Answer:
[tex]\displaystyle \frac{x^2}{5}+\frac{y^2}{9}=1[/tex]
Step-by-step explanation:
We want to find the locus of a point such that the sum of the distance from any point P on the locus to (0, 2) and (0, -2) is 6.
First, we will need the distance formula, given by:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
Let the point on the locus be P(x, y).
So, the distance from P to (0, 2) will be:
[tex]\begin{aligned} d_1&=\sqrt{(x-0)^2+(y-2)^2}\\\\ &=\sqrt{x^2+(y-2)^2}\end{aligned}[/tex]
And, the distance from P to (0, -2) will be:
[tex]\displaystyle \begin{aligned} d_2&=\sqrt{(x-0)^2+(y-(-2))^2}\\\\ &=\sqrt{x^2+(y+2)^2}\end{aligned}[/tex]
So sum of the two distances must be 6. Therefore:
[tex]d_1+d_2=6[/tex]
Now, by substitution:
[tex](\sqrt{x^2+(y-2)^2})+(\sqrt{x^2+(y+2)^2})=6[/tex]
Simplify. We can subtract the second term from the left:
[tex]\sqrt{x^2+(y-2)^2}=6-\sqrt{x^2+(y+2)^2}[/tex]
Square both sides:
[tex](x^2+(y-2)^2)=36-12\sqrt{x^2+(y+2)^2}+(x^2+(y+2)^2)[/tex]
We can cancel the x² terms and continue squaring:
[tex]y^2-4y+4=36-12\sqrt{x^2+(y+2)^2}+y^2+4y+4[/tex]
We can cancel the y² and 4 from both sides. We can also subtract 4y from both sides. This leaves us with:
[tex]-8y=36-12\sqrt{x^2+(y+2)^2}[/tex]
We can divide both sides by -4:
[tex]2y=-9+3\sqrt{x^2+(y+2)^2}[/tex]
Adding 9 to both sides yields:
[tex]2y+9=3\sqrt{x^2+(y+2)^2}[/tex]
And, we will square both sides one final time.
[tex]4y^2+36y+81=9(x^2+(y^2+4y+4))[/tex]
Distribute:
[tex]4y^2+36y+81=9x^2+9y^2+36y+36[/tex]
The 36y will cancel. So:
[tex]4y^2+81=9x^2+9y^2+36[/tex]
Subtracting 4y² and 36 from both sides yields:
[tex]9x^2+5y^2=45[/tex]
And dividing both sides by 45 produces:
[tex]\displaystyle \frac{x^2}{5}+\frac{y^2}{9}=1[/tex]
Therefore, the equation for the locus of a point such that the sum of its distance to (0, 2) and (0, -2) is 6 is given by a vertical ellipse with a major axis length of 3 and a minor axis length of √5, centered on the origin.
someone help me with this
Find the perimeter of this semi-circle with radius,
r
= 26cm.
Give your answer as an expression in terms of
π?
Answer:
26x2,
52xπ
Step-by-step explanation:
The perimeter of this semi-circle with a radius of 26 cm will be 81.64 cm.
What is the circumference of a circle?It is the close curve of an equidistant point drawn from the center. The radius of a circle is the distance between the center and the circumference.
Let 'r' be the radius of the circle. The circumference of the circle will be
C = 2πr units
The radius of the semicircle is given as,
r = 26 cm
Then the circumference of the semicircle is half of the circle. Then we have
C = 1/2 x 2πr
C = πr
At r = 26 cm, then we have
C = 3.14 x 26
C = 81.64 cm
The perimeter of this semi-circle with a radius of 26 cm will be 81.64 cm.
