<p>The following questions are from the grid in portion of a math section from test 6, section 4 of 11 practice tests for the SAT & PSAT 2009 Edition by Princeton Review </p>
<ol>
<li><p>Let the function g be degined by g(x) = 2x - 3. If g(k) = g(2k - 3), what is the value of g(4k)?</p></li>
<li><p>((2a-4)/5) + ((3a+1)/5)= b
In the equation above, how much greater is a than b? </p></li>
</ol>
<p>How do you solve these two questions? The answer explanation from the book is very vague and did not help me lol. Thanks :)!</p>
<p>for 12 is the answer (-51) ?
i will explain once i get a confirmation that this is the right answer.</p>
<p>for 16 is the answer (3/5)?
i will explain once i get a confirmation that this is the right answer. </p>
<p>^and ***</p>
<p>for 12 is the answer 16k - 6?</p>
<ol>
<li>Let the function g be degined by g(x) = 2x - 3. If g(k) = g(2k - 3), what is the value of g(4k)?</li>
</ol>
<p>g(k) = 2k - 3
g(2k - 3) = 2(2k - 3) - 3 = 4k - 6 - 3 = 4k - 9
So we have g(k) and g(2k - 3) and know from the question that they equal each other, so set them equal:</p>
<p>2k - 3 = 4k - 9
2k = 6
k = 3</p>
<p>g(4k) = 2(4k) - 3 = 8k - 3 = 8(3) - 3 = 21</p>
<ol>
<li>((2a-4)/5) + ((3a+1)/5)= b
In the equation above, how much greater is a than b? </li>
</ol>
<p>Multiply both sides of the equation by 5, giving you
2a - 4 + (3a + 1) = 5b
5a - 3 = 5b
5a - 5b = 3
5(a - b) = 3
a - b = 3/5</p>
<p>a is 3/5 greater than b</p>
<p>@Salzarah: You got 16 right but 12 wrong, unless I made a silly mistake.</p>
<p>The answer to question 12 is 21 and the answer to question 16 is .6 which is also 3/5.</p>
<p>@Yamster</p>
<p>Thanks so much =)!</p>
<p>oops stupid mistake…ugh yea its 21 (i said -9+3 = 12 … sigh =/ )
ok so number 12. here are the steps:</p>
<p>1) You are given g(k) = g(2k - 3) … ok so what is g(k)? To solve for g(k) see that
g(x) = 2x-3. So therefore plug in k into g(x) to obtain : g(k) = 2k-3. Easy.</p>
<p>2) What is g(2k-3)? To solve for that you must see that because you have g(x) = 2x-3
you can plug in (2k-3) for x and obtain : g(2x-3) = 2(2k-3) - 3 </p>
<p>3) Simplify : g(2x-3) = 2(2k-3) - 3 … so … g(2x-3) = 4k-9</p>
<p>4) Because g(k) = g(2k - 3) and g(k) = 2k-3 and g(2x-3) = 4k-9…do this: 2k-3 = 4k-9</p>
<p>5) Solve for k which is 3</p>
<p>6) Plug in 3 for k in g(4k)…so you get g(12)</p>
<p>7) Again remember x is a number and g(x) = 2x-3… so… g(4k) = g(12) = 2(12) - 3</p>
<p>8) = 21</p>
<p>YAY</p>