X-Axis
When a figure flips over the X-axis, the X coordinate stays the same while the Y-coordinate’s sign is flipped.

Y- axis

When a figure is flipped over the Y- axis the Y coordinate stays the same while the X axis coordinate’s sign is flipped

Example- (x,y)
X axis flipped
(2,5) —> (2,-5)

Y axis flipped
(3,5) —-> (-3,5)

5 0

3 years ago

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The center of a cricle ids (h,7) and the radius is 10. The circle passes through (3,-1). Find all possible values of h.

Nostrana [21]

$center\ of\ a\ circle:(a;\ b)\\\\radius:r\\\\(x-a)^2+(y-b)^2=r^2\\\\========================\\\\(h;\ 7);\ r=10\\\\(x-h)^2+(y-7)^2=10^2\\\\========================$

$The\ circle\ passes\ throught\ (3;-1).\\\\Substitute\ x=3\ and\ y=-1:\\\\(3-h)^2+(-1-7)^2=100\\\\(3-h)^2+(-8)^2=100\\\\(3-h)^2+64=100\ \ \ /-64\\\\(3-h)^2=36\iff3-h=\pm\sqrt{36}\\\\3-h=-6\ or\ 3-h=6\\-h=-6-3\ or\ -h=6-3\\-h=-9\ or\ -h=3\\h=9\ or\ h=-3\\\\Answer:h=9\ or\ h=-3$

6 0

3 years ago

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An expirement consists of rolling two fair number cubes. What is the probability that the sum of the two numbers will be 4? Expr

ExtremeBDS [4]

Answer:

$\dfrac{1}{12}$

Step-by-step explanation:

Given:

Two fair number cubes i.e. two dice consisting the numbers 1, 2, 3, 4, 5, 6 on their faces and have equal probability of each number.

The dice are rolled.

To find:

Probability of getting the sum of two numbers as 4.

Solution:

First of all, let us have a look at the total possibilities when two dice are rolled:

([1][1], [1][2], [1][3], [1][4], [1][5], [1][6],

[2][1], [2][2], [2][3], [2][4], [2][5], [2][6],

[3][1], [3][2], [3][3], [3][4], [3][5], [3][6],

[4][1], [4][2], [4][3], [4][4], [4][5], [4][6],

[5][1], [5][2], [5][3], [5][4], [5][5], [5][6],

[6][1], [6][2], [6][3], [6][4], [6][5], [6][6])

These are total 36 possible outcomes.

For getting a sum as 4:

Possible number of favorable cases are 3 (as highlighted in BOLD in above)

Formula for probability of an event E can be observed as:

$P(E) = \dfrac{\text{Number of favorable cases}}{\text {Total number of cases}}$

Required probability is:

$\dfrac{3}{36} = \bold{\dfrac{1}{12}}$

5 0

4 years ago