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How do I find the answer to (10/11)² - 1/11 • 1 1/12 ? No matter how I work it I'm told my answer is wrong.

How do I find the answer to (10/11)² - 1/11 • 1 1/12= ? No matter how I work it I'm told my answer is wrong. Note: 99 119/132 isn't the answer. I got that by (10/11)² = 100/121, 1/11 • 1 1/12= 13/132, so 100/121 - 13/132 = 99 119/132

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1 + 1 + 1 + 1 + 1 90% Fail - PuzzlersWorld.com


1 + 1 + 1 +1 + 1 1 + 1 + 1 + 1 + 1 1 + 1 x 0 + 1 = ? 90% can't answer it ... of 11, 12, 1. He said they were all wrong so I decided to do some ... their work up and ...
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11:11 What Does It Mean? - Ask-Angels.com


... 11. There is really no right or wrong answer when it comes to the ... I have told my staff and also told ... 11/11/11. Ever since, no matter where I’m at, ...
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1 Corinthians 1:1-11:13 NIV - Paul, called to be an apostle ...


... we are homeless. 12 We work hard with our ... you yourselves cheat and do wrong, and you do this to your brothers ... 1 Corinthians 11:10 Or have a sign of ...
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Questions & Answers. Find the Answer to your Question.


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Coincidence and 11:11 - 11 - Great Dreams


I have experienced 12:12 and 1:1, two 11:11 ... I've been seeing 11:11 and other no.s like 4:44,1:11 etc ... You must do the work entailed to enable yourself to ...
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Meet the Latitude 11 EDU, Dell's Windows 10 S answer to the ...


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How do I find the answer to (10/11)² - 1/11 • 1 1/12 ? No matter how I work it I'm told my answer is wrong.

How do I find the answer to (10/11)² - 1/11 • 1 1/12= ? No matter how I work it I'm told my answer is wrong. Note: 99 119/132 isn't the answer. I got that by (10/11)² = 100/121, 1/11 • 1 1/12= 13/132, so 100/121 - 13/132 = 99 119/132 Please note that your last computation, 100/121 - 13/132 = 99 119/132 is where you went wrong. You final result, 99 119/132, you would get from, 100 - 13/132 = 99 119/132. It looks as though you simply forgot to divide by 121! The answer is: 100/121 - 13/132 = (100*132 – 13*121) / (121 * 132) 100/121 - 13/132 = (13200 – 1573) / (15,972) 100/121 - 13/132 = (11,627) / (15,972) = 1057/1452  (take out a factor of 11, top and bottom) Answer: 1057/1452
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How to Find Square Root

98=49*2, so sqrt(98)=sqrt(49)*sqrt(2)=7sqrt(2)=7*1.4142=9.8994 approx. There's another way using the binomial theorem. 98=100-2=100(1-0.02). sqrt(100)=10 so sqrt(98)=10(1-0.02)^(1/2) because square root is the same as power 1/2. (1+x)^n expands to 1+nx+(n(n-1)/1*2)x^2+(n(n-1)(n-2)/1*2*3)x^3+... Putting n=1/2 and  x=-0.02, we get sqrt(98)=10(1-0.02)^(1/2)=10[1-(1/2)0.02+((1/2)(-1/2)/2)0.0004+...]. This gives us: 10(1-0.01-0.00005+...)=10*0.98995=9.8995. A third method is to use an iterative process, which means you keep repeating the same action over and over again. Look at this: x=10-(2/(10+x)). If we solve for x we get x=sqrt(98); but we're going to find x in an iterative way. Start with x=0 and work out the right hand side: 10-2/10=9.8. This gives us a new value for x, 9.8, which we feed back into the right hand side: 10-(2/(10+9.8))=10-2/19.8=9.8989..., giving us another value for x, 9.8989... which we feed back into the right hand side: 10-(2/(10+9.8989...))=9.89949..., giving us yet another value for x and so on. Very quickly we build up accuracy with each x. You can do this on a calculator, a basic one that doesn't even have square roots, using the memory to hold values for you. Here's a very simple program, where STO means store in memory (if your calculator doesn't have STO use MC (memory clear) followed by M+ (add to memory)); MR means read memory (the steps show what calculator keys to press in order; / may be ÷ on your calculator): 0= +10=STO 10-2/MR= GO TO STEP 2 OR STOP (display should show the answer for sqrt(98)) Note: In STEP 3 the division must be carried out before subtracting from 10, otherwise you get the wrong answer. If your calculator doesn't do this you need to replace STEP 3 with: 0-2=/MR=+10= You should only have to go round the loop a few times before you get a really accurate result. To find the square root of 2 directly the iteration equation is x=1+1/(1+x) and the program is: 0= +1=STO 1/MR+1= GO TO STEP 2 OR STOP STEP 3 should work on all calculators.
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What is Mike's speed given the information below

