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Alla [95]
3 years ago
15

Craig uses a ruler to determine the length of two pieces of metal. He records the length of each piece of metal as a rational nu

mber. Which statement best explains whether the sum of the two lengths Craig recorded must also be a rational number?
A. When adding two rational numbers a/b and c/d, the numerators a and c do not have to be integers. Therefore, the sum does not have to be a rational number.

B.When adding two rational numbers a/b and c/d, the common denominator bd does not have to be an interger. Therefore, the sum does not have to be a rational number.

C. When adding two rational numbers a/b and c/d, the sum is ac/bd, and both the numerator and denominator are integers. Therefore, the sum must be a rational number.

D. When adding two rational numbers a/b and c/d, the sum is ad+bc/bd, and both the numerator and denominator are integers. Therefore, the sum must be a rational number.
Mathematics
1 answer:
icang [17]3 years ago
7 0
<span>A. When adding two rational numbers a/b and c/d, the numerators a and c do not have to be integers. Therefore, the sum does not have to be a rational number. I think this is right might nor be :/
</span>
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Explanation:

The domain is the set of allowed x input values, aka the set of all allowed x coordinates of the points. We see that -4 < x \le 3. It might help to draw vertical lines through the endpoints until you reach the x axis. Note the open hole at x = -4 to indicate we do not include this as part of the domain (hence the lack of "or equal to" for the first inequality sign).

The interval -4 < x \le 3 then can be condensed into the shorthand form (-4, 3] which is the domain in interval notation.

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The range describes all possible y outputs. We see that y = 5 is the largest it gets and y = -5 is the lower bound. It might help to draw horizontal lines through the endpoints until you reach the y axis. The open hole means -5 is not part of the range.

The range as a compound inequality is -5 < y \le 5. This condenses into the shorthand of (-5, 5] which is the range in interval notation.

Verbally, the range is the set of y values such that y is between -5 and 5. It can't equal -5 but it can equal 5.

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