Arrange the circles (represented by their equations in general form) in ascending order of their radius lengths.x2 + y2 − 2x + 2y − 1 = 0
x2 + y2 − 4x + 4y − 10 = 0
x2 + y2 − 8x − 6y − 20 = 0
4x2 + 4y2 + 16x + 24y − 40 = 0
5x2 + 5y2 − 20x + 30y + 40 = 0
2x2 + 2y2 − 28x − 32y − 8 = 0
x2 + y2 + 12x − 2y − 9 = 0
Answers
x²+y²-2x+2y-1 = 0;
x²+y²-4x+4y-10 = 0;
5x²+5y²-20x+30y+40 = 0;
x²+y²-8x-6y-20 = 0;
x²+y²+12x-2y-9 = 0;
4x²+4y²+16x+24y-40 = 0; and
2x²+2y²-28x-32y-8 = 0
Explanation:
For each of these, we want to write the equation in the form
(x+h)²+(y+k)² = r².
To do this, we evaluate the terms 2hx and 2ky in each equation. We will take half of this; this will tell us what h and k are for each equation.
For the first equation:
2hx = -2x and 2ky = 2y.
Half of -2x = -1x and half of 2y = 1y; this means h = -1 and k = 1:
(x-1)² + (y+1)² + ___ - 1 = 0
When we multiply (x-1)², we get
x²-2x+1.
When we multiply (y+1)², we get
y²+2y+1.
This gives us 1+1 = 2 for the constant. We know we must add something to 2 to get -1; 2 + ___ = -1; the missing term is -3. Add that to each side (to have r² on the right side of the equals) and we have
(x-1)² + (y+1)² = 3
This means that r² = 3, and r = √3 = 1.732.
For the second equation, 2hx = -4x and 2ky = 4y; this means h = -4/2 = -2 and k = 4/2 = 2. This gives us
(x-2)² + (y+2)² -10 + ___ = 0.
Multiplying (x-2)² gives us
x²-4x+4.
Multiplying (y+2)² gives us
y²+4x+4.
This gives us 4+4= 8 for our constant so far.
We know 8 + ___ = -10; this means the missing term is -18. Add this to each side of the equation to have
(x-2)²+(y+2)² = 18; r² = 18; r = √18 = 3√2 = 4.243.
For the third equation, 2hx = -8x and 2ky = -6y. This means h = -8/2 = -4 and k = -6/2 = -3. This gives us:
(x-4)²+(y-3)²-20 = 0
Multiplying (x-4)² gives us
x²-8x+16.
Multiplying (y-3)² gives us
y²-6y+9.
This gives us 16+9 = 25 for the constant. We know that 25+___ = -20; the missing term is -45. Add this to each side for r², and we have that
r²=45; r = √45 = 3√5 = 6.708.
For the next equation, we factor 4 out of the entire equation:
4(x²+y²+4x+6y-10)=0.
This means 2hx = 4x and 2ky = 6y; this gives us h = 4/2 = 2 and k = 6/2 = 3. This gives us
4((x+2)²+(y+3)² - 10) = 0.
Multiplying (x+2)² gives us
x²+4x+4.
Multiplying (y+3)² gives us
y²+6y+9.
This gives us a constant of 4+9 = 13. We know 13+__ = -10; this missing value is -23. Since we had factored out a 4, that means we have 4(-23) = -92. Adding this to each side for r², we have
r²=92; r = √92 = 2√23 = 9.59.
For the next equation, we factor out a 5 first:
5(x²+y²-4x+6y+8) = 0. This means that 2hx = -4x and 2ky = 6y; this gives us h = -4/2 = -2 and k = 6/2 = 3:
5((x-2)²+(y+3)²+8) = 0.
Multiplying (x-2)² gives us
x²-4x+4.
Multiplying (y+3)² gives us
y²+6y+9.
This gives us a constant of 4+9 = 13. We know that 13+__ = 8; the missing value is -5. Since we factored a 5 out, we have 5(-5) = -25. Adding this to each side for r² gives us
r²=25; r = √25 = 5.
