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)
Related Questions
Nine split into four groups is two, with a ___ of one.
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can someone help me understand this, please? For some reason my answer is correct but I need to understand how did I found the correct answer
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Answer with step-by-step explanation:
The way the question is worded, this actually shouldn't be correct. The correct answer should be [tex]3:4[/tex].
Because the trapezoids are similar, we can find the ratio of their perimeters by actually just finding the ratio of their sides.
Why?
By definition, the corresponding sides of a polygon are in a constant proportion. The perimeter is simply the sum of all sides of the polygon. Since we're just adding the sides, the proportion will still be maintained.
Therefore, we'll just need to ratio of their corresponding sides. The only two corresponding sides that are marked are [tex]\overline{RS}[/tex] and [tex]\overline{AB}[/tex].
The ratio of [tex]\overline{RS}:\overline{AB}[/tex] is [tex]18:24\implies \boxed{3:4}[/tex].
The reason why it ideally should be [tex]3:4[/tex] and not [tex]4:3[/tex] is because the question states [tex]RTSU\sim ABCD[/tex], which mentions [tex]RSTU[/tex] first, so our answer should follow this respective order. I believe you were marked right anyways because the specific order is not specified, but generally, you want to give your answer respectively by default.
To solve for the missing length, which operation should you perform?
Answers
Answer:
? = 15 yards
Step-by-step explanation:
h² + b² = ?²
9² + 12² = ?²
81 + 144
225
√225 = 15
Answer:
Pythagorean theorem
Step-by-step explanation:
You should use the Pythagorean theorem
a^2+b^2 = c^2 where a and b are the legs and c is the hypotenuse
9^2+ 12^2 = ?^2
81 +144 = ?^2
225 = ?^2
Take the square root of each side
sqrt(225) = sqrt(?^2)
15 =?
hey there, please help me. thank you
Answers
Answer:
S.S.S
Step-by-step explanation:
When three sides of a triangle are respectively equal to three corresponding sides of another triangle, they are said to be congruent .
hope it is helpful to you
Solve for x.
5(x – 10) = 30 – 15x
Answers
Answer:
x=4Step-by-step explanation:
[tex]\sf 5(x - 10) = 30 - 15x[/tex]
[tex]\sf 5x-50=30-15x[/tex]
[tex]\sf 5x-50+50=30-15x+50[/tex]
[tex]\sf 5x=-15x+80[/tex]
[tex]\sf 5x+15x=-15x+80+15x[/tex]
[tex]\sf 20x=80[/tex]
[tex]\sf \frac{20x}{20}=\frac{80}{20}[/tex]
[tex]\sf x=4[/tex]
602.88 rounded to 2 decimal place is ?
Answers
Answer:
it will be 603.00
it will. e counted from the right to the left
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
pls help with both of them
will give brainliest and everything
Answers
So π (1.3)^2(4.83)
Why 1.3 but not 2.6 though? Because 2.6 is the diameter, to find the radius, divide the diameter by 2, so 1.3.
And so the volume of the cylinder is 29.74083in^3 or 29.74in^3 rounded to the nearest hundredth.
The volume for a triangular prism is
(bh/2)h, or (base•height/2)height.
So to find the base, take the length and width and times it.
3 1/2•1=3 1/2
The base is 3 1/2, or 3.5 inches. The height is given as 4 inches.
(3.5•4/2)4=28
The volume of the triangular prism is 28 in^3
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
4x= -8
x = -2
(2y+4y)/2=15
6y/2=15
6y=30
y=5
A plane has traveled 26 miles on a course heading 48º east of north. How far north (x) has the plane traveled at this point, to the nearest tenth of a mile?
Answers
Answer: [tex]17.4\ \text{miles}[/tex]
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
The distance traveled in North is given by with the help of figure
[tex]\Rightarrow x=26\cos 48^{\circ}\\\\\Rightarrow x=26\times 0.669\\\\\Rightarrow x=17.4\ \text{miles}[/tex]
A square has the same perimeter as a triangle. The triangle's area is 16 root 3. What is the hypotenuse of the square?
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
16\sqrt{3} = L²
L = 4×3
L = 12
Using pythagiras theorem to get the hypotenuse
Hyp² = 12²+12²
Hyp² = 144+144
Hyp² = 288
Hyp = \sqrt {288}
Hyp = 12\sqrt{2}
Hence the hypotenuse of the square is 12\sqrt{2}
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Answer:
Angle a = Angle D
Answer:
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Step-by-step explanation:
If someone were to have 300 feet of fencing, what is the maximum area they can enclose?
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Answer:
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Step-by-step explanation:
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75×75=5,625
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Either enter an exact answer in terms of π or use 3.14 for π
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Answer:
volume of a cone formula = V=πr²h/
3
V=3.14(5)²3/3
V≈78.54
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?
Answers
Answer:
6h + 1
Step-by-step explanation:
number of hours: h
pay per hour: 30
pay for the hours: 30h
add sales bonus: 30h + 5
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Answer: 6h + 1
a bucket contains 3 1/2 gallon of water. If Marie adds 5 gallons more, how many gallons of water will there be in all?
Answers
Answer:
8 1/2
because 3 + 5= 8+ 1/2= 8 1/2
BRAINLIEST IF CORRECT
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Answer:
1st and 3rd answer
Step-by-step explanation:
1st answer - Having a sample that is not random does not allow you to generalize the results of the experiment/study to the population because it is not representative of the population in the first place.
3rd answer - The definition of a random sample is that each member of the population has an equal chance of being selected.
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Which is the graph of the linear inequality 1/2x - 2y > -6?
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Answer:
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Step-by-step explanation:
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Thus, we have:
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URGENT PLZ HELP: Graph y = tanx for -pi/4 ≤ x ≤ x/4.
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Step-by-step explanation:
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х
4
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Answer:
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Step-by-step explanation:
A number greater than 4 is rolled on a six-sided number cube. What is the probability of the complement of this event? Express your answer as a fraction in simplest form.
Answers
===========================================================
Explanation:
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set B = dice values 4 or less = {1,2,3,4}
Sets A and B are considered complementary because one or the other must happen. You must either roll something larger than 4 (set A) or you must roll something from set B.
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Answers
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HELP ME WITH THIS pLEASE ILL MARK U THE BRAINLIEST
Answers
3% = 0.20 x 3
= 0.60
Answer is A