find locus of a point which moves so that
it's distance from the point (2,1) is double its distance from (1,2)
Answers
Answer:
hi,
Step-by-step explanation:
Let say P=(x,y) a point of the locus
[tex]Distance\ from\ P\ to\ (2,1)= \sqrt{(x-2)^2+(y-1)^2} \\Distance\ from\ P\ to\ (1,2)= \sqrt{(x-1)^2+(y-2)^2} \\\\\sqrt{(x-2)^2+(y-1)^2} =2*\sqrt{(x-1)^2+(y-2)^2} \\\\(x-2)^2+(y-1)^2=4*((x-1)^2+(y-2)^2)\\\\3x^2-4x+3y^2-14y+15=0\\\\[/tex]
[tex]3x^2-4x+3y^2-14y+15=0\\3(x^2-2*\dfrac{2}{3} x)+3(y^2-2*\dfrac{7}{3}*y) +15=0\\3(x^2-2*\dfrac{2}{3}*x+\dfrac{4}{9})+3(y^2-2*\dfrac{7}{3}*y+\dfrac{49}{9} ) +15-\dfrac{4}{3}-\dfrac{49}{3}=0\\\\3(x-\dfrac{2}{3})^2+3(y-\dfrac{7}{3})^2-\dfrac{8}{3}=0\\\\\\\boxed{(x-\dfrac{2}{3})^2+(y-\dfrac{7}{3})^2=\dfrac{8}{9}}\\\\[/tex]
Locus is the circle of center (2/3,7/3) and radius =2√2 /3.
Related Questions
Solve for x: the quantity of x plus 20 over 2 = 3x
Question 6 options:
x = 10
x = 4
x = −14
x = −17
Answers
Answer:
B. x = 4
Step-by-step explanation:
Answer: X = 4
Step-by-step explanation:
(x + 20)/2 = 3x
x + 20 = 2*3x
x + 20 = 6x
20 = 6x - x
20 = 5x
20/5 = x
x = 4
I need help I’m been stuck on this section forever
Answers
B
8
С
Find the length of "c" to the
nearest tenth using the
Pythagorean Theorem.
Enter
Answers
Answer:
10.6
Step-by-step explanation:
Pythagorean theorem: a² + b² = c²
Where a and b = the legs and c = hypotenuse
We are given two legs and need to find the hypotenuse
Given:
Short leg (a) = 7
Long leg (b) = 8
Hypotenuse = c
Now to find the value of c we simply plug in the values of the variables into the Pythagorean theorem and solve for c
Pythagorean theorem: a² + b² = c²
a = 7, b = 8, c = c
Plug in values
7² + 8² = c²
Now solve for c
Simplify exponents
49 + 64 = c²
Add
113 = c²
Taking the square root of both sides
c = 10.6 ( rounded to the nearest tenth )
Answer:
c = 10.6
Step-by-step explanation:
[tex]h {}^{2} = p {}^{2} + b {}^{2} \\ c {}^{2} = (8) {}^{2} + (7) {}^{2} \\ c = \sqrt{64 + 49} \\ c = \sqrt{113} \\c = 10.6[/tex]
Midpoints & endpoints
Answers
Answer:
The coordinates of A are (1, -4)
Step-by-step explanation:
The formula for finding a midpoint is ((x1 + x2) / 2, (y1 + y2) / 2)
However, in this problem, we're already given the midpoint. We're trying to find an endpoint. So, the equation changes into:
((x + 9) / 2 = 4, (y + 0) / 2 = -2)
For the x and y coordinates, multiply both sides by 2
(x + 9 = 8, y = -4)
(x = -1, y = -4)
Rewrite as coordinates.
(-1, -4)
A washer and a dryer cost 860 combined. The washer costs 90 less than the dryer. What is the cost of the dryer?
Answers
Answer:
340
Step-by-step explanation:
860 ÷ 2 = 430
430 - 90 = 340
If angle f and g are complementary. And f is 4 times bigger than angle g what are their measures
Answers
Answer:
Step-by-step explanation:
3
1/2x-3/10=5/2x+7/10
Answers
Answer:
-Isolate the variable by dividing each side by factors that don't contain the variable.
Exact Form:
x= -1/2
Decimal Form:
x=0.5
Step-by-step explanation:
Isolate the variable by dividing each side by factors that don't contain the variable.
