1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
snow_tiger [21]
2 years ago
7

If the endpoints of the diameter of a circle are (−6, 6) and (6, −2), what is the standard form equation of the circle? A) x2 +

(y + 2)2 = 36 B) x2 + (y + 2)2 = 52 C) x2 + (y − 2)2 = 36 D) x2 + (y − 2)2 = 52

Mathematics
1 answer:
vazorg [7]2 years ago
6 0

Answer:

  D)  x² + (y − 2)² = 52

Step-by-step explanation:

The center of the circle is the midpoint of the diameter, so is the average of the end points:

  (h, k) = ((-6, 6) +(6, -2))/2 = (0, 4)/2 = (0, 2)

Then the distance between the center and an end point is the radius. It is found using the distance formula:

  r = √((x2 -x1)² +(y2 -y1)²) = √((-6 -0)² +(6 -2)²) = √(36 +16) = √52

Putting these values into the standard form equation for a circle ...

  (x -h)² +(y -k)² = r²

gives ...

  (x -0)² +(y -2)² = (√52)²

  x² +(y -2)² = 52 . . . . . matches choice D

You might be interested in
A jogger runs 8 miles north and then 5 miles west. What is the shortest distance, to the nearest tenth of a mile, he must travel
Stells [14]

Answer:

most likely has to run 13 miles southeast or 5 miles east and  8 west  

Step-by-step explanation:

5 0
2 years ago
The length of a rectangle is 3 less than twice the width. If the area of the rectangle is 20 square inches, what are the dimensi
atroni [7]

Answer:

length is 5

width is 4

Step-by-step explanation:

8 0
3 years ago
Jimmy threw a baseball in the air from the roof of his house. The path followed by the baseball can be modeled by the function f
erastovalidia [21]

Answer:

Step-by-step explanation:

The first part of A is easy. Look at the quadratic function, and the constant, the very last number with no t stuck to it represents the height from which the object in question was originally launched. Our constant is 40, so the height of the roof from which the baseball was thrown is 40 feet. Part 2 of A is not quite as simple because it requires factoring using the quadratic formula.Before we do that, let's make our numbers a bit more manageable, shall we? Let's factor out a -8 to get

f(t) = -(t^2-6t-5) and a = 1, b = -6, c = -5.

Filling in the quadratic formula now looks like this:

t=\frac{6+-\sqrt{6^2-4(1)(-5)} }{2(1)} and

t=\frac{6+-\sqrt{36+40} }{2} and

t=\frac{6+-\sqrt{56} }{2} so the 2 solutions are

t=\frac{6+\sqrt{56} }{2}=6.74sec and

t=\frac{6-\sqrt{56} }{2}=-.742sec and since we know time can NEVER be negative, the time it takes for the baseball to hit the ground from a height of 40 feet is 6.74 seconds. Onto part B.

In order to determine exactly how high the baseball did go, we have to find the vertex of the function. We do this by completing the square and getting the function into vertex, or work, form. Begin by setting the quadratic equal to 0, moving over the constant, and then factoring out the leading coefficient. The rule for completing the square are kinda picky in that you have to have a 1 as the leading coefficient, and righ now ours is a -8. So following the rules I stated above:

-8(t^2-6t)=-40 Next is the take half the linear term, square it, and then add it to both sides. Our linear term is a -6. Half of -6 is -3, and -3 squared is 9, so we add 9 into the parenthesis first:

-8(t^2-6t+9)=-40+??

Because this is an equation, we can't add 9 to one side without adding the equivalent to the other side. But, we cannot forget about that -8 sitting out front there, refusing to be ignored. We didn't just add in a 9, we actually added in a -8 times 9 which is -72. That's what goes on the right side in place of the ??.

-8(t^2-6t+9)=-40-72

The reason we complete the square is found on the left side of the equals sign. We have, in the process of completing the square, formed a perfect square binomial that will serve as the h in our vertex (h, k) where h is the number of seconds it takes for the baseball to reach its max height of k, whatever k is. That's what we have to find out. Putting the left side into its simplified perfect square binomial and adding the numbers on the right gives us:

-8(t-3)^2=-112

For the last step, add over the -112 and set it back equal to f(t):

-8(t-3)^2+112=f(t) From that we determine that the vertex is (3, 112). The max height of this baseball was 112 feet...so no, it did not make it up to the height of 120 feet that Jimmy wanted for the baseball.

6 0
2 years ago
Find the exact value by using a half-angle identity. (6 points)
Elenna [48]

Answer:

c

Step-by-step explanation:

4 0
3 years ago
Is each question Statistical or Not statistical to classify each question.
wariber [46]
Q 1. 1,776 and  1,396

q 2. 1,250

q 3. 3.5 million
7 0
3 years ago
Other questions:
  • If m (RQ = 118°,<br><br> then ∠T =<br><br> 59<br> 118<br> 336
    14·2 answers
  • Look at this set of 8 numbers:33769234 how would the range change if the number 6 replaced the number 7 in the set
    6·1 answer
  • Based on the figure below, what is the value of x?<br><br><br> 5<br><br> 7<br><br> 11<br><br> 15
    10·2 answers
  • -2 X-9=3. Please help<br> 3
    5·2 answers
  • Jan walks 40 meters in 15 seconds what is her rate?
    11·1 answer
  • Graph the circle 2+ y2 - 14x + 2y + 41 = 0.
    12·2 answers
  • A candy company used exactly 8 pints of chocolate to make two boxes of candy what is the rate of pints per chocolate box
    13·1 answer
  • Which equation matches the graph
    7·1 answer
  • Free brainliest here
    12·2 answers
  • james got 19 questions right on a math test. These questions made up 76% of the test.How many questions were there on the test?​
    13·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!