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damaskus [11]
2 years ago
15

Determine the radius and center of the circle with the following equation x^2+y^2-12x+24y-10=6

Mathematics
1 answer:
PolarNik [594]2 years ago
8 0

Answer:

Center: (6, -12)

Radius: 4

Step-by-step explanation:

<u>Complete the squares</u>

<u />x^2+y^2-12x+24y-10=6\\\\x^2-12x-10+y^2+24y=6\\\\x^2-12x-10+46+y^2+24y+144=6+46+144\\\\(x^2-12x+36)+(y^2+24y+144)=196\\\\(x-6)^2+(y+12)^2=196

Comparing with the standard form equation (x-h)^2+(y-k)^2=r^2, since r^2=196, then the radius of the circle is r=14. Also, the center of the circle would be (h,k)\rightarrow(6,-12).

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Gavin likes biking. This week his goal is to bike about 65 total miles over four days. Each day he wants to ride 1.5 times as fa
IRISSAK [1]

Step-by-step explanation:

let the first-day ride be x

Then the second-day ride will be =1.5 x

The third-day ride will be=1.5(1.5x)      

The Fourth-day ride will be=1.5*1.5(1.5x)  

hence for the four days the distance covered is

65=x+1.5x+1.5*1.5x+1.5*1.5*1.5x

65=x+1.5x+2.25x+3.375x

65=8.125x

divide both sides by 8.125 we have

x=65/8.125

x=8mile

the first-day ride be x=8miles

the second-day ride will be =1.5 x =1.5*8= 12miles

The third-day ride will be=1.5(1.5x) = 18miles

The Fourth-day ride will be=1.5*1.5(1.5x) = 27miles

5 0
3 years ago
Solve the following proportion n/6=15/3
Natalka [10]

We can simplify 15/3 to 5.


N/6 = 5. Then multiply both sides of the equation by 6, giving us N = 30.



5 0
3 years ago
The decimal 1.2 is a modeled below.
guajiro [1.7K]
The answer to this question is A. 3
6 0
2 years ago
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Kamila [148]
T=10.8, was the multiplication Symbol a part of the quest
7 0
2 years ago
Add (-12x + 6) + (4x - 12).
yulyashka [42]

Step-by-step explanation:

it's obviously the equation is equals to zero,

-12x + 16 = 0

-12x = -16

-12. 12

like terms cancel each other to remaining with x

thus,

x = 4/3

<h2>AND</h2>

4x - 12 = 0

4x = 12

4. 4

like terms cancel each other to remaining (make x subject of the formula) with x

thus,

x = 3

6 0
2 years ago
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