Number 8 please please please
1 answer:
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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).
Both equations are equivalent, so there are infinitely many solutions.
Answer:
A. (1, -2)
B. the lines intersect at the solution point: (1, -2).
Step-by-step explanation:
A. The equations can be solve by substitution by using the y-expression provided by one of them to substitute for y in the other.
This gives ...
3x -5 = 6x -8
Adding 8-3x to both sides, we get ...
3 = 3x
Dividing both sides by 3 gives ...
1 = x
Substituting this value into the first equation, we can find y:
y = 3(1) -5 = -2
The solution is (x, y) = (1, -2).
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B. The lines intersect at the solution point, the point that satisfies both equations simultaneously. That point is (1, -2).