In the first part of the problem, Andrew, traveling at a speed of v1, travels 4 miles, while Mike, traveling at speed v2, travels (d - 4) miles. They leave from their respective starting points at the same time, so the time it takes for them to meet and pass is the same for both. t = d / s 1. t1 = 4/v1 = (d - 4) / v2 Multiply both sides by v1 to eliminate the denominator on the left side, and multiply both sides by v2 to eliminate the denominator on the right side. 2. (4 / v1) * v1 * v2 = ((d - 4) / v2) * v1 * v2 3. 4v2 = (d - 4) v1 Divide both sides by four to get the value of v2 4. v2 = ((d - 4)v1) / 4 In the second part of the problem, Andrew has reached Simburgh (d) and turned around, travelling another 2 miles, or (d + 2), while Mike has reached Kirkton and turned around, travelling another (d - 2) miles, for a total of d + (d - 2) = (2d - 2) miles. Again, their times are equal when they meet and pass. 5. t2 = (d + 2) / v1 = (2d - 2) / v2 As in the first part, multiply both sides by v1 to eliminate the denominator on the left side, and multiply both sides by v2 to eliminate the denominator on the right side. 6. ((d + 2) / v1) * v1 * v2 = ((2d - 2) / v2) * v1 * v2 7. (d + 2)v2 = (2d - 2)v1 Divide both sides by (d + 2) go get the value of v2 8. v2 = ((2d - 2)v1) / (d + 2) We have two equations for v2, equation 4 and equation 8. The problem states that v2 remains the same throughout the journey. Therefore: ((d - 4)v1) / 4 = ((2d - 2)v1) / (d + 2) Once again, multiply both sides by both denominators. (((d - 4)v1) / 4) * 4 * (d + 2) = (((2d - 2)v1) / (d + 2)) * 4 * (d + 2) v1 * (d - 4) * (d + 2) = v1 * (2d - 2) * 4 Divide both sides by v1, eliminating speed from this equation. (d - 4) * (d + 2) = (2d - 2) * 4 d^2 - 4d + 2d - 8 = 8d - 8 d^2 - 2d - 8 = 8d - 8 Subtract 8d from both sides and add 8 to both sides. (d^2 - 2d - 8) - 8d + 8 = (8d - 8) + 8d + 8 = 0 d^2 - 10d = 0 Factor out a d on the left side. d * (d - 10) = 0 One of those factors is equal to 0 (to give a zero answer). d = 0 doesn't work; we already know the distance is more than 4 miles. d - 10 = 0 d = 10    <<<<<   That's the answer to the first question, how far is it? We'll substitute that into equation 4 to find v2 in relation to v1. v2 = ((d - 4)v1) / 4 = ((10 - 4)v1) / 4 v2 = 6v1 / 4 = (6/4)v1 v2  = 1.5 * v1   <<<<<< That's the answer to the second question No matter what speed you choose for Andrew (v1), Mike's speed is one-and-a-half times faster. Let's set Andrew's speed to 6mph and solve equation 1. t1 = 4/v1 = (d - 4) / v2 t1 = 4mi / 6mph = (10 - 4) / (1.5 * 6mph) 4/6 hr = 6/9 hr 2/3 hr = 2/3 hr With Andrew travelling at 4 mph, and Mike travelling at 6 mph, it took both of them 2/3 of an hour to reach a point 4 miles from Kirkton.
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How to find equation of the circle passing through (9,1), (-3,-1) and (4,5)

The equation of a circle is more specific: (x-h)^2+(x-k)^2=a^2, where (h,k) is the centre and a the radius. Plug in the points: (9-h)^2+(1-k)^2=(-3-h)^2+(-1-k)^2=(4-h)^2+(5-k)^2=a^2 This can be written (9-h)^2+(1-k)^2=(3+h)^2+(1+k)^2=(4-h)^2+(5-k)^2=a^2 Leaving a out of it for the moment we can use pairs of equations, using difference of squares: 12(6-2h)+2(-2k)=0, 36-12h-2k=0, 18-6h-k=0, so k=18-6h. 7(-1-2h)+6(-4-2k)=0, -7-14h-24-12k=0, -31-14h-12k=0 or 31+14h+12k=0, 31+14h+12(18-6h)=0, 31+14h+216-72h=0. 247-58h=0 so h=247/58 This looks suspiciously ungainly. So rather than continuing, I'm going to call the three points: (Q,R), (S,T), (U,V) to provide a general answer to all questions of this sort. (Q-h)^2+(R-k)^2=(S-h)^2+(T-k)^2=(U-h)^2+(V-k)^2=a^2 [(equation 1)=(equation 2)=(equation 3)=a^2] Take the equations in pairs and temporarily ignore a^2. Equations 1 and 2: (Q-S)(Q+S-2h)+(R-T)(R+T-2k)=0 Q^2-S^2-2h(Q-S)+R^2-T^2-2k(R-T)=0 2k(R-T)=Q^2+R^2-(S^2+T^2)-2h(Q-S), so k=(Q^2+R^2-(S^2+T^2)-2h(Q-S))/(2(R-T)) Equations 2 and 3: S^2-U^2-2h(S-U)+T^2-V^2-2k(T-V)=0, so k=(S^2+T^2-(U^2+V^2)-2h(S-U))/(2(T-V)) At this point, we can substitute for k and end up with an equation involving the unknown h only: (Q^2+R^2-(S^2+T^2)-2h(Q-S))/(2(R-T))=(S^2+T^2-(U^2+V^2)-2h(S-U))/(2(T-V)) (T-V)(Q^2+R^2-(S^2+T^2)-2h(Q-S))=(R-T)(S^2+T^2-(U^2+V^2)-2h(S-U)) (T-V)(Q^2+R^2-(S^2+T^2))-2h(T-V)(Q-S)=(R-T)(S^2+T^2-(U^2+V^2))-2h(R-T)(S-U) 2h((R-T)(S-U)-(T-V)(Q-S))=(R-T)(S^2+T^2-(U^2+V^2))-(T-V)(Q^2+R^2-(S^2+T^2)) h=((R-T)(S^2+T^2-(U^2+V^2))-(T-V)(Q^2+R^2-(S^2+T^2)))/((R-T)(S-U)-(T-V)(Q-S)). Once h is found we can calculate k, and then we can substitute the values for h and k in any equation to find a^2 which is equal to each of the three equations. When we use Q=9, R=1, S=-3, T=-1, U=4, V=5 or -5, we appear to get very ungainly solutions. One way to find which values need to be changed may be to plot the values and work out where the circle should fit and where its centre has less complex values. If V=6 or -6, there is a simple solution: (x-3)^2+y^2=37 (centre at (3,0), a^2=37=6^2+1^2. (-3-3)^2=(9-3)^2=6^2; (-6)^2=6^2; (2-3)^2=(4-3)^2=1; (-1)^2=1^2 shows the combination of points that would lie on the circle: (9,1), (9,-1), (-3,1), (-3,-1), (4,6), (4,-6), (2,6), (2,-6) and this includes points A and B, but not C. Note that the equation k=18-6h is valid for h=3, k=0.
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hpw do you estimate an answer to a problem with a remainder?

