Use the reciprocal method. the first term is really 4 divided by 3/4. which is also the same as 4 multiplied by 4/3. that number is 16/3 of course. you then find a common denominator between the 2 terms. 16/3 and 3/2 can both have the denominator 6. The first term gets changed to 32/6 and the second can be changed to 9/6 and when 32/6 - 9/6 is done, it comes out to 23/6
23/6
x2 + y2 + 6x - 6y + 2 = 0
To complete square to a quadratic equation in its standard form we have:
ax2 + bx + c
Completing squares:
P (x) = (x + b / 2) ^ 2 - b ^ 2/4 + c
Keeping this in mind, we can complete square then:
x2 + y2 + 6x - 6y = -2
(x2 + 6x) + (y2 - 6y) = -2
((x + b / 2) ^ 2 - b ^ 2/4 + c) + ((y + b / 2) ^ 2 - b ^ 2/4 + c) = -2
((x + 6/2) ^ 2 - 6 ^ 2/4 + 0) + ((y + (-6) / 2) ^ 2 - (-6) ^ 2/4 + 0) = -2
((x + 3) ^ 2 - 9) + ((y - 3) ^ 2 - 9) = -2
((x + 3) ^ 2) + ((y - 3) ^ 2) - 9 - 9 = -2
((x + 3) ^ 2) + ((y - 3) ^ 2) - 18 = -2
((x + 3) ^ 2) + ((y - 3) ^ 2) = -2 + 18
((x + 3) ^ 2) + ((y - 3) ^ 2) = 16
((x + 3) ^ 2) + ((y - 3) ^ 2) = 4 ^ 2
Answer:
center: (-3, 3), r = 4
Answer:
x > 5
Step-by-step explanation:
isolate x by subtracting 7 from both sides
x > 12 - 7
x > 5
3(√x+1-5)=27
divide both sides by 3
√x+1-5= 27
add 5 to both sides
√x+1=27+5
√x+1=32
take square of both sides
x+1=32
subtract 1 from each sides
x=32-1
x=31
To determine the perimeter of the trapezoid, we just have to determine the distance between the pair of points which can be calculated through the equation,
d = √(x₂ - x₁)² + (y₂ - y₁)²
Substituting,
(1,4) and (-2,0) d = √(1 - -2)² + (4 - 0)² = 5
(-2,0) and (7,0) d= √(-2 - 7)² + (0 - 0)² = 9
(7,0) and (3,4) d = √(7 - 3)² + (0 - 4)² = 5.66
(3,4) and (1,4) d = √(3 - 1)² + (0 - 0)² = 2
The perimeter is the sum of the distances. Thus, the answer is 21.66.