Answer:
the third option
Step-by-step explanation:
what does that mean ?
to "rationalize" it is to transform it into a rational number (that is a number that can be described as a/b, and is not an endless sequence of digits after the decimal point without a repeating pattern).
a square root of a not square number is irrational (not rational).
so, what this question is asking us to get rid of the square root part in the denominator (the bottom part).
for this we need to multiply to and bottom with the same expression (to keep the whole value of the quotient the same) that, when multiplied at the bottom, eliminates the square root.
what can I multiply a square root with to eliminate the square root ? the square root again - we are squaring the square root.
so, what works for 9 - sqrt(14) as factor ?
we cannot just square this as
(9- sqrt(14))² = 81 -2sqrt(14) + 14
we still have the square root included.
but remember the little trick :
(a+b)(a-b) = a² - b²
without any mixed elements.
so, we need to multiply (9-sqrt(14)) by (9+sqrt(14)) to get
81-14 = 67 which is a rational number.
therefore, the third answer option is correct.
Answer:
Range=65
Step-by-step explanation:
The highest is 66 the lowest is 1 so 66-1=65
Considering the given table, we have that:
- The function has a relative maximum when x is near 3.
- As x approaches positive infinity, the value of the function approaches negative infinity.
<h3>When a function has a relative maximum?</h3>
A function has a relative maximum when it changes from increasing to decreasing.
Looking at the given table, it happens when x is near 3.
Also, looking at the table, for x > 3 the function is decreasing, hence as x approaches positive infinity, the value of the function approaches negative infinity.
More can be learned about functions at brainly.com/question/24737967
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Answer: x² - 25
Step-by-step explanation:
