Blue Book Math Help!!!!

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<p>Hi everyone, I want to say thank you to all of you who have been helping me....I've had so many questions this past week and I really appreciate your help!!!</p>

<p>As for my questions, #7 and #8 on page 776. andd #15 on page 779.</p>

<p>7) Ahmad has containers of two different sizes. Total capacity of 16 containers of one size is x gallons, and total capcity of 8 containers of hte other size is also x gallons. In terms fo x, what si the capacity in gallons of each ofhte larger containers..... answer is x/2</p>

<p>8) Rectangle ABCD lies in the xy coordinate plane so that its sides are not parallel to the axes. What is the product of the slopes of all four sides of rectangle ABCD. answer is 0</p>

<p>15) If 2^x + 2^x + 2^x + 2^x = 2^7
answer is 5.</p>

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<p>Number 15:</p>

<p>2^x + 2^x + 2^x + 2^x = 2^7</p>

<p>2^7 = 128
2^x + 2^x + 2^x + 2^x = 4(2^x)</p>

<p>4(2^x) = 128
2^x = 32
x = 5 </p>

<p>there are probably more efficient ways to do this
but this is how i approached it</p>

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<h1>8 is 1, not 0 (Check the answer key again).</h1>

<p>Since the sides of a rectangle are all perpendicular, the slope of each are the reciprocal of the perpendicular sides. So if one side has a slope of x, the other 2 will have -1/x, while the last side that is parallel to the first will have x. If you multiply all 4, you get 1.</p>

<p>As for #7, I don't quite get it either. So I'll also be waiting for someone to answer it.</p>

<p>Edit: I checked the answer key for #7 and it is x/8, which is then really obvious because all you do is x/16 and x/8 for the two different sizes and see which one is larger.</p>

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<p>7) Ahmad has containers of two different sizes. Total capacity of 16 containers of one size is x gallons, and total capcity of 8 containers of hte other size is also x gallons. In terms fo x, what si the capacity in gallons of each ofhte larger containers..... answer is x/8</p>

<p>you see variables in the question and in the answer choices---this is a classic indicator that you can use the great strategy of 'substitution'</p>

<p>Substitute in real values for the variables in order to make this question more approachable. (they're all just riddles disguised as math problems).
Also--try to "picture" the problem.</p>

<p>let's say that x = 10 gallons
So the total capacity of 16 containers of one size is 10 gallons and
the total capacity of 8 containers of the other size is 10 gallons.</p>

<p>Now ask your yourself 2 questions (for every math question)
Q1) what am I being asked to solve for??
Q2) what do I know from the info given??</p>

<p>A1)You're being asked to solve for the capacity of EACH of the LARGER containers.
A2)What do we know about the SIZE of these containers? Which ones are larger? Ahh yes. The ones that carry 10 gallons among just 8 containers instead of 16. So what is the carrying capacity of each one??
10 gallons/8 containers = 1.25 gallons</p>

<p>Now which of the answer choices gives you this value: 1.25 when you plug in the value that you chose for x?? (10)</p>

<p>D) x/8
and that is the CORRECT answer.</p>

<p>(you mis-wrote it in the initial question)</p>

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<p>thanks so much!!!!</p>

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<p>Problem #15: Vinvam's explanation was right on. Here's a slightly modified approach so that you don't actually do 2^7.</p>

<p>Given: 2^x + 2^x + 2^x + 2^x = 2^7
1/ Through associative property: 2^x + 2^x + 2^x + 2^x = 4(2^x)
2/ 4(2^x) = (2^2)(2^x)
3/ So (2^2)(2^x) = 2^7
4/ Add exponents when you multiply them, so 2+x=7; hence x=5</p>