Simplify. (3x3 + 2x2 + 10) + (3x3 + 2x2 + 10x)
2 answers:
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Answer: Choice A
Note: the range should be . See explanation below.
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We can plug in any real number for x to get some output for y. The domain is the set of all real numbers in which we say which is interval notation. It represents the interval from negative infinity to positive infinity.
The range is the set of possible outputs. The smallest output possible is y = -5 which occurs at the vertex (3,-5). We can get this y value or larger. So we can describe the range as the set of y values such that and that translates to the interval notation
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The square bracket says "include this endpoint" while the curved parenthesis says to exclude the endpoint. Your teacher mistakenly wrote for choice A, when they should have written
I think either your teacher made a typo or somehow the formatting messed up. Either way, choice A is the closest to the answer.
The sum of the lengths of two legs of the 30°-60°-90° right triangle is 6.69 centimeters. Using the ratio of sides for the 30°-60°-90° triangle, the sum is calculated.
<h3>What is the ratio of sides for the 30°-60°-90° triangle?</h3>The ratio for the 30°-60°-90° triangle is 1:√3:2 or x:x√3:2x
where x corresponds to the length opposite the 30° angle and x√3 is opposite of the 60° angle and 2x is opposite to the 90° angle.
<h3 /><h3>Calculation:</h3>It is given that the triangle is a right triangle with angles 30°-60°-90°
For such a triangle, the ratio of side lengths is x: x:2x
we have the length of the hypotenuse is
So, 2x =
⇒ x =
So,
the other length of the other leg is x√3 = √6 × √3 = 3 √2
Then, the sum of these two legs = √6 + 3√2 = 6.69 centimeters.
Learn more about the ratio of sides of a 30°-60°-90° triangle here:
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