What ordered pair is a solution of the equation 2x-y=9
2 answers:
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Answer:
If d<2, there is no intersection
If d=2, there is one intersection
If 2<d<8, there are two intersections
If d=8, there is one intersection
if d>8, there is no intersection
Step-by-step explanation:
If d<2 (the difference between both radius is 2), the little circle is inside the big one. Thus there is no intersection.
If d=2, the little circle is inside but tangent to the big one. There is one intersection then.
If 2<d<8, there are two intersections since the little circle has a portion outside the big one, and another portion inside.
If d=8, the little circle is tangent to the big one from outside. There is one intersection then.
if d>8, the little circle is completely exterior to the big one. Thus, there is no intersection.
Please find attached the figure for d = 10. The big circle is centered and the other is offset by 10.
Answer:
No <em>real</em> solutions (or has two complex roots)
Step-by-step explanation:
The discriminant, <em>b</em>² - 4<em>ac</em>, is the expression (<u><em>radicand </em></u>) of the quadratic equation:
.
The value of the discriminant determines the <u>nature</u> and the <u>number of solutions</u> given by the quadratic equation.
A discriminant with a negative value (or b² - 4ac < 0 ) means that the quadratic equation has no real solutions or two complex solutions. Quadratic equations with a negative discriminant also have no x-intercepts; thus, its graph will not cross the x-axis.