Answer:
1. C. 1/4(4) + 1/4(9) (A, 1/4(13), is essentially C simplified (without figuring it out).)
2. G - -4
3. A - -4(-5) + (-4)x
4. J - 1/6x + 1/6y
5. A - 60(10 + 2)
Step-by-step explanation:
1.
1/4(4 + 9) <em>We can distribute 1/4 into 4 and 9.</em>
1/4(4) + 1/4(9) <em>Now while we have our answer, this can be further simplified.</em>
1/4(13) <em>What's on the left is the simplified 2-term equation.</em>
<em>So really, either C or A will be the answer. But due to the format of #3, I put C as my answer. B & D were out because there wasn't any extra multiplication.</em>
2.
-2/5(15 - 5) <em>Subtract 5 from 15 to get 10.</em>
-2/5(10) <em>Multiply -2/5 by 10 to get -20/5</em>
-20/5 <em>Divide -20 by 5 to get -4.</em>
-4, so G is the answer. <em>This was negative, so H & J were out to begin with. F was out as soon as I solved the problem.</em>
3.
-4(-5 + x) <em>Distribute -4 into -5 + x.</em>
-4(-5) + (-4)x, so A is the answer. <em>Don't get tricked! B may look right, but there should be a negative sign in front of the 5, hence why it's incorrect.</em>
4.
1/6(x + y) <em>Distribute 1/6 into x + y.</em>
1/6x + 1/6y, so J is the answer. <em>F & G are already out because you don't multiply the variables by each other. H is also out because there wasn't any multiplication involved other than x + y being multiplied by 1/6.</em>
5.
Only 60(10 + 2) would have worked, so A is the answer. The tickets would have cost 720 dollars (600 + 120). <em>B would have equated to 624 (24 + 600), C would have been 132 (6 * 22), and D would have been 600. (10 * 60).</em>
, it follows that 
:
, and 
is non-negative throughout this domain.