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 expressions/397147: I need to know if i am evaluating this expression right? 9xy-4xz+3yz, x=7, y=3, and z=2 I got 151 as the answer. What I did: 9(7)(3)-4(7)(2)+3(3)(2), 9(21)-4(14)+3(6), 189-56+18=151, 1 solutions Answer 281531 by jim_thompson5910(28598)   on 2011-01-19 22:50:33 (Show Source): You can put this solution on YOUR website!You are correct. when x=7, y=3, and z=2. Good job.
 Equations/397098: Find the slope, if it exists, of the line containing the pair of points. (2,5) and (3,-1).1 solutions Answer 281495 by jim_thompson5910(28598)   on 2011-01-19 21:46:20 (Show Source): You can put this solution on YOUR website!Note: is the first point . So this means that and . Also, is the second point . So this means that and . Start with the slope formula. Plug in , , , and Subtract from to get Subtract from to get Reduce So the slope of the line that goes through the points and is If you need more help, email me at jim_thompson5910@hotmail.com Also, feel free to check out my tutoring website Jim
 Evaluation_Word_Problems/397095: how do i write an algebraic expession for nine times m then incresed by six??1 solutions Answer 281494 by jim_thompson5910(28598)   on 2011-01-19 21:44:12 (Show Source): You can put this solution on YOUR website!"nine times m" means and " incresed by six" means we're adding 6 to the previous result to get So the answer is If you need more help, email me at jim_thompson5910@hotmail.com Also, feel free to check out my tutoring website Jim
 Exponents-negative-and-fractional/397079: Rewrite the following expression with positive exponents. In case you can't see it, that exponent is a 1 solutions Answer 281486 by jim_thompson5910(28598)   on 2011-01-19 21:38:19 (Show Source): You can put this solution on YOUR website!Recall that where k is some positive number So in our case, this means that If you need more help, email me at jim_thompson5910@hotmail.com Also, feel free to check out my tutoring website Jim
 Equations/397064: Solve for x: x^2-5x+6=01 solutions Answer 281481 by jim_thompson5910(28598)   on 2011-01-19 21:22:47 (Show Source): You can put this solution on YOUR website! Start with the given equation. Notice that the quadratic is in the form of where , , and Let's use the quadratic formula to solve for "x": Start with the quadratic formula Plug in , , and Negate to get . Square to get . Multiply to get Subtract from to get Multiply and to get . Take the square root of to get . or Break up the expression. or Combine like terms. or Simplify. So the solutions are or If you need more help, email me at jim_thompson5910@hotmail.com Also, feel free to check out my tutoring website Jim
 Exponents/397013: This one is really bugging me: I understand that 2(2^n-1) (that is, two times two to the n-1 power) is equal to 2^n since the rule is "add the exponents if the bases are equal"). But why can't I compute it this way: 2(2^n-1) = 4^n-1 which could be rewritten as (2^2)^n-1 which, following the rule "multiply exponents when you have something to a power taken to another power" would then distribute as 2^2(n-1) = 2^2n-2. But this is a completely different answer! This doesn't make any since so surely I am making an obvious mistake. But given, for example 2(x^n+1) don't get 2x^n+1??? Thank you!1 solutions Answer 281477 by jim_thompson5910(28598)   on 2011-01-19 21:12:56 (Show Source): You can put this solution on YOUR website!This is what's going on (skip this part if you know this already) Start with the given expression. Rewrite as Now we're going to use the identity Multiply (by adding exponents) using the identity given above Add So ---------------------------------------------------- Now your question is why isn't equal to . The simple reason why not is because you can't simply multiply the bases. Remember that is really For example, we know that . So But if we multiply the bases, then which is NOT true. Also, you CANNOT rewrite into because the two are completely different. If you're skeptical about that, plug various values of 'n' into each expression and you'll see different results. So unfortunately, your line of reasoning was based on a false assumption which lead to that contradiction. If you need more help, email me at jim_thompson5910@hotmail.com Also, feel free to check out my tutoring website Jim
