If the two linear equations have the same slope (and the SAME y-intercept), the equations represent the same line. Since a line intersects with itself everywhere, there will be an infinite number of solutions (intersecting everywhere.)
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Answer:
(x + 3)² + (y - 7)² = 81
Step-by-step explanation:
the equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k ) are the coordinates of the centre and r the radius
here (h, k ) = (- 3, 7 ) and r = 9 , then
(x - (- 3) )² + (y - 7)² = 9² , that is
(x + 3)² + (y - 7)² = 81
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Answer:
D. x = 15; y = 5√3
Step-by-step explanation:
You don't need to know any trig to select the correct answer. You only need to know that the lengths of both sides must be less than the length of the hypotenuse. It is also helpful to know that √3 is about 1.732, so 10√3 ≈ 17.32.
Since x < 10√3, only answer choices A and D are viable.
Since y < 10√3, only answer choice D is viable.
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If you want to solve this using trig relations, you can recall that the sides of a 30°-60°-90° triangle have the ratios 1 : √3 : 2. This means short side y is half the length of the hypotenuse 10√3, so y = 5√3. It also means longer side x is √3 times y, so is x = (5√3)√3 = 5·3 = 15.
x = 15; y = 5√3