The purpose of the estimate is not to get an accurate answer, but just an indication of what the answer should be approximately, so that when the actual answer is determined, you can compare it with the estimate. They should be fairly close. If they are, this gives you confidence in your ability to work out the answer. If they're not, you may have made a mistake in your calculations. With practice, you become used to estimating quickly and that gives you a rough expectation of what the answer should be. So when you're doing a division it's not the remainder you need to be concerned about, but rather a rough idea of what the answer is going to be when calculated thoroughly. For example, if you were asked to divide 490 by 21, you could quickly estimate this by using 500 in place of 490 and 20 in place of 21, because these substitute numbers are close enough, or compatible with the actual numbers. 500 divided by 20 is 25. That can be done quickly in your head. 490/21 is going to be roughly 25. The actual answer is 23 with a remainder of 7. The estimate doesn't try to predict the remainder, but 25 is close enough to 23 to tell you that the real answer is probably correct. If you calculated 490/21 to be something way different from 25, you would suspect something had gone wrong in your calculations. So that's it: the estimate is just a quick fire judgment, before you take the time to do the proper calculation. An estimate is, or should be a quick mental calculation and not a laborious or lengthy exercise. For some numbers there is a way of predicting the remainder without doing any division at all. The obvious one is dividing by 2, because all odd numbers will give remainder 1. Dividing by 4 requires dividing only the last two digits by 4 and noting the remainder. Dividing by 8 requires dividing the last three digits and noting the remainder. Dividing by 5 is just a matter of noting whether the number ends in zero or 5. If it does there's no remainder; if it doesn't the remainder is found by subtracting 5 or zero from the last digit, depending on the size of the digit. If the digit is between 1 and 4 then so is the remainder; if it's between 6 and 9 then the remainder is found by subtracting 5. When dividing by 9, we don't do any division at all: we simply add up the digits making the number and if the result is 10 or more we add the digits of the result and we keep doing this until we end up with a single digit. If this digit is 9 the number is divisible exactly by 9; otherwise the digit is the actual remainder (this method is not surprisingly called the 9's remainder, and it can be used to check addition, subtraction and multiplication with a 90% accuracy level). Division by 11 is slightly more tricky, but consists of, starting with the last digit, add the alternate digits of the number then subtract the sum of the remaining digits. If the result is positive then that is the remainder; if negative then add 11 to find the remainder; for example, to find the remainder of 98765 divided by 11, we add 5+7+9=21 and subtract 6+8=14: 21-14=7, so the remainder is 7. Another example: remainder of dividing 23451 by 11; 1+4+2-(5+3)=-1+11=10, so the remainder is 10. If the result of the alternate subtraction exceeds 11 repeat the process: 190827 gives 7+8+9-(2+0+1)=21 so the next step is 1-2=-1, add 11=10, so 10 is the remainder.
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Rolles theorem on f(x) = Xsqrt(64-X^2) on the interval [-8,8]?

your derivative should have been sqrt(64-x^2) - x^2/sqrt(64-x^2) The minus sign coming from the derivative of (-x^2) Setting the derivative to zero, sqrt(64-x^2) - x^2/sqrt(64-x^2) = 0   multiply both terms by sqrt(64 - x^2) (64 - x^2) - x^2 = 0 64 = 2x^2 32 = x^2 x = +/- 4.sqrt(2) Answer: option b
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10 vedic maths rules for class IX

