A small book publisher knows that 20 books weigh 37 lbs. How much do 34 books weigh
2 answers:
Answer:
Step-by-step explanation:
Let's create a proportion using this setup:
We know that 20 books weight 37 pounds. We don't what 34 books weigh, so the weight is x pounds.
Cross multiply. Multiply the first numerator by the second denominator. Then, the first denominator and second numerator.
Since we are solving for x, we have to isolate the variable. It is being multiplied and the inverse of multiplication is division. Divide both sides by 20.
34 books weigh <u>62.9 pounds.</u>
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9514 1404 393
Answer:
D.
Step-by-step explanation:
The wording "when x is an appropriate value" is irrelevant to this question. That phrase should be ignored. (You may want to report this to your teacher.)
When you look at the answer choices, you see that all of them are negative except the last one (D). When you look at the problem fraction, you see that it is positive.
The only reasonable choice is D.
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Your calculator can check this for you.
√12/(√3 +3) ≈ 3.4641/(1.7321 +3)
= 3.4641/4.7321 ≈ 0.7321 = -1 +√3
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If you want to "rationalize the denominator", then multiply numerator and denominator by the conjugate of the denominator. The conjugate is formed by switching the sign between terms.
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<em>Additional comment</em>
We "rationalize the denominator" in this way to take advantage of the relation ...
(a -b)(a +b) = a² -b²
Using this gets rid of the irrational root in the denominator, hence "rationalizes" the denominator.
We could also have multiplied by (3 -√3)/(3 -√3). This would have made the denominator positive, instead of negative. However, I chose to use (√3 -3) so you could see that all we did was change the sign from (√3 +3).