The equation x2 + y2 − 2x + 2y − 1 = 0 is the general form of the equation of a circle. What is the standard form of the equation?
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Answer:
Step-by-step explanation:
Standard form of the equation is
To get standard form we apply completing the square method
Take coefficient of x and y . Divide it by 2 and then square it
and 1^2=1
Add and subtract 1
Now write the parenthesis in square form
, add 3 on both sides
is the standard form
(x^2 - 2x) + (y^2 + 2y) - 1 = 0
(x^2 - 2x + 1) + (y^2 + 2y + 1) - 1 - 1 - 1 = 0
(x - 1)^2 + (y + 1)^2 - 3 = 0
(x - 1)^2 + (y + 1)^2 = 3
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The value of X and Y vary directly, and when X= 4 Y equals -10. Find the value of Y when X equals 10.
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Answer:
b
Step-by-step explanation:
angle b = angle e = 90 (given) R
if ac = df H
bc = ef (given) S
x^2-6x+20=6x
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Answer:
x=10 or x=2
Step-by-step explanation:
msg me if ya need step
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To find the distance between the points (a, a) and (b, b), we can use the distance formula. The distance formula calculates the distance between two points in a coordinate plane.
The distance between two points (x1, y1) and (x2, y2) is given by the formula:
Distance = √((x2 - x1)² + (y2 - y1)²)
In this case, since the points are (a, a) and (b, b), we substitute a for both x1 and y1, and b for both x2 and y2:
Distance = √((b - a)² + (b - a)²)
Simplifying this expression further:
Distance = √((b - a)² + (b - a)²) = √(b² - 2ab + a² + b² - 2ab + a²) = √(2a² + 2b² - 4ab)
Therefore, the distance between the points (a, a) and (b, b) is √(2a² + 2b² - 4ab).
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14x + 70y = 820. Where we have taken y to be the number of bottles and x to be the number of cans.
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3.7cm : 1850km
1cm : 1850/3.7 km
1cm : 500km
Scale statement for map is : 1cm : 500km.
That is 1cm on map represents 500km.
1cm : 500km. Recall 1km = 1000m = 100 000cm
1cm : 500* 100000cm
1cm : 50 000 000cm
1: 50 000 000.
Scale factor is 50 000 000.
Final answer:
The scale of the map is 1 cm : 500 km, meaning 1 cm on the map corresponds to an actual distance of 500 km on the ground. This is the scale factor used to create the map.
Explanation:
The scale of a map is a ratio that represents the relationship between the distance on the map and the actual distance on the ground. In this case, the actual distance between Vancouver and Winnipeg is 1850 km, while the distance on the map is 3.7 cm. Therefore, the scale of the map can be represented as 1 cm : 500 km (because 1850 km / 3.7 cm = approximately 500 km).
This means that 1 cm on the map represents an actual distance of 500 km on the ground, which is the scale factor used to create the map. Therefore, the scale statement for the map would be "1 cm on the map represents 500 km on the ground" or it can be written shorthand as 1:50,000,000 (considering 1 km = 1,000,000 cm).
Learn more about Map Scale here:
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