find the equation of a circle with a point at ( 10 , - 4 ) and a point at ( -2 , - 4 )
Answers
Answer:
Solution given:
letA=(10,-4)
B=(-2,-4)
centre[C](h,k)=[tex]\frac{10-2}{2},\frac{-4-4}{2}=(+4,-4)[/tex]
radius=[tex]\sqrt{(4-10)²+(-4+4)²}=6[/tex]units
we have
Equation of a circle is;
(x-h)²+(y-k)²=r²
(x-4)²+(y+4)²=36
or.
x²-8x+16+y²+8y+16=36
x²-8x+8y+y²=36-32
x²-8x+8y+y²=4
The equation is (x-4)²+(y+4)²=36 or x²-8x+8y+y²=4.
Answer:
[tex] \rm\displaystyle (x - 4) ^{2} + {(y + 4)}^{2} = 36[/tex]
Step-by-step explanation:
the given points are the diameter points of circle because notice that in the both points y coordinate is the same therefore it's a horizontal diameter
since (10,-4),(-2,-4) are the diameter points of the circle the midpoint of the diameter will be the centre of the circle
remember midpoint formula,
[tex] \displaystyle M = \left( \frac{x _{1} + x_{2} }{2} , \frac{ y_{2} + y_{2}}{2} \right)[/tex]
let,
[tex] \displaystyle x _{1} = 10[/tex][tex] \displaystyle x _{2} = - 2[/tex][tex] \displaystyle y _{1} = - 4[/tex][tex] \displaystyle y _{2} = -4[/tex]thus substitute:
[tex] \rm\displaystyle M = \left( \frac{10 + ( - 2)}{2} , \frac{ - 4 + ( - 4)}{2} \right)[/tex]
simplify addition:
[tex] \rm\displaystyle M = \left( \frac{8}{2} , \frac{ - 8}{2} \right)[/tex]
simplify division:
[tex] \rm\displaystyle M = \left( 4, - 4 \right)[/tex]
so the centre of the circle is (4,-4)
since it's a horizontal diameter the the redious will be the difference between the x coordinate of the Midpoint and the any x coordinate of the given two points but I'll use (-2,-4) therefore the redious is
[tex] \displaystyle r = 4 - ( - 2)[/tex]
simplify which yields:
[tex] \displaystyle\boxed{ r =6}[/tex]
recall the equation of circle
[tex] \displaystyle (x - h) ^{2} + {(y - k)}^{2} = {r}^{2} [/tex]
we acquire that,
h=4k=-4r=6therefore substitute:
[tex] \rm\displaystyle (x - 4) ^{2} + {(y - ( - 4))}^{2} = {6}^{2} [/tex]
simplify:
[tex] \rm\displaystyle (x - 4) ^{2} + {(y + 4)}^{2} = 36[/tex]
and we are done!
also refer the attachment
(the graph is web resource of desmos)
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Step-by-step explanation:
Mike works h hours in a week. To find his weekly pay he multiplies his hours by his pay of $30 per hour and adds $5 for his sales bonus. He's decided that he wanted to take one-fifth of his weekly pay and place it in his savings. Which simplified expression represents the amount that will go into his savings each week?
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Answer:
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Answers
Answer:
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Answer:
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Answer with step-by-step explanation:
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Answers
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Answers
Answer:
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[tex]\sf 5x-50=30-15x[/tex]
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Answers
Answer:
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225
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Answer:
Pythagorean theorem
Step-by-step explanation:
You should use the Pythagorean theorem
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9^2+ 12^2 = ?^2
81 +144 = ?^2
225 = ?^2
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sqrt(225) = sqrt(?^2)
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Answers
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Answers
Answer:
12\sqrt{2}
Step-by-step explanation:
To get the hypotenuse, first we need to get the side length of the square
Area of the square = L²
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Answers
Answer:
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Step-by-step explanation:
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Answer:
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Answer:
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Step-by-step explanation:
Since OP is parallel to LM, the two triangles are similar, because they share all three angles. By definition, the corresponding sides of a similar polygon must be in a constant proportion.
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Answers
===========================================================
Explanation:
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Answers
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Step-by-step explanation:
Given
A plane has traveled 26 miles on a course heading [tex]48^{\circ}[/tex] east of north
Taking the component of travel in North direction
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Answers
A is the point with coordinates (x, 2y).
B is the point with coordinates (3x, 4y).
The midpoint of AB has coordinates (-4, 15).
Work out the values of x and y.
Answers
Answer:
x= -2 , y=5
Step-by-step explanation:
(x+3x)/2 = -4
4x/2 = -4
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x = -2
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y=5
solve it : -
[tex] \sqrt{6 \times 24} [/tex]
_______
Answers
Answer:
12
Step-by-step explanation:
sqrt(6*24)
sqrt(144)
sqrt(12*12)
12
Answer:
12
Step-by-step explanation:
6×24=144
Sq. Root of 144=12