What is the following quotient? StartFraction 1 Over 1 + StartRoot 3 EndRoot EndFraction StartFraction StartRoot 3 EndRoot Over
2 answers:
Answer:
D. StartFraction negative 1 + StartRoot 3 EndRoot Over 2 EndFraction
Step-by-step explanation:
Multiply numerator and denominator by the conjugate of the denominator. Then the denominator is the difference of squares, which will be rational. This simplification is called "rationalizing the denominator."
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Answer:
On a coordinate plane, 2 quadrilaterals are shown. The larger quadrilateral has points (negative 5, 3), (1, 3), (4, 0), (negative 2, 0). The smaller quadrilateral has points (negative 1, 0), (negative 2, 1), (0, 1), and (1, 0).
Step-by-step explanation:
<u>Larger quadrilateral</u>
Length of the top and bottom segments are 6 units.
Length of the left and right sides:
d = √[(-5 - (-2))² + (3 - 0)²] = √[3² + 3²] = √(2*3²) = 3√2 units
From point (-5, 3) to point (-2, 0) the slope is:
m = (3 - 0)/(-5 - (-2)) = -1
<u>Smaller quadrilateral</u>
Length of the top and bottom segments are 2 units.
Length of the left and right sides:
d = √[(-2 - (-1))² + (1 - 0)²] = √[1² + 1²] = √2 units
From point (-2, 1) to point (-1, 0) the slope is:
m = (1 - 0)/(-2 - (-1)) = -1
If you dilate the smaller quadrilateral by a factor of 3, you get the larger quadrilateral (they have the same slope, and 3 times length of the smaller quadrilateral is equal to the length of the larger quadrilateral).
