We do the midpoint formula to find the center of the circle to get the left side of the equation.
Midpoint = [(X₁ + X₂) / 2 , (Y₁ + Y₂) / 2]
Now plug in:
[(8 + 4) / 2 , (- 6 - 2) / 2]
(12 / 2 , - 8 / 2)
(6, - 4)
The center of the circle is (6, -4)
Now we plug it into the equation of a circle:
(x - h)² + (y - k)² = r² where (h, k) is the center of the circle and r is the radius.
(x - 6)² + (y + 4)² = r² is the left side of the equation. This will eliminate options A and C
Now we do the distance formula using the center and an endpoint to get the radius. The formula for distance is:
√((X₂ - X₁)² + (Y₂ - Y₁)²)
We plug in using either of the endpoints.
√((4 - 6)² + (- 2 - (- 4))²)
√((-2)² + 2²)
√(4 + 4)
√8
√8 is your radius
(√8)² = 8
Your correct answer is (x - 6)² + (y + 4)² = 8, Option D
Answer:
19/30 written as decimal is 0.63333
Step-by-step explanation:
Divide numerator by denominator of fraction.
Answer:
C. 3(2x + 5y) is the algebraic expression equivalent to the expression
Step-by-step explanation:
From the question, the given expression is 6x + 15y.
Factorizing this expression gives 3(2x + 5y). Hence, the algebraic expression equivalent to the expression 6x + 15y is 3(2x + 5y). (Option C).
Checking the remaining options
A. 3(2x - 5y)
Expanding this gives 6x - 15y. It is not equivalent to the given expression
B. 3(5x - 2y)
Expanding this gives 15x - 6y. It is not equivalent to the given expression
D. 3(5x + 2y)
Expanding this gives 15x + 3y. It is not equivalent to the given expression.
Hence, C. 3(2x + 5y) is the algebraic expression equivalent to the expression.
Answer: (4,-5) is the answer
At 8 hours of service, the two limousine rental companies charge the same amount.
Step-by-step explanation:
Given,
Initial fee of Executive Limousine rental = $200
Per hour charges of service = $40
Let,
x be the number of hours.
E(x) = 40x+200
Initial fee of Jet Limousine rental = $120
Per hour charges of service = $50
J(x) = 50x + 120
For the charges to be same;
E(x) = J(x)
Dividing both sides by 10
At 8 hours of service, the two limousine rental companies charge the same amount.
Keywords: function, addition
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