2 instead of 5: 34/5 can be calculated by multiplying 34 by 2 instead of dividing by 5. 34*2=68. We just move the decimal point one place to the left: 34/5=6.8. 124/5=24.8 because 124*2=248. Move the decimal point: 248 becomes 24.8. 34*5 is the same as 34/2=17 but we add a zero to make 17 into 170. 73*5 is the same as 73/2=36.5 then move the decimal point one place to the right (or add zero): 36.5 becomes 365=73*5. So we only need to know how to multiply and divide by 2 to divide and multiply by 5. We just move the decimal point. Divisibility by 9 or remainder after dividing by 9. All multiples of 9 contain digits which added together give 9. As we add the digits together, each time the result goes over 9 we add the digits of the result together and use that result and continue in this way up to the last digit. Is 12345 divisible by 9? Add the digits together 1+2+3=6. When we add 4 we get 10, so we add 1 and zero=1 then we add 5 to get 6. The number is not exactly divisible by 9, but the remainder is 6. We can also ignore any 9's in the number. Now try 67959. We can ignore the two 9's. 6+7=13, and 1+3=4; 4+5=9, so 67959 is divisible by 9. Multiplying by 11. Example: 132435*11. We write down the first and last digits 1 ... 5. Now we add the digits in pairs from the left a digit step at a time. So 1+3=4; 3+2=5: 2+4=6; 4+3=7; 3+5=8. Write these new digits between 1 and 5 and we get 1456785=132435*11. But we had no carryovers here. Now try 864753*11. Write down the first and last digits: 8 ... 3. 8+6=14, so we cross out the 8 and replace it with 8+1=9, giving us 94 ... 3. Next pair: 6+4=10. Again we go over 10 so we cross out 4 and make it 5. Now we have 950 ... 3. 4+7=11, so we have 9511 ... 3. 7+5=12, giving us 95122 ... 3; 5+3=8, giving us the final result 9512283.  Divisibility by 11. We add alternate digits and then we add the digits we missed. Subtract one sum from the other and if the result is zero the original number was divisible by 11. Example: 1456785. 1 5 7 5 make up one set of alternate digits and the other set is 4 6 8. 1+5+7=13. We drop the ten and keep 3 in mind to add to 5 to give us 8. Now 4 6 8: 4+6=10, drop the ten and add 0 to 8 to give us 8 (or ignore the zero). 8-8=0 so 11 divides into 1456785. Now 9512283: set 1 is 9 1 2 3 and set 2 is 5 2 8; 9+1=0 (when we drop the ten); 2+3=5; set 1 result is 5; 5+2+8=5 after dropping the ten, and 5-5=0 so 9512283 is divisible by 11. Nines remainder for checking arithmetic. We can check the result of addition, subtraction, multiplication and (carefully) division. Using Method 2 above we can reduce operands to a single digit. Take the following piece of arithmetic: 17*56-19*45+27*84. We'll assume we have carried out this sum and arrived at an answer 2365. We reduce each number to a single digit using Method 2: 8*2-1*9+9*3. 9's have no effect so we can replace 9's by 0's: 8*2 is all that remains. 8*2=16 and 1+6=7. This tells us that the result must reduce to 7 when we apply Method 2: 2+3+6=11; 1+1=2 and 2+5=7. So, although we can't be sure we have the right answer we certainly don't have the wrong answer because we arrived at the number 7 for the operands and the result. For division we simply use the fact that a/b=c+r where c is the quotient and r is the remainder. We can write this as a=b*c+r and then apply Method 2, as long as we have an actual remainder and not a decimal or fraction. Divisibility by 3. This is similar to Method 2. We reduce a number to a single digit. If this digit is 3, 6 or 9 (in other words, divisible by 3) then the whole number is divisible by 3. Divisibility by 6. This is similar to Method 6 but we also need the last digit of the original number to be even (0, 2, 4, 6 or 8). Divisibility by 4. If 4 divides into the last two digits of a number then the whole number is divisible by 4. Using 4 or 2 times 2 instead of 25 for multiplication and division. 469/25=469*4/100=1876/100=18.76. 538*25=538*100/4=134.5*100=13450. We could also double twice: 469*2=938, 938*2=1876, then divide by 100 (shift the decimal point two places to the left). And we can divide by 2 twice: 538/2=269, 269/2=134.5 then multiply by 100 (shift the decimal point two places left or add zeroes). Divisibility by 8. If 8 divides into the last three digits of a number then the whole number is divisible by 8. Using 8 or 2 times 2 times 2 instead of 125 for multiplication and division. Similar to Method 9, using 125=1000/8. Using addition instead of subtraction. 457-178. Complement 178: 821 and add: 457+821=1278, now reduce the thousands digit by 1 and add it to the units: 278+1=279; 457-178=279. Example: 1792-897. First match the length of 897 to 1792 be prefixing a zero: 0897; complement this: 9102. 1792+9102=1894. Reduce the thousands digit by 1 and add to the result: 894+1=895. Example: 14703-2849. 2849 becomes 02849, then complements to 97150. 14703+97150=111853; reduce the ten-thousands digit by 1 and and add to the result: 11854. Squaring numbers ending in 5. Example: 75^2. Start by writing the last two digits, which are always 25. Take the 7 and multiply by 1 more than 7, which is 8, so we get 56. Place this before the 25: 5625 is the square of 75. The square of 25 is ...25, preceded by 2*3=6, so we get 625. All numbers ending in 0 or 5 are exactly divisible by 5 (see also Method 1). All numbers ending in zero are exactly divisible by 10. All numbers ending in 00, 25, 50 or 75 are divisible by 25. Divisibility by 7. Example: is 2401 divisible by 7? Starting from the left with a pair of digits we multiply the first digit by 3 and add the second to it: 24: 3*2+4=10; now we repeat the process because we have 2 digits: 3*1+0=3. We take this single digit and the one following 24, which is a zero: 3*3+0=9. When we get a single digit 7, 8 or 9 we simply subtract 7 from it: in this case we had 9 so 9-7=2 and the single digit is now 2. Finally in this example we bring in the last digit: 3*2+1=7, but 7 is reduced to 0. This tells us the remainder after dividing 2401 by 7 is zero, so 2401 is divisible by 7. Another example: 1378. 3*1+3=6; 3*6=18 before adding the next digit, 7 (we can reduce this to a single digit first): 3*1+8=3*1+1=4; now add the 7: 4+7=4+0=4;  3*4=12; 3*1+2+8=5+1=6, so 6 is the remainder after dividing 1378 by 7.  See also my solution to: http://www.mathhomeworkanswers.org/72132/addition-using-vedic-maths?show=72132#q72132
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i cant remember how to factor a quadratic equation

