Answers:
Center = (-2.5, 0.5)
Radius = 2.1213 units approximately
Note: The center written in fraction form is (-5/2, 1/2)
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Work Shown:
x^2 + y^2 + 5x - y + 2 = 0
x^2 + 5x + y^2 - y + 2 = 0
x^2 + 5x + y^2 - y = -2
x^2 + 5x + 6.25 + y^2 - y = -2 + 6.25 <<--- see note1 below
(x^2 + 5x + 6.25) + y^2 - y = 4.25
(x + 2.5)^2 + y^2 - y = 4.25
(x + 2.5)^2 + y^2 - y + 0.25 = 4.25 + 0.25 <<--- see note2 below
(x + 2.5)^2 + (y^2 - y + 0.25) = 4.5
(x + 2.5)^2 + (y - 0.5)^2 = 4.5
The equation is in the form (x-h)^2 + (y-k)^2 = r^2
where,
h = -2.5 = -5/2
k = 0.5 = 1/2
r = sqrt(4.5) = 2.1213 approximately
So that's why the center is (-5/2, 1/2) = (-2.5, 0.5) and the radius is approximately 2.1213 units
note1: I took half of 5 to get 5/2 = 2.5 then I squared it to get (2.5)^2 = 6.25; The value 6.25 is added to both sides. This is done to complete the square for the x terms
note2: Similar to note1, but done for the y terms now. I took half of -1 to get -1/2 = -0.5 and then squared it to get (-0.5)^2 = 0.25, which is added to both sides
Answer:
Step-by-step explanation:
total sides = 6
p (rolling a 1) =
p (rolling a 2) =
Note:
or - add
and - multiply
∴
∴
hence, p (rolling a 1 or 2) =
Answer:
(a) 1/2
(b) 9/10
Step-by-step explanation:
Probability is given by number of possible outcomes ÷ number of total outcomes
(a) Number of possible outcomes = 5 questions, number of total outcomes = 10 questions
Probability (I answer all 5 problems correctly) = 5/10 = 1/2
(b) Probability (I answer at least 4 of the problems correctly) means I either answer 4 of the problems or all 5 problems correctly = 4/10 + 5/10 = 9/10
Answer:
B. Craig multiplies 2x + 4y = 16 by 2 and then subtracts the equations. He finds the result is a contradiction, so there is no solution.
hope it helps :)
To round to the nearest tenth - look at the number to the right of the tenth value ( the hundredth) and follow the rule
<em>5 or more round up, 4 or less round down
</em>As 1 is lower than 4, we round down.
36.11 therefore rounds down to 36.1