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4 years ago

In the diagram below, which distance represents the distance from point D to

Mathematics

1 answer:

11Alexandr11 [23.1K]4 years ago

4 0

Answer
A.CD
Cause theCD is the mid point of triangle ADB which divides triangle in two half if you look carefully you can understand the diagram ☺️☺️

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Using the following equation, find the center and radius: x2 −2x + y2 − 6y = 26 (5 points)

Lisa [10]

Answer:

Center: (1,3)

Radius: 6

Step-by-step explanation:

Hi there!

$x^2-2x + y^2 - 6y = 26$

Typically, the equation of a circle would be in the form $(x-h)^2+(y-k)^2=r^2$ where $(h,k)$ is the center and $r$ is the radius.

To get the given equation $x^2-2x + y^2 - 6y = 26$ into this form, we must complete the square for both x and y.

1) Complete the square for x

Let's take a look at this part of the equation:

$x^2-2x$

To complete the square, we must add to the expression the square of half of 2. That would be 1² = 1:

$x^2-2x+1$

Great! Now, let's add this to our original equation:

$x^2-2x+1+y^2-6y = 26$

We cannot randomly add a 1 to just one side, so we must do the same to the right side of the equation:

$x^2-2x+1+y^2-6y = 26+1\\x^2-2x+1+y^2-6y = 27$

Complete the square:

$(x-1)^2+y^2-6y = 27$

2) Complete the square for y

Let's take a look at this part of the equation $(x-1)^2+y^2-6y = 27$ :

$y^2-6y$

To complete the square, we must add to the expression the square of half of 6. That would be 3² = 9:

$y^2-6y+9$

Great! Now, back to our original equation:

$(x-1)^2+y^2-6y+9= 27$

Remember to add 9 on the other side as well:

$(x-1)^2+y^2-6y+9= 27+9\\(x-1)^2+y^2-6y+9= 36$

Complete the square:

$(x-1)^2+(y-3)^2= 36$

3) Determine the center and the radius

$(x-1)^2+(y-3)^2= 36$

$(x-h)^2+(y-k)^2=r^2$

Now, we can see that (1,3) is in the place of (h,k). 36 is also in the place of r², making 6 the radius.

I hope this helps!

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3 years ago

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Felipe takes a commuter train to get to work. He pays a one-time fee to store his bike at the train station. He pays a

mihalych1998 [28]

Answer:

80 represents the monthly fees and 50 represents the fixed one-time fee to store the bike at the train station.

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4 years ago

Does the associative property hold true for division of integers

LuckyWell [14K]

Answer:

The associative property of integers does not hold true for subtraction and division of integers, as, in the case of subtraction and division, the order of the numbers is important and cannot be changed.

Step-by-step explanation:

For example, 2 - (8 - 9) = 2 - (-1) = 3. Now, if we change the order as 8 - (2 - 9) = 8 - (-7) = 15

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3 years ago

What two dimensional cross sections can we create by slicing a cube

coldgirl [10]

Two squares are created from a cross section of a cube

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3 years ago

How many times do 12 go into 209?

Olenka [21]

209/12 is 17.41, so 12 goes into 209 17 times.

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3 years ago