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1 answer:
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Answer:
The roots of the equation are x = and x =
and there are no real roots of the equation given above
Step-by-step explanation:
To solve:
5x² − 3x + 17 = 9
or
⇒ 5x² − 3x + 17 - 9 = 0
or
⇒ 5x² − 3x + 8 = 0
Now,
the roots of the equation in the form ax² + bx + c = 0 is given as:
x =
in the above given equation
a = 5
b = -3
c = 8
therefore,
x =
or
x =
or
x = and x =
or
x = and x =
here i = √(-1)
Hence,
The roots of the equation are x = and x =
and there are no real roots of the equation given above
The distance between the points (d) is found using the Pythagorean theorem.
Imagine the two points as defining the hypotenuse of a right triangle. The lengths of the legs of the triangle are the horizontal distance between the points and the vertical distance between the points. The the theorem tells us
d² = 4² + 7²
d² = 16 + 49
d² = 65
d = √65 ≈ 8.1
The distance between the points is
C 8.1
_____
You know that the distance must be longer than the longest leg (7) and must be shorter than the sum of the two legs (4+7=11). The only answer choice between 7 and 11 is 8.1.
Imagine the two points as defining the hypotenuse of a right triangle. The lengths of the legs of the triangle are the horizontal distance between the points and the vertical distance between the points. The the theorem tells us
d² = 4² + 7²
d² = 16 + 49
d² = 65
d = √65 ≈ 8.1
The distance between the points is
C 8.1
_____
You know that the distance must be longer than the longest leg (7) and must be shorter than the sum of the two legs (4+7=11). The only answer choice between 7 and 11 is 8.1.