course Mth 151 ??b?????????assignment #028
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20:05:54 7.1.18 4(x-9) = 8(x+3). Show how you solved the equation for x.
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RESPONSE --> 4(x-9) = 8(x+3) 4x-36 = 8x+24 +36 +36 4x = 8x + 60 -8x -8x -4x = 60 /-4 /-4 x= -15 confidence assessment: 3
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20:06:00 ** Divide both sides by 4 to get x - 9 = 2(x+3). Then apply the Distributive Law to get x - 9 = 2 x + 6. Then add -x to both sides: x - 9 - x = 2 x + 6 - x. Simplify -9 = y + 6. Add -6 to both sides -9 - 6 = y + 6 - 6. Simplify -15 = x. The solution is x = -15.**
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RESPONSE --> OK self critique assessment: 3
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20:11:49 7.1.39 (2r - 3 ) / 7 + 3/7 = -r/3. Show how you solved the equation for r.
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RESPONSE --> (2r-3)/7 + 3/7 = -r/3 (2r-3) + 3 = 2r 2r/7 = -r/3 Cross multiply: 2r*3 = -r7 6r = -r7 The only number that can work for r is 0. confidence assessment: 3
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20:12:09 ** You don't want to deal with fractions so you do best to multiply both sides by the common denominator 21 to get 21 (2r - 3) / 7 + 21 * 3 / 7 = 21 * (-r/3), which simplifies to 3 (2r - 3) + 9 = -7 r. The expand on the left using the Distributive Law: 6 r - 9 + 9 = - 7 r. -9 + 9 = 0; add 7 r to both sides: 6 r + 7 r = 0 so 13 r = 0 and r = 0 / 13 = 0. **
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RESPONSE --> OK self critique assessment: 3
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20:17:04 7.1.45 .20 ( 14000) + .14 t = .18 (14000 + t ). Show how you solved the equation for t.
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RESPONSE --> .20 (14000) + .14t = .18 (14000 + t) 2800 + .14t = 2520 + .18t -2520 - 2520 280 + .14t = .18t - .14t - .14t 280 = .04t /.04 /.04 7000 = t confidence assessment: 3
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20:17:21 CORRECT STUDENT SOLUTION WITH INSTRUCTOR COMMENT: .20(14,000)+.14t=.18(14,000+t) 2800+.14t=2520+.18t -.14t+2800+.14t=2520+.18t-.14t 2800=2520+.04t -2520+2800=2520+.04t-2520 280=.04t 280/.04=.04t/.04 7000=t INSTRUCTOR COMMENT: Correct solution but you're better off if you can avoid decimals and the attendant risk of misplacing one. One possible sequence of steps: First multiply both sides by 100 to avoid having to deal with decimals: 20 ( 14000) + 14 t = 18 ( 14000 + t). Divide both sides by the common factor 2: 10 ( 14000) + 7 t = 9 ( 14000 + t). Simplify: 140,000 + 7 t = 126,000 + 9 t. Add -9 to both sides: 140,000 + 7 t - 9 t = 126,000 + 9 t - 9 t. Simplify 140,000 - 2 t = 126,000. Add -140,000 to both sides: 140,000 - 2 t = 126,000 - 140,000. Simplify: -2 t = -14,000. Divide both sides by -2: t = 7000. **
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RESPONSE --> OK self critique assessment: 3
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20:31:21 7.1.70 A = 1/2 ( B + b ) * h. Show how you solved the equation for B
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RESPONSE --> A = 1/2 (B + b) * h A = 1/2Bh + 1/2bh A = (Bh + bh) / 2 *2 *2 2A = Bh + bh -bh -bh 2A - bh = Bh /h /h (2A - bh)/h = B confidence assessment: 3
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20:32:39 ** You need to isolate B: First multiply both sides by 2 and get 2A= (B+b) *h . Next divide both sides by h to get 2A / h = B + b. Then subtract b: 2A / h - b = B. Thus B = 2A / h - b. **
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RESPONSE --> This solution is simpler than the one I arrived at, but I think that mine was correct also. self critique assessment: 2
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20:38:37 7.2.18 20 million more viewers on Thursday than on Saturday; the total number is 102 million. How many watch each night?
