25 less then the quotient of 10 and a number in word form

Write an equation of the circle that has a diameter with endpoints (12, 3) and (-18,3).

Mademuasel [1]

The equation of the circle that has a diameter with endpoints (12, 3) and(-18,3) is x² + y² + 6x - 6y - 207 = 0

<h3>Coordinates of center of circle</h3>

Since the endpoints of the diameter are (x₁, y₁) = (12,3) and (x₂, y₂) = (-18,3), the coordinates of the center of the circle are the midpoints of the diameter. So, the midpoints are

x = (x₁ + x₂)/2 = (12 + (-18))/2 = (12 - 18)/2 = -6/2 = -3 and
y = (y₁ + y₂)/2 = (3 + 3)/2 = 6/2 = 3.

So, the coordinates of the center of the circle are (-3, 3)

<h3>The radius of the circle</h3>

The radius of the circle r = √[(x₁ - h)² + (y₁ - k)²] where

(x₁, y₁) = coordinates of end of diameter = (12, 3) and

(h, k) = coordinates of center of circle = (-3, 3)

So, substituting the values of the variables into r, we have

r = √[(x₁ - h)² + (y₁ - k)²]

r = √[(12 - (-3))² + (3 - 3)²]

r = √[(12 + 3)² + 0²]

r = √[15² + 0²]

r = √15²

r = 15

<h3>The equation of the circle</h3>

The equation of a circle with center (h,k) is given by

(x - h)² + (y - k)² = r² where r = radius of circle.

Substituting the values of the variables into the equation, we have

(x - h)² + (y - k)² = r²

(x - (-3))² + (y - 3)² = 15²

(x + 3)² + (y - 3)² = 15²

x² + 6x + 9 + y² - 6y + 9 = 225

x² + 6x + y² - 6y + 9 + 9 - 225 = 0

x² + y² + 6x - 6y - 207 = 0

The equation of the circle that has a diameter with endpoints (12, 3) and(-18,3) is x² + y² + 6x - 6y - 207 = 0

Learn more about equation of a circle here:

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5 0

2 years ago

Can someone help me? It’s Geometry !

Alenkinab [10]

Answer:

answer is 175

Step-by-step explanation:

i solved it by similarity in triangle small triangle and big triangle are similar to each other.

3 0

3 years ago

Compare the two graphs and explain the transformation that was applied to f(x) in order to look exactly like the graph of g(x).

Neporo4naja [7]

The two graphs are represented below.

Answer and Step-by-step explanation: One graph can "transform" into another through changes in the function.

There are 3 ways to change a function:

Shifting: it adds or subtracts a constant to one of the coordinates, thus changing the graph's location. When the y-coordinate is added or subtract and the x-coordinate is unchanged, there is a vertical shift. If it is the x-coordinate which changes and y-coordinate is kept the same, the shift is a horizontal shift;
Scaling: it multiplies or divides one of the coordinates by a constant, thus changing position and appearance of the graph. If the y-coordinate is multiplied or divided by a constant but x-coordinate is the same, it is a vertical scaling. If the x-coordinate is changed by a constant and y-coordinate is not, it is a horizontal scaling;
Reflecting: it's a special case of scaling, where you can multiply a coordinate per its opposite one;

Now, the points for f(x) are:

(-5,0) (0,6) (5,-4) (8,0)

And the points for g(x) are:

(-5,-3) (0,-9) (5,1) (8,-3)

Comparing points:

(-5,0) → (-5,-3)

(0,6) → (0,-9)

(5,-4) → (5,1)

(8,0) → (8,-3)

It can be noted that x-coordinate is kept the same; only y-coordinate is changing so we have a vertical change. Observing the points:

(-5,0-3) → (-5,-3)

(0,6-15) → (0,-9)

(5,-4+5) → (5,1)

(8,0-3) → (8,-3)

Then, the vertical change is a Vertical Shift.

Another observation is that y-coordinate of f(x) is the opposite of g(x). for example: At the second point, y-coordinate of f(x) is 6, while of g(x) is -9. So, this transformation is also a Reflection.

Range of a function is all the values y can assume after substituting the x-values.

Domain of a function is all the values x can assume.

Reflection doesn't change range nor domain of a function. However, vertical or horizontal translations do.

Any vertical translation will change the range of a function and keep domain intact.

Then, for f(x) and g(x):

graph translation domain range

f(x) none [-5,8] [-4,6]

g(x) vertical shift [-5,8] [-9,1]

In conclusion, this transformation (or translation) will affect the range of g(x)

5 0

3 years ago

Martha Jones received a $540 discount loan to purchase a new sewing machine. The loan was offered at 12.5% for 90 days. Find the

Ede4ka [16]

16.88

523.12

at least for the question i got

4 0

3 years ago

PLEASE HELP I BEG CLICK ON THIS!! It’s not that hard :(((( sorry if blurry

mash [69]

Answer:

b hope i helped you have a good day

8 0

3 years ago