Answer: x = -1/2
Step-by-step explanation:
1/2 x - 3/10 = 5/2 x + 7/10
-1/2 x on both sides
-3/10 = 4/2 x +7/10
subtract 7/10 from both sides
-1 = 4/2x
simplify
2x = -1
divide 2 on both sides
x = -1/2
8. Solve the following for z: b = dz + g
Answers
Answer:
[tex] \: z = \frac{b - g}{d} [/tex]
Step-by-step explanation:
[tex]b = dz + g \\ b - g = dz \\ \frac{b - g}{d} = z \\ hence \: z = \frac{b - g}{d} [/tex]
14 +3n = 8n - 3(n - 4)
Answers
Answer:
n=1
Step-by-step explanation:
Start by distributing the -3 to (n-4)
14+3n=8n-3n+12
Then combine like terms on the right
14+3n=5n+12
Subtract 12 from both sides
2+3n=5n
Subtract 3n from both sides
2=2n
Divide both sides by 2
1=n
HELP WILL MARK AS BRAINLIEST!!!
MAGIC SQUARE HELP PLEASE
Answers
Answer:
Top Middle: 2/10 or 1/5 or 4/20
Bottom right: 2/20 or 1/10
Middle right: 2/10 or 1/5
Middle Middle: 7/40
Help (Geomotry)!!!!
Answers
x + 7 + 3x + 20 = 6x - 5
4x + 27 6x - 5
4x - 6x-27-5
-2x = -32
x = -32: (-2)
x = 16
Therefore
MN = 3x + 20 = 3 16+ 2048 + 20 = 68 Answer: MN = 68.
my family uses 3 cartons of milk a day . how many cartons did we use in january
Answers
Answer:
93 cartons
Step-by-step explanation:
January-31
no of cartons-3 × 31=93
Is this a function? {(-3, 1), (1, -2), (3, 0), (4, 5)}
Answers
evaluate the impact of risky behaviour on your personal expectations in relation to your career help with maths too
Answers
Step-by-step explanation:
In triangle ADE:
sum of all angles is 180.
3x-10+58+42=180
3x+90=180
3x=180-90
3x=90
x=90/3
x=30
As line DA and CB are parallel:
angle D=angle C
angle y=58
In angle BCE, sum of angles is 180.
z+58+42=180
z+100=180
z=180-100
z=80
Some math help please?
Answers
Answer:
∠ LMP = 77° , ∠ NMP = 103°
Step-by-step explanation:
The 2 angles on the straight line sum to 180° , that is
∠ LMP + ∠ NMP = 180 , substitute values
- 16x + 13 - 20x + 23 = 180 , that is
- 36x + 36 = 180 ( subtract 36 from both sides )
- 36x = 144 ( divide both sides by - 36 )
x = - 4
Then
∠ LMP = - 16x + 13 = - 16(- 4) + 13 = 64 + 13 = 77°
∠ NMP = - 20x + 23 = - 20(- 4) + 23 = 80 + 23 = 103°
Simplify (2^-1 +5^-1)^2 *(-5/8)^-2
Answers
Answer: 1.2544
Step-by-step explanation:
2^-1 = 1/2
5^-1 = 1/5
1/2+1/5 = 7/10
(7/10)^2=49/100=0.49
(-5/8)^-2 = 64/25=2.56
(2^-1 +5^-1)^2 *(-5/8)^-2 = 0.49 * 2.56 = 1.2544
Solve - 3 [ ( x + 2 ) ( x - 1 ) - x ^ { 2 } + 1 ] + 3 ( x - 1 ) (and could you please explain it to me?? I really don't get it. Thanks!)
Answers
Answer:
Step-by-step explanation:
[tex](x+2)(x-1)= x^2+2x-x-2= x^2 +x -2\\\\( x + 2 ) ( x - 1 ) - x ^ { 2 } + 1 =x^2+x-2-x^2+1=x-1\\\\- 3 [ ( x + 2 ) ( x - 1 ) - x ^ { 2 } + 1 ] =-3(x-1)=-3x+3\\\\- 3 [ ( x + 2 ) ( x - 1 ) - x ^ { 2 } + 1 ] + 3 ( x - 1 ) =-3x+3+3x-3=6x\\[/tex]
Im bad at money :/ do please help me
Answers
The third answer
1 quarter, 6 dimes, 1 nickel, 7 pennies
If it says area does it mean
A, addition
B, subtract
C, multiplication
E, division
F, equals
Answers
Answer:
C. Multiplication
Step-by-step explanation:
To find the area, you multiply the width and length.
