Answer:
Center = (5, -2) and radius = √33
Step-by-step explanation:
The equation of a circle is given by the formula;
(x-a)² + (y-b)² = r² ; where (a,b) is the center of the circle and r is the radius of the circle.
In this case;
2x² - 20x + 2y² + 8y =40 ;
Dividing both sides of the equation by 2 we get;
x² - 10x + y² + 4y = 20
we can then use the completing the square on both x and y terms.
x² - 10x + y² + 4y = 20
x² + 2(-5)x + 25 + y² + 2(2) y + 4 = 20 +9 + 4
In standard form we get;
(x-5)² + (y+2)² = 33
Therefore;
Center = (5, -2) and radius = √33
Answer:
16 yd. This is the park's actual length.
Step-by-step explanation:
Write and solve an equation of ratios:
1 1/4 cm 8 yd
------------ = -----------
2 1/2 cm x
Note that 2(1 1/4 cm) = 2 1/2 cm, so the above equation becomes:
1 8 yd
----- = ---------
2 x
Solving for x, we get x = 16 yd. This is the park's actual length.
Answer:
13.7477270849 to 19.7230829233.
Step-by-step explanation:
1. Using the pythagorean theorem, a²+b²=c², we try different combinations of given lengths 10 and 17.
2. If 10 and 17 are legs and 10²+17²=√389 = 19.7230829233, then c=19.7230829233.
3. If 10 is a leg and 17 is a hypotenuse,
10²+b²=17²
100+b²=289
b²=189
b=13.7477270849
4. The case of 17 is a leg and 10 is a hypotenuse is not possible because the hypotenuse is the longest side.
5. The range of the length of the 3rd side is 13.7477270849 to 19.7230829233.
Answer:
(0,-8) and (2.6,0)
Step-by-step explanation:
according to desmos
Answer:
−5x − 2y − 3
Explanation:
2x + 5 − 3y − 7x + y − 8
= 2x + 5 + −3y + −7x + y + −8
[ Combine Like Terms ]
= 2x + 5 + −3y + −7x + y + −8
= (2x + −7x) + (−3y + y) + (5 + −8)
= −5x + −2y + −3
