordinates of the vertices of triangle a'b'c' after triangle ABC is dilated using a scaling factor of 3

Find the coordinates of the vertices of triangle a'b'c' after triangle ABC is dilated using the given scale factor then graph triangle ABC and its dilation

A (1,1) B(1,3) C(3,1) scale factor 3

Can a matrix with dimensions of 2 X 4 be added to another matrix with dimensions of 2 X 5

No. Matrix addition (or subtraction) is defined only for matrices of the same dimensions.

1 3 is reflected over the y axis What are the coordinates of the image

-1,3

Can a matrix with dimensions of 3 X 6 be added to another matrix with dimensions of 6 X 3

No, but it can be multiplied:

The new matrix is 3x3. EG:

100100 100 200

010010 x 010 = 020

001001 001 002

100

010

001

How do the coordinates of a point change when it is reflected over the x-axis

Reflecting the the x-axis (line y=0) leaves the x-coordinate unchanged and negates the y-coordinate:

(x, y) -> (x, -y)

For example:

(1, 2) -> (1, -2)

(3, -4) -> (3, 4)

Can a matrix with dimensions of 2 X 4 be added to another matrix with dimensions of 2 X 4

Yes.

If A B C and D are points on a number line B is the midpoint of Ac what is the coordinate

The 'x' coordinate of B is the average of the 'x' coordinates of A and C.

The 'y' coordinate of B is the average of the 'y' coordinates of A and C.

Multiplication of 2x2 matrices is commutative

No. Multiplication of matrices is, in general, non-commutative, due to the way multiplication is defined.

How many degrees has the minute hand moved through in 1 over 6 of half a rotation

1/6 of half a rotation = 1/12 of a rotation = 1/12 of 360 degrees = 360/12 = 30 degrees.

Triangle abc has vertices a 1 2 3 b 4 0 5 and c 3 6 4 Show that abc is a right triangle

Your question doesn't seem to make any sense but if the sides of the triangle are 3, 4 and 5 then it is a right angle triangle because it complies with Pythagoras' theorem.

What is the image of point 3 and 5 if the rotation is 180 degrees

What is the image of point (3, 5) if the rotation is

What does reflection over the y-axis mean

Example: if you have a point with the coordinates (2,4), a reflection over the y-axis will result in the point with coordinates (-2,4).

What is the image of point 3 5 if the rotation is 90

The image is (-5, 3)

What is the reflection image of 5 -3 across the y axis

The y-axis is the symmetry line, so that (5, -3) and (-5, -3) are symmetric points.

What is the image of point (4 3) if the rotation is -180º

It is: (-4, -3)

Which graph shows a reflection across the x-axis

y = -f(x) is a reflection of y = f(x) in the x axis.

What is the line over which a figure is reflected

It is the axis of reflection.

What is the A coordinate Triangle ABC is reflected over the x-axis. Triangle ABC has points A (10 2) B (8 3) and C (6 4). What is the A' coordinate

It is (10, -2).

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