Squares, Rectangles, Rhombuses: l x w = a
Triangles: l x w
2
Question 5
Kaya is riding her dirt bike on a road and spots a pothole ahead.
Kaya slows her car from 20.0 m/s to 5.0 m/s in 3.0 seconds. What
was her acceleration?
Answers
2. χΣ -4
Please help
Answers
Step-by-step explanation:
1)x is less than 7
2)x is greater than and equal to -4
Sarah is going on a trip. She drives for 2 hours and 50 minutes, rests for 30 minutes and drives
for another 1 hours 10 minutes.
What is her total travel time in hours and minutes
Answers
Answer:
4hr and 30 min
Step-by-step explanation:
2hr and 50 min + 30 min = 3hr and 20 min
3hr and 20 min + 1hr and 10min = 4 hr and 30min
20=x+12
What is the value of x, please help me, thank you.
Answers
Answer:
20-12= x
8=x
x=8
Step-by-step explanation:
I think check once to confirm tho
Answer:
8
Step-by-step explanation:
20 = x + 12 Subtract 12 from both sides to get x on it's own.
20-12= x Simplify
8 = x
x = 8 Here is your answer!
Hope this helps,
Please mark me the brainliest!
Which pair of transformations moves quadrilateral 1 to quadrilateral 2?
a:Reflect over the line y = -3, then rotate it 90 degrees counterclockwise about the origin
b:Reflect it over the x-axis, then rotate it 180 degrees about the origin
c:Rotate it 90 degrees counterclockwise about the point (-3, -3) then translate it 8 units to the right
d:Translate it 8 units to the right, then reflect it over the line y=-3
Answers
Answer:
Answer choices:
a. Reflection takes it to Q2, further rotation takes it back to Q3
Incorrectb. Reflection takes it to Q2, rotation takes to Q4 with right shape.
Correctc. Rotation takes is to Q4, translation keeps in same Q but with wrong shape
Incorrectd. Translation takes it to Q4, reflection keeps it in same Q but with wrong shape
IncorrectBecause the shape is present in Q3
So reflection over x axis takes it to Q2
Then 180° rotation about origin takes it to Q4
Hence Option B is correct
PLEASE HELP I WILL GIVE BRAINLIEST TO THE CORRECT ANSWER
himari is solving the equation 4 ( x - 3 ) = 16. Her first step is 4x - 12 = 16
which step could be the next step? select all that apply.
1. 4x - 12 + 12 = 16 + 12
2. 4x - 12 - (-12) = 16 - (-12)
3. 1/4 x ( 4x - 12 ) = 16 x (1/4)
4. 4x/4 - 12 = 16/4
5. 4 x ( 4x - 12 ) = 16 x 4
Answers
Answer:
1. could be the next step.
3. could be the next step.
Step-by-step explanation:
What is 0.304 in fractions?
Answers
Answer:
[tex]\frac{38}{125}[/tex]
Hope this helped! Also, it would really help me out if you gave me a Brainliest. It boosts my confidence and makes my day! Would really appreciate! Thank you! (Also, if the answer is wrong, please tell me and I will check as fast as I can)
solve for X: -0.6x>3
Answers
Answer:
x < -5
Step-by-step explanation:
-0.6x > 3
=> Dividing 0.6 on both sides
=> -x > 3/0.6
=> -x > 5
=> x < -5 [When we multiply -1 on both sides the sign changes]
The solution to the inequality -0.6x > 3 is x < -5.
To solve for x in the inequality -0.6x > 3, we need to isolate x on one side of the inequality.
First, to divide both sides of the inequality by -0.6 to remove the coefficient in front of x.
Remember that when dividing or multiplying both sides of an inequality by a negative number, we need to reverse the inequality sign.
So, dividing both sides by -0.6 gives
x < 3 / -0.6
Simplifying the right side of the inequality, we have:
x < -5
Therefore, the solution to the inequality -0.6x > 3 is x < -5.
Learn more about inequality ;
brainly.com/question/14164153
#SPJ6
if two planes intersect, then their intersection is a point true or false
Answers
I believe that it is true
Step-by-step explanation:
sorry if im wrong
Answer:
False.
Step-by-step explanation:
Suppose y varies directly with x, and y = 12 when x= - 4. Find x when y= 15.
Answers
Answer:x=-5
Step-by-step explanation:
Identify the perfect squares.
Select all that apply:
Answers
Answer:
81, 64, 49
Step-by-step explanation:
81/9=9
64/8=8
49/7=7