More about the circumference of a circle link is given below.
https://brainly.com/question/27177006
#SPJ5
PLZZZ HELP ME OUT........................ PLZZ
Answer:
a) constant of proportionality is 3/5
b) 3.5cm per 1 minute
c) 21 cm water in trough after 6 min
d) 70 cm
Step-by-step explanation:
d) 21 / 6 = x / 20
7 / 3 = x / 20
2x = 140
x = 70
Hiiii Can someone please help me please
A, B, C, or D
F, G, H, or J
Ill give lots of points because there's two Please help me thank you BRAINLIEST ANSWER btw ❤️
Answer:
B, H
Step-by-step explanation:
The electrician charges 45 dollars per hour and 30 at the beginning. We are multiplying the hours, h, by 45 to get 45h. We add 30 to get C=45h+30
Jerome will always earn 75 dollars, but he also gets 10 percent commission, which is 0.10.
Answer:
B and H are the correct answers
Is there a way to quickly find a function if you have a handful of ordered pairs?
ex. (-6, 10) (-4, 7) (-2, 4) (0, 3) (2, 0) (4, -3)
Paul won 37 super bouncy balls playing hoops at county fair. At school he gave two to every student in his math class. He only had 3 remaining. How many students are in his class?
Answer:
17 students
Step-by-step explanation:
If he started with 37 and ended with 3 we have to subtract those three first so that we know how many we are actually working with so, 37-3=34. 34 balls is the amount distributed among the class. 34/2 is 17.
A circle fits in a square with sides of 12 inches. What is the approximate area of the shaded region between the square and the circle? (Use 3.14 for Pi and round to the nearest whole number.)
A. 31 in squared
B. 69 in squared
C. 106 in squared
D. 125 in squared
Answer:
A
Step-by-step explanation:
Have to find x,y and z.
Answer:
z= 2√2
x=2
y=2√2
A circle has a diameter of 26 units. What is the area of the circle to the nearest
hundredth of a square unit?
A 81.68
B 530.93
C 2,123.72
D 8.494.87
Answer:
b
Step-by-step explanation:
area = pie x radius(2)
= 3.142 x 13 (2)
= 530.998
find the trigonometric ratio
this is geometry with trig
Answer:
tanZ = [tex]\frac{20}{15}[/tex]
Step-by-step explanation:
tanZ = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{XY}{ZY} }[/tex] = [tex]\frac{20}{15}[/tex]
a) Write 5.1 x 10^-1as an ordinary number.
Answer:
0.51
Step-by-step explanation:
can someone plz help i need it quick
Answer:
The correct answer is 70.
60+50=110
180-110=70
the angels x and y are equivalent
Step-by-step explanation:
hoped this helped
✩brainliest appreciated✩
Answer:
the answer is dododoodod
Step-by-step explanation:
PLS HELP
PLSSSSSSSSSSS
Answer:
y=-15
.2020202020charactersneeded
Two trains, Train A and Train B, weigh a total of 381 tons. Train A is heavier than Train B.
The difference of their weights is 193 tons. What is the weight of each train?
I need this answer quick!
Answer:
Train A is 287 tons
Train B is 94 tons
Step-by-step explanation:
My method of solving it may have been a bit different from how you were taught. I divided 381 by 2 to give both trains an equal weight of 190.5 tons. I then divided the difference, 193, by 2 to get 96.5 tons. I subtracted the new difference from the weight of Train B and added it to train A. To double check, you can grab a calculator and see that their weights are equal to 381.
Plz help me I will give you brainliest and 10 points
Answer:
0.08522
Step-by-step explanation:
A spinner is shown below.
Which of the following relative frequencies match the expected probability?
PLLLS helpppp mee this is due now T-T
Answer:
Step-by-step explanation:
Answer:
= 2 and 5
Step-by-step explanation:
( 4 - 7x ) + ( 2x - 2 ) = 0
4 - 7x = 2x - 2 = 0
-7x -2x - 2 + 4 = 0
-5x - 2 = 0
-5 x = 0 or -2 = 0
x = 5 x = 2
1.How do you know you have a direct variation in the
relationship between two quantities?
Answer:
Say you have y=2x. That is direct variation and will always pass through the origin when graphed. When x is multiplied by a number, the y value will also be changed by that number. If you add a y-intercept and change y=2x to, for example, y=2x+2, the x and the y will no longer be related by a constant ratio.