 Probability-and-statistics/397022: Evaluate each expression 5! - 2!1 solutions Answer 281468 by jim_thompson5910(28598)   on 2011-01-19 21:00:28 (Show Source): You can put this solution on YOUR website! So If you need more help, email me at jim_thompson5910@hotmail.com Also, feel free to check out my tutoring website Jim
 Circles/397031: I'm stuck on a question, please help!! :) " Determine the equation of a circle with a diameter whose endpoints are P(5,-6) and Q(1,2)" I used the midpoint formula and got (3,-2) for the midpoint, and then sketched out the graph and ended up with 8 for the hypotenuse and 4 for the other side. So then I went "PQ=4^2+8^2=16 =16+64=80 " and then went " PQ = sqrt ( 80 ) " And now I'm stuck! How do I finish the question? And am I even doing this right??1 solutions Answer 281464 by jim_thompson5910(28598)   on 2011-01-19 20:55:13 (Show Source): You can put this solution on YOUR website!You find the midpoint, which is the center of the circle. Since you found the midpoint to be (3,-2), this means that the center of the circle is (3,-2). This is only possible because the line segment PQ is the diameter. Recall that the equation of the circle with radius 'r' and center (h,k) is So because the center of the circle is (3,-2), this means that and . Plug these values into the equation above to get and simplify to get So all we need to find out is the value of . So we need to find the value of the radius 'r'. It turns out that the distance from the center (3,-2) to either point will be equal to the radius (draw a picture if you're not sure) So to find 'r', let's find the distance from P(5,-6) to the center (3,-2) Note: is the first point . So this means that and . Also, is the second point . So this means that and . Start with the distance formula. Plug in , , , and . Subtract from to get . Subtract from to get . Square to get . Square to get . Add to to get . So this distance is units. So This then means that So Plug this last value into the equation from the beginning to get So the equation of the circle with a diameter whose endpoints are P(5,-6) and Q(1,2) is If you need more help, email me at jim_thompson5910@hotmail.com Also, feel free to check out my tutoring website Jim
 Probability-and-statistics/397035: Find the z-score for the given raw score, mean, and standard deviation. Assume a normal probability distribution. Raw score = 66, μ = 60, and σ = 6.1 solutions Answer 281462 by jim_thompson5910(28598)   on 2011-01-19 20:45:23 (Show Source): You can put this solution on YOUR website!Recall that So So If you need more help, email me at jim_thompson5910@hotmail.com Also, feel free to check out my tutoring website Jim
 Probability-and-statistics/397043: If posts are spaced 9 feet apart, how many posts are needed for 54 feet of straight-line fence?1 solutions Answer 281461 by jim_thompson5910(28598)   on 2011-01-19 20:44:17 (Show Source): You can put this solution on YOUR website!If you need 54 ft of fence, and the posts are 9 ft apart, then you'll need posts If you need more help, email me at jim_thompson5910@hotmail.com Also, feel free to check out my tutoring website Jim
 Quadratic_Equations/397042: x^2-4x-5=01 solutions Answer 281460 by jim_thompson5910(28598)   on 2011-01-19 20:43:07 (Show Source): You can put this solution on YOUR website! Start with the given equation. Notice that the quadratic is in the form of where , , and Let's use the quadratic formula to solve for "x": Start with the quadratic formula Plug in , , and Negate to get . Square to get . Multiply to get Rewrite as Add to to get Multiply and to get . Take the square root of to get . or Break up the expression. or Combine like terms. or Simplify. So the solutions are or If you need more help, email me at jim_thompson5910@hotmail.com Also, feel free to check out my tutoring website Jim
