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lapo4ka [179]
3 years ago
9

14. The diameter of a circle has endpoints A(-8, -5) and B(4, 11). Write the equation of the circle. (**hint: you must find the

center and radius)
Mathematics
1 answer:
Tatiana [17]3 years ago
5 0

Answer:

x² + y² - 12x - 16y = 280

Step-by-step explanation:

The diameter of a circle has endpoints A(-8,-5) and B(4,11)

The equation of a circle is given by: (x - a)² + (y - b)² = r² , Where x and y are points on the circle and (a, b) is the center of the circle. r is the radius.

To find the center of the circle:

Center = (\frac{4 - -8}{2},\frac{11 - -5}{2}) = (6, 8)

The length of the diameter is the square root of change in y squared plus change in x squared.

The length of the diameter squared = (11 - -5)² + (4 - -8)² = 400

The diameter is \sqrt[]{400} = 20 units

Taking another point (x,y) on the circle,

The equation of the circle will be:

(x - 6)² + (y - 8)² = 20²

Simplifying this gives;

x² - 12x + 36 + y² - 16y + 84 = 400

x² + y² - 12x - 16y = 400 - 84 - 36

x² + y² - 12x - 16y = 280

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How many miles are equivalent to 3.1 kilometers? 1 kilometer is about 0.62 mile
Anton [14]

Answer:

1.922 miles is equivalent to 3.1 kilometers.

Step-by-step explanation:

Given:

1 km = 0.62 miles.

3.1 km = ? miles

Now, in order to find the number of miles equivalent to 3.1 km, we use unitary method with the help of the conversion factor.

From the conversion factor, we can conclude that kilometer is a smaller unit compared to that of mile.

So, conversion factor = \frac{0.62\ miles}{1\ km}

The formula to transform 'n' kilometers to miles is given as:

=Conversion\ factor\times n

Therefore, 3.1 km = \frac{0.62\ miles}{1\ km}\times 3.1\ km

3.1 km = 1.922 miles

Therefore, 1.922 miles is equivalent to 3.1 kilometers.

4 0
3 years ago
Sarah bought 6 2/3 yards of material. She used 3/4 of the material to make a costume for the school play. How much material did
Lelechka [254]
You’re full of cap don’t cap next time you’re capping the answer is 5/3
7 0
3 years ago
An airplane is sighted at the same time by two
tiny-mole [99]

I got 2.2

Step-by-step explanation:

I probably did the math wrong but i did my best and i hope this helped even a little!

4 0
2 years ago
Can someone answer question 2a and b only please
Mice21 [21]

Answer:

2a)  -2

b) 8

Step-by-step explanation:

<u>Equation of a parabola in vertex form</u>

f(x) = a(x - h)² + k

where (h, k) is the vertex and the axis of symmetry is x = h

2 a)

Using the equation of a parabola in vertex form, a parabola with vertex (2, -6):  

f(x) = a(x - 2)² - 6

If one of the x-axis intercepts is 6, then

                 f(6) = 0

⇒ a(6 - 2)² - 6 = 0

⇒         16a - 6 = 0

⇒              16a = 6

⇒                  a = 6/16 = 3/8

So f(x) = 3/8(x - 2)² - 6

To find the other intercept, set f(x) = 0 and solve for x:

                    f(x) = 0

⇒ 3/8(x - 2)² - 6 = 0

⇒      3/8(x - 2)² = 6

⇒           (x - 2)² = 16

⇒              x - 2 = ±4

⇒                   x = 6,  -2

Therefore, the other x-axis intercept is -2

b)

Using the equation of a parabola in vertex form, a parabola with vertex (2, -6):  

f(x) = a(x - 2)² - 6

If one of the x-axis intercepts is -4, then

                 f(-4) = 0

⇒ a(-4 - 2)² - 6 = 0

⇒         36a - 6 = 0

⇒              36a = 6

⇒                  a = 6/36 = 1/6

So f(x) = 1/6(x - 2)² - 6

To find the other intercept, set f(x) = 0 and solve for x:

                    f(x) = 0

⇒  1/6(x - 2)² - 6 = 0

⇒       1/6(x - 2)² = 6

⇒           (x - 2)² = 36

⇒              x - 2 = ±6

⇒                   x = 8,  -4

Therefore, the other x-axis intercept is 8

8 0
2 years ago
What is the answer to |-2|+|-3|
Nastasia [14]

Answer:

5

Step-by-step explanation:

the absolute value of -2 is 2

the absolute value of -3 is 3.

Since the question is adding the absolute values, the answer is 5

7 0
3 years ago
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