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Snowcat [4.5K]
3 years ago
11

Choose the equation for the given circle in standard form: x^2 + y^2 - 4x + 14y +28 =0

Mathematics
1 answer:
finlep [7]3 years ago
7 0

Answer:

<h2>(x-2)²+(y+7)² = 25</h2><h2></h2>

Step-by-step explanation:

The general standard form of an equation is written in expressed as shown;

(x-a)²+(y-b)² = r²

(a,b) is the centre of the circle and r is the radius

Given the equation of the circle x^2 + y^2 - 4x + 14y +28 =0, we need to find the centre of the circle and its radius.

comparing the equation given with x²+y²+2gx+2fy+c =0

(-g, -f) is the centre

radius = √g²+f²-c

On comparison,

2gx = - 4x

g = -4/2

g = -2

2fy =  14y

f = 14/2

f = 7

c = 28

r = √(-2)²+7²-28

r = √4+49-28

r = √25

r = 5

comparing centre (a,b) to (-g, -f)

a = -g = -(-2)

a = 2

b = -f = -7

b = -7

substituting the centre (a, b) and the radius r into the equation

(x-a)²+(y-b)² = r²

The required equation will be (x-2)²+(y+7)² = 5²

(x-2)²+(y+7)² = 25

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Kira, goran, &amp; joe sent a total of 90 text messages during the weekend. Goran sent 5 fewer messages than Kira. Joe sent 3 ti
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Answer:

Kira sent 19 text messages, Goran sent 14  text messages  and Joe sent 57  text messages.

Step-by-step explanation:

Let be "k" the number of text messages that Kira sent during the weekend, "g" the number of text messages that Gora sent during the weekend and "j" the number of text messages that Joe sent during the weekend.

We know know that they sent a total of 90 text messages then:

k+g+j=90

Goran sent 5 fewer messages than Kira. This is:

g=k-5

And Joe sent 3 times as many messages as Kira. Then:

j=3k

The steps to solve this are:

- Substitute the second equation and the third equatio into the first equation  and then solve for "k":

k+(k-5)+(3k)=90\\\\5k-5=90\\\\5k=90+5\\\\k=\frac{95}{5}\\\\k=19

- Substitute this value into the second equation to find "g":

g=19-5=14

- Substitute the value of "k" into the third equation to find "j":

j=3(19)=57

4 0
4 years ago
Which best summmarize the pyhagorean theorem
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Answer: the sum of the squares of the lengths of the legs of a right triangle equal the square of the length of the hypotenuse

Step-by-step explanation: hope it helps

6 0
3 years ago
An instructor gives a class a set of 10 problems and says that the nal exam will consist of a random selection of 5 of the probl
sweet-ann [11.9K]

Answer:

probability that he or she will answer at least 4 problems correctly = 0.5

Step-by-step explanation:

probability that he or she will answer at least 4 problems correctly is given as;

P (at least 4 correctly) = P (exactly 4 correctly) + P (all 5 correctly)

Since there are 10 problems. 4 is from the 7 problems chosen and 1 is from the 3 problems we can't figure out. Thus, P(exactly 4 correctly) = 7C4 x 3C1

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3 years ago
Beverley has quarters and dimes in her pocket. She has 21 coins with a total value of $3.00. How many of each type of coin does
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Answer:

Step-by-step explanation:

If all 21 coins were dimes, she'd have $2.10. But she has 90 more cents than that. Now for each coin that's a quarter, not a dime, she has 15 cents more. 90/15= 6. So there are 6 quarters, and 21-6 = 15 dimes.

Now we do it backwards to see if it's right. 6 quarters is $1.50, 15 dimes is $1.50, add those together and you get $3. So it's right. 6 quarters, 15 dimes.

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Answer:

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Hope this helps!! Have an Awesome day!!! :-)

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