There are two possibilities.  One is that this factors nicely (we know it does in this case).  The other is that it doesn't factor nicely (givings us irrational answers like x = 3.584538257389025 etc.).  The steps below should work if the equation factors nicely, but won't work if the answers are irrational / not friendly. Note:  Once you get used to it, you won't have to follow all of these steps and do all of this stuff every time.  You'll get used to it, like how you don't have to do a multiplication problem on paper to know that 10 * 10 = 100.  Here's the step by step procedure though. 6x^2 + 7x - 3 = 0 We're looking for something like (?x + ??)(???x + ????) The number on the x^2 is 6, so the numbers in front the x's (? and ???) have to multiply together and make 6.  That means ? and ??? should be 1 and 6, 6 and 1, 2 and 3, or 3 and 2.  That means we should have something like: (x + ??)(6x + ????) or (2x + ??)(3x + ????) Now look at the number without an x in the equation:  -3.  The only way to factor 3 is 1 and 3.  But, since we're starting with -3, the factors can be 1 and -3 or -1 and 3.  That means we now have something like this: (x + 1)(6x - 3) or (2x + 1)(3x - 3) (x - 1)(6x + 3) or (2x - 1)(3x + 3) (x + 3)(6x - 1) or (2x + 3)(3x - 1) (x - 3)(6x + 1) or (2x - 3)(3x + 1) So that's all eight possible combinations.  Which one is right? In the equation we have 7x in the middle.  We have to get a 7 to sit on the x. Look at (x + 1)(6x - 3).  The number sitting on the x in the equation is made by x * -3 + 1 * 6x = -3x + 6x = 3x.  That didn't make 7 to sit on the x, so we know (x + 1)(6x - 3) is wrong. (x + 1)(6x - 3) or (2x + 1)(3x - 3) (x - 1)(6x + 3) or (2x - 1)(3x + 3) (x + 3)(6x - 1) or (2x + 3)(3x - 1) (x - 3)(6x + 1) or (2x - 3)(3x + 1) Let's go through the other possibilities and see what we get (x + 1)(6x - 3): 3x or (2x + 1)(3x - 3): -3x (x - 1)(6x + 3): -3x or (2x - 1)(3x + 3): 3x (x + 3)(6x - 1): 17x or (2x + 3)(3x - 1): 7x (x - 3)(6x + 1): -17x or (2x - 3)(3x + 1): 3x The only possibility that makes a 7 to sit on the x is (2x + 3)(3x - 1), so that's our answer. 6x^2 + 7x - 3 = (2x + 3)(3x - 1)
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seven times a two digit number

