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# Recent problems solved by 'bucky'

bucky answered: 2188 problems
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 expressions/70638: HELP!!!! I KEEP GETTING TWO DIFFERENT ANSWERS. Evaluate: Evaluate. (15 – 5) ÷ [(12 ÷ 2 · 2) – 2] show every step taken. 1 solutions Answer 50436 by bucky(2189)   on 2007-02-14 08:51:20 (Show Source): You can put this solution on YOUR website!(15 – 5) ÷ [(12 ÷ 2 · 2) – 2] . First do the work inside the parentheses. The (15-5) becomes just 10. . Then go to the interior set of parentheses in the next expression. That is the parentheses that contain (12 ÷ 2 · 2). First do the multiplication and divisions from left to right. That means the first thing to do is divide 12 by 2 to get 6. Then multiply that by 2 to get 12. So you can replace (12 ÷ 2 · 2) by 12. [There were no additions or subtractions in these parentheses so you didn't need to do any adds or take aways next from left to right. . At this point the original problem has been simplified to: . 10 ÷ [12 - 2] . Do the work in the brackets (which are a different way of showing parentheses) and you get that 12 - 2 = 10. The equation is now reduced to 10 divided by 10 and the answer to that is obviously +1. . The rules for working in single line problems are: . First do the work inside parentheses Second work on any terms that have exponents Third do the multiplications and divisions in order from left to right Fourth do the additions and subtractions in order from left to right . [Note that in working inside parentheses you may have to use the second, third, and fourth rules before going on to the next set of parentheses.] . Easier to say than it is to recognize what to do next, isn't it? It sure would have been easier to see if the original problem had been written: . . But that's just my opinion ...
 Linear_Algebra/70643: 9(2X-1) 4(X-5) ------ = ----- 7 31 solutions Answer 50434 by bucky(2189)   on 2007-02-14 08:10:04 (Show Source): You can put this solution on YOUR website! . This is in the form of a proportion ... two fractions set equal to each other. There are ways that you can work through common denominators and do simplifications, but a common method is that a lot of students use for solving proportions that aren't way complex is to begin by cross-multiplying them ... multiplying the denominator on one side by the numerator on the other side and setting the two products equal. For this problem the would multiply the and the would multiply the . You can do that multiplication in your head and get the resulting equation: . . Next do the multiplications on both sides to get: . . The rest is straightforward. Add +140 to both sides to eliminate the 140 on the left side: . . Then add -54x to both sides to eliminate the 54x on the right side: . . Finally, to solve for x, just divide both sides by -26 and the answer becomes: . . That's the answer. If you do the division you get a decimal answer of . . Hope this helps you a little to see a way of working problems such as these that are in proportional form. This method is not the only way the problem could be done, but it's a convenient way at times.
 Linear-systems/70587: This question is from textbook Intermediate Algerba (3,_),(_,-1),2x-3y=51 solutions Answer 50423 by bucky(2189)   on 2007-02-14 01:16:30 (Show Source): You can put this solution on YOUR website!(3,_),(_,-1),2x-3y=5 . This is two separate problems. The first problem is that you are given (3,_) and the equation . 2x - 3y = 5 . The 3 in (3,___) represents x. Substitute 3 for x in the equation and solve for y: . 2(3) - 3y = 5 . Multiply out the left side to get: . 6 - 3y = 5 . Subtract 6 from both sides: . -3y = -1 . Divide both sides by -3 to end up with: . y = (-1/-3) = 1/3 . So the missing entry in (3,_) is 1/3 and the answer becomes (3, 1/3) . The second problem involves the answer set (_, -1) for the equation 2x - 3y = 5. Substitute -1 for y in the equation to get: . 2x - 3(-1) = 5 . And multiply out to get: . 2x + 3 = 5 . Subtract 3 from both sides: . 2x = 2 . Divide both sides by 2 and the result is: . x = 1 . So the missing x value in (_, -1) is 1 and the answer set is (1, -1) . Hope this helps you to understand what the problem was looking for.
