Find the reciprocal of the second fraction (flip numerator and denominator's spots) and multiply the two fractions.
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:
B. 77
Step-by-step explanation:
7 + x = 84
Subtract 7 from both sides
x = 77
<h3>The measure of angle y is 35.68 degrees</h3>
<em><u>Solution:</u></em>
Given that,
hypotenuse 12
Opposite 7
Find the measure of angle y
y is unknown and is between the hypotenuse and adjacent side
The figure is attached below
In a right triangle, the sine of the angle is the ratio of the side opposite to the angle to the hypotenuse
Therefore,
Thus measure of angle y is 35.68 degrees
The length of the air conditioner is 24 feet.
Volume = 3600 feet ³
Width = 15 feet
Height = 10 feet
Length = Unknown
Therefore, the value of the length will be calculated thus:
Volume = Length × Width × Height
3600 = Length × 15 × 10
Length = 3600 / (15 × 10)
Length = 3600 / 150
Length = 24
The length is 24 feet
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