 Equations/396220: 2(4x-7)-3x=x+141 solutions Answer 281124 by jim_thompson5910(28598)   on 2011-01-18 14:50:13 (Show Source): You can put this solution on YOUR website! Start with the given equation. Distribute. Combine like terms on the left side. Add to both sides. Subtract from both sides. Combine like terms on the left side. Combine like terms on the right side. Divide both sides by to isolate . Reduce. ---------------------------------------------------------------------- Answer: So the answer is
 Finance/396243: The sum of $5,992 was spent for 214 shares of stock. What was the cost per share? I believe I divide 5,992 by 214 but I am not sure could someone please help me.1 solutions Answer 281122 by jim_thompson5910(28598) on 2011-01-18 14:35:55 (Show Source): You can put this solution on YOUR website!You are correct. The cost per share would be dollars a share.  Polynomials-and-rational-expressions/396190: I did the following problem by synthetic division. Since this problem is rather llloooonnnngggg, I decided I need to have someone double check this. Could a tutor please look this over and tell me if I've done this correctly? I would greatly appreciate it! Thx! Here is the problem: x^7+x^5-10x^3+12/ (x+2) Since the divisor isn't in "x-c" form, I had to alter that. Also, lots of terms were missing in this problem, so I had to alter that, too. (That is what made this problem looonnnggg!) After I altered it, the problem looked like this: x^7+0x^6+x^5+0x^4-10x^3+0x^2+0x+12 / (x-(-2)) My synthetic division went like this: -2_| 1 0 1 0 -10 0 0 12 -2 4 -10 20 -20 40 -80 _____________________________________ 1 -2 5 -10 10 -20 40 -68 as remainder So my answer is: x^6-2x^5+5x^4-10x^3+10x^2-20x+40-68/(x-(-2)) YIKES!! Ok, is this correct, or do I need to go back to the drawing board with this? Any help would be welcomed!!! Thank you!!1 solutions Answer 281107 by jim_thompson5910(28598) on 2011-01-18 13:05:30 (Show Source): You can put this solution on YOUR website!You are correct. Good job.  Percentage-and-ratio-word-problems/396153: the cost of the item is$56 after a 20% discount....what is original price? how do you get the answer?1 solutions Answer 281093 by jim_thompson5910(28598)   on 2011-01-18 11:45:30 (Show Source): You can put this solution on YOUR website!Unfortunately the first answer is incorrect. Why? Because a 20% discount subtracts 20% of the original price from the original price. It's not simply 20% of the original price. This is a common pitfall with these types of problems. Let x = original price. Since "the cost of the item is \$56 after a 20% discount", this means that . Basically, the original price is x and 20% of this price is 0.2x. Subtract 0.2x from x to get the discount price of and set this equal to the known discount price of 56 Start with the given equation. Subtract Divide both sides by 0.8 to isolate x. Divide. So the original price is 70 dollars. Check: Notice that 20% of 70 dollars is 0.2*70 = 14 dollars So subtract 14 dollars from 70 dollars to get: 70 - 14 = 56 So this confirms our answer.
 absolute-value/395865: I know that -|10| + |10|=20 what about this |-10 + 10| = does this mean it's 20 or would it be 0? what about is it's like this -|-10 + 10| =1 solutions Answer 280936 by jim_thompson5910(28598)   on 2011-01-17 17:54:02 (Show Source): You can put this solution on YOUR website!Unfortunately, that's incorrect. -|10|+|10| = 0 because -|10| = -10 and |10| = 10 So -|10|+|10| = 0 -10+10 = 0 10 - 10 = 0 0 = 0 You're thinking of |-10|+|10| For the other two... |-10 + 10| = |10-10| = |0| = 0 -|-10 + 10| = -|10-10| = -|0| = -0 = 0 If you need more help, email me at jim_thompson5910@hotmail.com Also, feel free to check out my tutoring website Jim
 Numeric_Fractions/395862: 5/8x -1/2=41 solutions Answer 280934 by jim_thompson5910(28598)   on 2011-01-17 17:43:33 (Show Source): You can put this solution on YOUR website! Start with the given equation. Multiply both sides by the LCD to clear any fractions. Distribute and multiply. Add to both sides. Combine like terms on the right side. Divide both sides by to isolate . ---------------------------------------------------------------------- Answer: So the solution is If you need more help, email me at jim_thompson5910@hotmail.com Also, feel free to check out my tutoring website Jim