Step-by-step explanation:
When multiplying or dividing integers, if the signs are the same, you keep the sign for the answer.
GIVING BRAINLIST PLEASE ANSWER CORRECT!!!
False
True
2 3/5 x 5/6 plz help
Answer:
2 1/6
Step-by-step explanation:
2 3/5 x 5/6
convert the 2 3/5 to an improper fraction so it can be easier to multiply
2 3/5 = 13/5
13/5 * 5/6
All you need to do is multiply across. Both denominators, and both numerators.
13 * 5 = 65 (numerator)
5 * 6 = 30 (denominator)
65/30 and that is in an improper form
2 5/30 = 2 1/6 = In a simplified mixed number
2 1/6
Hope this helped!
Have a supercalifragilisticexpialidocious day!
What is the solution to this inequality? -9x - 15 2
A. x > 2
B. x > -2
C. x < -2
D. x < 2
Answer:
Step-by-step explanation:
x>-2
Becuase multiply it and divide
Elijah is planning a circular flower garden with a 12 foot diameter. He will put plastic edging along the flowerbed. How many feet of edging will Elijah need to enclose his flower garden? Round to the nearest tenth place. (Use 3.14 for π)
Answer:
[tex]37.7\ \text{foot}[/tex]
Step-by-step explanation:
The length of the edging will be equal to the circumference of the circular flower garden.
Here, the diameter of the circular garden is [tex]d=12\ \text{foot}[/tex]
Circumference of a circle is given by
[tex]C=\pi d\\\Rightarrow C=3.14\times 12\\\Rightarrow C=37.68\approx 37.7\ \text{foot}[/tex]
The length of the edging is [tex]37.7\ \text{foot}[/tex].
What was the price for one notebook?
Answer:
A notebook at the dollar store costs between 1-2 dollars
Graph the line with the equation y = 22 - 2.
y
10
9
8
7
6
5
4
3
2
-10 -9
-8
-7 -6
-5
-4
-3
-2
-
1
2
3
4
5 6
7
8
9 10
-1
If a line passes through (4,13) and (6,19) what is the slope? And can you please explain how you got your answer
Answer:
The slope is 3.
Step-by-step explanation:
The equation for slope is either [tex]\frac{y2-y1}{x2-x1}[/tex] or [tex]\frac{y1-y2}{x1-x2}[/tex]. So this should be [tex]\frac{19-13}{6-4}[/tex], which is 3.
Answer:
Slope =
6
—
2
Step-by-step explanation:
First find the rise over run
Second use the format
Y2-y1
———-
X2-x1
Using the format you will get this
19-13
——
6-4
Next solve
Which then you get
6
—
2
g−9=−19
Help plz
Pleaseeeeee
Answer:
g = -10
Step-by-step explanation:
SOMEONE DO THESE QUESTIONS FOR ME ASAP!! - GIVING BRAINLIEST
Answer:
1 Question= 26
2 Question=41
3 Question= 57
4 Question= 15
5 Question = 20
Step-by-step explanation:
Solve by completing the square x^2-10x-24=0
Step-by-step explanation:
=x²-10x-24
=x²-4x+6x-24
=x(x-4)+6(x-4)
=(x-4)(x+6)
hope it helps.
You brought a magazine for $3 and some candy bars for $2 each. You spent a total of $19. How many candy bars did you buy?
Answer:
8
Step-by-step explanation:
Answer:
Candy bars: $13
Step-by-step explanation:
$3 magazine + $13 total of candy bars = $19
One less than five times a number is fewer
than twenty-four.
Answer:
x < 5
Step-by-step explanation:
[tex]5x - 1 < 24\\5x < 25\\x < 5[/tex]
Answer:
any number under 5
Step-by-step explanation:
5(5) -1 =24
so anything under that would equal fewer than 24
Is this what you're asking?