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RESPONSE --> s = the number of viewers on Saturday t = the number of viewers on Thursday s + (s + 20,000,000) = 102,000,000 2s + 20,000,000 = 102,000,000 - 20,000,000 -20,000,000 2s = 82,000,000 /2 /2 s= 41,000,000 t = s+20,000,000 t = 61,000,000 There were 41 million viewers on Saturday and 61 million viewers on Thursday. confidence assessment: 3
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20:40:22 ** If we have 20 million more on Thursday then if x = number of Saturday viewers in millions, the number of Thursday viewers is x + 20, again in millions. The total number is 120 million so we have # of Thursday viewers + # of Saturday viewers = 120; using our expressions we have (x + 20) + x = 120 so that 2x + 20 = 120. Adding -20 to both sides we get 2x + 20 - 20 = 120 - 20 or 2x = 100. Dividing both sides by 2 we get (2x) / 2 = 100 / 2 so that x = 50. Thus the number of Saturday viewers is 50, representing 50 million, and the number of Thursday viewers is x + 20 = 70, representing 70 million.GE and GM total 13.5 billion; GE .3 billion less than GM. Show how you set up and solved an equation to obtain the profits of both companies.
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RESPONSE --> I may have misread the question, but I thought you asked for a total of 102 million, not 120 million. self critique assessment: 2
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20:40:56 ** If GE makes .3 billion less than GM then if x = GM profits in billions we can say that the GE profits are x - .3. Thus we have x + (x-.3) = 13.5. This gives us 2x - .3 = 13.5 so that 2x = 13.5 + .3 = 13.8 and x = 13.8 / 2 = 6.9. It follows that x - .3 = 6.9 so that x = 6.9-.3 = 6.6. So GM profits are 6.9 billion and GE profits are 6.6 billion. **
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RESPONSE --> The program skipped the question and only gave me the answer. self critique assessment: 2
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20:59:12 7.2.40 Water added to 3 gal of 4% soln to get 3% soln. Show how you solved the problem by setting up and solving an equation.
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RESPONSE --> 3 * .04 = (3 + x) .03 .12 = .09 + .03x -.09 -09 .03 =.03x /.03 /.03 x = 1 gallon confidence assessment: 3
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20:59:30 ** You need to first specify what x is. If x is the number of gallons of water added, then : After adding 3 gallons we have 3 + x gallons of 3% solution. Originally we had .04 * 3 gallons of the solute, and since we add only water that's what we still have after adding the water. But now the solute is in 3+x gallons of solution and its concentration is 3%. We have the same amount of solute after as before, since all we added was water, so .04 * 3 = .03 * ( 3 + x ). We solve this equation to get x, the number of gallons of water added. We obtain x = 1. The number of gallons added will be exactly 1. **
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RESPONSE --> OK self critique assessment: 3
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21:08:51 7.2.50 Equal #'s of nickels and quarters, twice as many half-dollars; total $2.60. Show how you solved the problem by setting up and solving an equation.
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RESPONSE --> Number of Coins Denomination Value x .05 .05x x .25 .25x 2x .50 x .05x + .25x + x = 2.6 1.3 x = 2.6 /1.3 /1.3 x = 2 2 nickels, 2 quarters, 4 half dollars confidence assessment: 3
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21:08:59 **If x is the number of nickles then we have x quarters and 2x half-dollars. So the amount of money we have is .05 x + .25 x + .5 (2x). This amount is 2.60 so .05 x + .25 x + .5 (2x) = 2.60. Simplifying the left-hand side: .05 x + .25 x + x = 2.60 1.30 x = 2.60 so that x = 2.60 / 1.30 = 2. We have 2 nickles, 2 quarters and 4 half-dollars.**
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RESPONSE --> OK self critique assessment: 3
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