 Complex_Numbers/395849: If i=sqrt(-1), then 4i(6i) A) 48 B) 24 C) -24 d) -48 1 solutions Answer 280933 by jim_thompson5910(28598)   on 2011-01-17 17:32:10 (Show Source): You can put this solution on YOUR website! So which means that the answer is choice C) If you need more help, email me at jim_thompson5910@hotmail.com Also, feel free to check out my tutoring website Jim
 Linear-equations/395856: 5/4p=4/3p+3/21 solutions Answer 280932 by jim_thompson5910(28598)   on 2011-01-17 17:31:08 (Show Source): You can put this solution on YOUR website! Start with the given equation. Multiply both sides by the LCD to clear any fractions. Distribute and multiply. Subtract from both sides. Combine like terms on the left side. Divide both sides by to isolate . Reduce. ---------------------------------------------------------------------- Answer: So the solution is If you need more help, email me at jim_thompson5910@hotmail.com Also, feel free to check out my tutoring website Jim
 Numeric_Fractions/395855: -4/5 + 7/5 perform int operation if possible simplfy. is quotient undefined1 solutions Answer 280931 by jim_thompson5910(28598)   on 2011-01-17 17:30:26 (Show Source): You can put this solution on YOUR website! So If you need more help, email me at jim_thompson5910@hotmail.com Also, feel free to check out my tutoring website Jim
 Complex_Numbers/395837: Hello, I a having a hard time with this complex numbers problem. Any help is greatly appreciated! The point (-4+bi)has been plotted on the complex plane ad r=8. If 0°≤θ≤180° find the value of b. Leave your answer as a radical. θ= Theta1 solutions Answer 280920 by jim_thompson5910(28598)   on 2011-01-17 16:50:11 (Show Source): You can put this solution on YOUR website!Hint: Recall that the number has the modulus . In your case, and . So
 Miscellaneous_Word_Problems/395833: Hello, I found a confusing word problem in my Algebra book today. The word problem is: Write the digits 1 – 9 using four 4’s (for each digit) and the four basic operations: addition, subtraction, multiplication, and division. Example: 0 = 44 – 44 I simply have no idea what this means would it be like 22+22=44? I do not understand what this word problem means1 solutions Answer 280918 by jim_thompson5910(28598)   on 2011-01-17 16:45:48 (Show Source): You can put this solution on YOUR website!They want you to create the numbers 0 through 9 only using four 4's and four arithmetic operations So in the example, they created 0 using 4 fours and subtraction. So another example would be creating 7: 7 = 4+4-4/4
 Numeric_Fractions/395729: solve the following equation for x: 2(6+3x)=9x1 solutions Answer 280916 by jim_thompson5910(28598)   on 2011-01-17 16:39:14 (Show Source): You can put this solution on YOUR website! Start with the given equation. Distribute. Subtract from both sides. Subtract from both sides. Combine like terms on the left side. Divide both sides by to isolate . Reduce. ---------------------------------------------------------------------- Answer: So the solution is If you need more help, email me at jim_thompson5910@hotmail.com Also, feel free to check out my tutoring website Jim
 Graphs/395741: 3(x - 2) > 4(2x + 11) 1 solutions Answer 280911 by jim_thompson5910(28598)   on 2011-01-17 16:32:41 (Show Source): You can put this solution on YOUR website! Start with the given inequality. Distribute. Add to both sides. Subtract from both sides. Combine like terms on the left side. Combine like terms on the right side. Divide both sides by to isolate . note: Remember, the inequality sign flips when we divide both sides by a negative number. Reduce. ---------------------------------------------------------------------- Answer: So the solution is So the answer in interval notation is Also, the answer in set-builder notation is Here's the graph of the solution set on the number line: Note: there is an open circle at the endpoint. If you need more help, email me at jim_thompson5910@hotmail.com Also, feel free to check out my tutoring website Jim