Short answer:  The two digit number is 36. Long answer: 7 * x1x2 = 4 * x2x1 "If the difference between the number is 3. . ." Last digits: x2: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 7*x2:  0, 7, 4, 1, 8, 5, 2, 9, 6, 1 x1:  0, 1, 2, 3, 4, 5, 6, 7, 8, 9 4*x1:  0, 4, 8, 2, 6, 0, 4, 8, 2, 6 The only way this works is when these last digits for 7*x2 and 4*x1 are the same.  That means the 7*x2 line can only be: 7*x2:  0, 4, 8, 2, 6 Which means the possible values for x2 are: x2:  0, 2, 4, 6, 8 Now let's look at x1.  Right now the possible values for x1 are: x1:  0, 1, 2, 3, 4, 5, 6, 7, 8, 9 But we have to end up with a choice from x1 and x2 having a difference of 3 (odd number).  There is no way to get an odd number by subtracting an even number from an even number.  That means x1 has to be odd.  Our possible values for x1 are now: x1:  1, 3, 5, 7, 9 And our possible values for x2 are: x2:  0, 2, 4, 6, 8 The possible combinations for x1x2 and x2x1 are: 10, 01 12, 21 14, 41 16, 61 18, 81 30, 03 32, 23 34, 43 36, 63 38, 83 50, 05 52, 25 54, 45 56, 65 58, 85 70, 07 72, 27 74, 47 76, 67 78, 87 90, 09 92, 29 94, 49 96, 69 98, 89 We want 7*x1x2 = 4*x2x1, so we can do 7 * the first column and 4 * the second column: 70, 4 84, 84 98, 164 112, 244 126, 324 210, 12 224, 92 238, 172 252, 252 266, 332 350, 20 364, 100 378, 180 392, 260 406, 340 490, 28 504, 108 518, 188 532, 268 546, 348 630, 36 644, 116 658, 196 672, 276 686, 356 But since we want 7*x1x2 to equal 4*x2x1, that list reduces to: 84, 84 252, 252 The corresponding x1 and x2 values are: 12, 21 36, 63 But the difference between x1 and x2 is 3, so we can't use x1 = 1, x2=2.  We have to use x1 = 3, x2 = 6. Answer:  The two digit number is 36. Check:  7 * 36 = 4 * 63 252 = 252 good. 6 - 3 = 3 good.
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whats the answer to -2x + 3 > 3(2x - 1)

We need to expand the brackets on the right: -2x+3>6x-3. Add 2x to each side of the inequality: 3>8x-3 and add 3 to each side: 6>8x. Another way of writing this is 8x<6. Divide through by 2: 4x<3 and divide through by 4: x<3/4. We added 2x to each side because that helps us to bring the x's together. We added 3 to each side to bring the numbers together. Now we've ended up with x's on one side and a number on the other. Just what we want. 2 is common to 6 and 8 so we simplify the inequality by dividing through by it. Then to get x instead of 4x we divided through by 4. Why is 6>8x the same as 8x<6? Well, think about it. 2<3, isn't it? So 3>2. That's true. If Jack is taller than Jill, then Jill is shorter than Jack. See how it works? You just reverse the inequality when the quantities swap sides. It's a good idea to check your answer by substituting a value for x in the original inequality, just to make sure we haven't made a mistake. The answer was that x must be less than 3/4 so let's try x=1/2. -2x+3 is -1+3=2. Now the right side: 2x-1 is 1-1=0 multiplied by 3 is still zero. Is the inequality correct? Yes it is, because 2 is greater than zero. If we put x=1 we should find that the inequality doesn't work out because x is bigger than 3/4. Let's see. The left is 3-2=1 and the right is 3. 1 isn't bigger than 3, so the inequality is false, as expected. If we put x=3/4 we will find that the left equals the right when it should be bigger than it. Looks like x<3/4 is right!
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