For the next equation, we first factor a 2 out:
2(x²+y²-14x-16y-4) = 0. This means 2hx = -14x and 2ky = -16y; this gives us h = -14/2 = -7 and k = -16/2 = -8:
2((x-7)²+(y-8)²-4) = 0.
Multiplying (x-7)² gives us
x²-14x+49.
Multiplying (y-8)² gives us
y²-16x+64.
This gives us a constant of 49+64=113. We know that 113+__ = -4; the missing value is -117. Since we first factored out a 2, this gives us 2(-117) = -234. Adding this to each side for r² gives us
r²=234; r = √234 = 3√26 = 15.297.
For the last equation, 2hx = 12x and 2ky = -2; this means h = 12/2 = 6 and k = -2/2 = -1:
(x+6)²+(y-1)²-9 = 0
Multiplying (x+6)² gives us
x²+12x+36.
Multiplying (y-1)² gives us
y²-2y+1.
This gives us a constant of 36+1 = 37. We know that 37+__ = -9; the missing value is -46. Adding this to each side for r² gives us
r² = 46; r=√46 = 6.78.
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On the map of an amusement park on a coordinate grid, the skating rink is at (−1.5, −1).Coordinate grid shown from negative 3 to positive 3 on x-axis and negative 3 to positive 3 on y-axis. There are increments of 1 over 2 for each grid line on each of the two axes. Only the whole numbers are labeled on either side of the axis. Which of these shows how to plot the point to mark the skating rink? From the origin, move 1.5 units to the left along the x-axis and 1 unit vertically down, and place the point. From the origin, move 1 unit to the left along the x-axis and 1.5 units vertically down, and place the point. From the origin, move 1 unit to the right along the x-axis and 1.5 units vertically down, and place the point. From the origin, move 1.5 units to the right along the x-axis and 1 unit vertically down, and place the point.
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What are equivalent fractions to 25/35
Answers
so, the first thing the question asks of you is to see that f(g(x)) = x. try it out, plugging g(x) in as the x-variable in the first equation:
f(g(x)) = (∛(x - 4))³ + 4
they were merciful in writing this problem, and thankfully your cube roots cancel out and don't cause you any trouble. continue solving:
f(g(x)) = (∛(x - 4))³ + 4 ... cube root and exponent cancel
f(g(x)) = x - 4 + 4 ... simplify
f(g(x)) = x
so, yep. that one worked. try out the second half of the question: g(f(x)) = x
g(f(x)) = ∛((x³ + 4) - 4) ... simplify inside your radical, cancelling out the 4s
g(f(x)) = ∛(x³) ... the cube root of x³ is x itself, so:
g(f(x)) = x
and there you are. you've confirmed that these are inverses.
Answers
Answer:
I don't really know because I am dumb sorry
Answer:
26
Step-by-step explanation:
Which situation could be described by this expression?
A.
Jack knows that he will buy 5 blue flowers. He does not know how many yellow flowers he will buy.
B.
Jack knows that each flower costs $5. He knows that he will buy 5 flowers.
C.
Jack knows that the flowers cost a total of $5. He does not know how many flowers he will get.
D.
Jack knows he will buy 5 flowers. He does not know how much each flower costs.
Answers
Answers
today is December 1
Answer:
happy December first to you to, Christmas is just down the road
Step-by-step explanation:
hope it helps, have a great rest of your day, mark brainliest please
Answers
The width of the rectangle with an area x² = 19x + 12 is (4x + 3).
What are the area and perimeter of a rectangle?
The area of a rectangle is the product of its length and width.
The perimeter of a rectangle is the sum of the lengths of all the sides.
We know the area of a rectangle is (length×widh).
Given, A rectangle has an area of 4x² + 19x + 12 and a length of (x + 4).
∴ width of the rectangle is = (4x² + 19x + 12)/(x + 4).
Or, we know that the product of two linear equations is a quadratic so,
4x² + 19x + 12.
4x² + 16x + 3x + 12.
4x(x + 4) + 3(x + 4).
(x + 4)(4x + 3).
So, the width of the rectangle is (4x + 3).
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