 expressions/395790: -10(7r+4)+6(7r+8)1 solutions Answer 280910 by jim_thompson5910(28598)   on 2011-01-17 16:29:23 (Show Source): You can put this solution on YOUR website! Start with the given expression. Distribute. Multiply. Combine like terms. So If you need more help, email me at jim_thompson5910@hotmail.com Also, feel free to check out my tutoring website Jim
 Expressions-with-variables/395791: How do u solve for x: 3(2x+4)=2+6x+10 1 solutions Answer 280908 by jim_thompson5910(28598)   on 2011-01-17 16:27:30 (Show Source): You can put this solution on YOUR website! Start with the given equation. Distribute. Combine like terms on the right side. Subtract from both sides. Subtract from both sides. Combine like terms on the left side. Combine like terms on the right side. Simplify. Since this equation is always true for any x value, this means x can equal any number. So there are an infinite number of solutions. If you need more help, email me at jim_thompson5910@hotmail.com Also, feel free to check out my tutoring website Jim
 Graphs/395802: 3(x - 2) > 4(2x + 11) 1 solutions Answer 280905 by jim_thompson5910(28598)   on 2011-01-17 16:25:54 (Show Source): You can put this solution on YOUR website! Start with the given inequality. Distribute. Add to both sides. Subtract from both sides. Combine like terms on the left side. Combine like terms on the right side. Divide both sides by to isolate . note: Remember, the inequality sign flips when we divide both sides by a negative number. Reduce. ---------------------------------------------------------------------- Answer: So the solution is So the answer in interval notation is Also, the answer in set-builder notation is Here's the graph of the solution set on the number line: Note: there is an open circle at the endpoint. If you need more help, email me at jim_thompson5910@hotmail.com Also, feel free to check out my tutoring website Jim
 Graphs/395822: -5(x-4)+3x>-16 1 solutions Answer 280904 by jim_thompson5910(28598)   on 2011-01-17 16:24:34 (Show Source): You can put this solution on YOUR website! Start with the given inequality. Distribute. Combine like terms on the left side. Subtract from both sides. Combine like terms on the right side. Divide both sides by to isolate . note: Remember, the inequality sign flips when we divide both sides by a negative number. Reduce. ---------------------------------------------------------------------- Answer: So the solution is So the answer in interval notation is Also, the answer in set-builder notation is Here's the graph of the solution set on a number line: Note: there is an open circle at the endpoint If you need more help, email me at jim_thompson5910@hotmail.com Also, feel free to check out my tutoring website Jim
 Graphs/395804: Solve -3t + 6 < 3. 1 solutions Answer 280902 by jim_thompson5910(28598)   on 2011-01-17 16:23:08 (Show Source): You can put this solution on YOUR website! Start with the given inequality. Subtract from both sides. Combine like terms on the right side. Divide both sides by to isolate . note: Remember, the inequality sign flips when we divide both sides by a negative number. Reduce. ---------------------------------------------------------------------- Answer: So the solution is If you need more help, email me at jim_thompson5910@hotmail.com Also, feel free to check out my tutoring website Jim
 Square-cubic-other-roots/395809: 4^1/2 x 4^4/31 solutions Answer 280900 by jim_thompson5910(28598)   on 2011-01-17 16:22:38 (Show Source): You can put this solution on YOUR website! So If you need more help, email me at jim_thompson5910@hotmail.com Also, feel free to check out my tutoring website Jim
 Equations/395819: 9/5x+2=7/3x+101 solutions Answer 280897 by jim_thompson5910(28598)   on 2011-01-17 16:21:12 (Show Source): You can put this solution on YOUR website! Start with the given equation. Multiply both sides by the LCD to clear any fractions. Distribute and multiply. Subtract from both sides. Subtract from both sides. Combine like terms on the left side. Combine like terms on the right side. Divide both sides by to isolate . Reduce. ---------------------------------------------------------------------- Answer: So the solution is If you need more help, email me at jim_thompson5910@hotmail.com Also, feel free to check out my tutoring website Jim