 Coordinate-system/70624: Can you please explain the problem...instructions..solve and graph the solution set...x + 16 > 10.1 solutions Answer 50420 by bucky(2189)   on 2007-02-14 00:35:52 (Show Source): You can put this solution on YOUR website! . Add -16 to both sides to solve the inequality for x: . . This means that x is not allowed to be -6 (because it is greater than -6) and x can be any value on the number line that is to the right of -6. . For example, let x = 0. The inequality of the original problem becomes: . . Which simplifies to: . . This inequality is correct ... 16 is greater than 10, so x can be 0 . Hope this helps you to understand how to work the inequality given in this problem. Graph it by excluding -6 and drawing the graph all the way to the right of -6 on the number line.
 Inequalities/70628: 5(2x+1)+4<8x+61 solutions Answer 50418 by bucky(2189)   on 2007-02-14 00:22:52 (Show Source): You can put this solution on YOUR website! . Operate on this just as you would on an equation. For the first step, you can multiply out the left side to get: . . Combine the +5 and the +4 on the left side. The inequality becomes: . . Eliminate the +9 on the left side by adding -9 to both sides: . . And add the +6 and -9 on the right side: . . Get rid of the 8x on the right side by adding -8x to both sides. The inequality simplifies to: . . Dividing both sides by 2 results in: . . This tells you that x can be anywhere on the number line below the value . But x cannot equal and it cannot be any value to the right of on the number line. . It doesn't happen in this problem, but remember this rule: if you multiply or divide an inequality by a negative number you must change the inequality sign to the opposite direction. . Hope this helps you see how to work with inequalities.
 Linear_Algebra/70626: I need to solve the following inequalities and show on the real number line. 3(2-3x)>5[x-2(x+5)]1 solutions Answer 50416 by bucky(2189)   on 2007-02-14 00:04:37 (Show Source): You can put this solution on YOUR website! . Start by treating this just as you would an equation and solve for x. First multiply out the left side. When you do the result is: . . Next on the right side multiply out the -2 times (x+5). When you do the inequality becomes: . . Then on the right side combine the x and -2x to get just -x. The inequality is then: . . Finally multiply out the right side: . . To cancel out the +6 on the left side, add a negative 6 to both sides. The inequality is then" . . And to cancel out the -5x on the right side, add +5x to both sides. The result is: . . To solve this for positive x, divide both sides by -4. But now you have to remember the rule ... whenever you divide or multiply both sides of an inequality by a negative number, the inequality reverses direction. Dividing by -4 and reversing the inequality gives you: . . This tells you that when x is less than 14 the inequality of the original problem is satisfied. And when x is 14 or more, the inequality of the original problem will not work. . Try a few values of x less than 14 and see if they don't work. Try x=14 and see why it doesn't work. And try a value or two for x greater than 14 to verify that they don't work. . Note 0 is less that 14, so you can try it. It makes all the x's disappear and the problem is simplified because of that. . Hope this helps you understand inequalities a little better. And don't forget the rule about multiplying or dividing inequalities by a negative number.
 absolute-value/70622: For the following set, which number has the largest absolute value? Show work 4,-1,12,-20,19,0 A) 0 B) 19 C) -20 D) -11 solutions Answer 50411 by bucky(2189)   on 2007-02-13 23:10:44 (Show Source): You can put this solution on YOUR website!The answer is -20 because the when you take the absolute value of any number becomes a positive number. In this problem taking the absolute value of -20 makes it + 20, and that is the largest number in the set. . . . . . . . Another way to look at this is that when you take the absolute value of a number you are finding the distance that number is from zero on the number line. The absolute value of -5 is the same as the absolute value of +5 because both numbers are 5 units away from 0 on the number line. In your problem -20 is 20 units from zero on the number line. . And another way to look at it is to just convert all the numbers to positive values and then choose the largest of these values as the answer to your problem. . Hope this helps you to visualize what the absolute value means regarding numbers. It just leaves positive numbers as positive, and it converts negative numbers to positive numbers.
 Equations/70520: Convert each rate using dimensional analysis 2.5 qt/min=___gal/h1 solutions Answer 50326 by bucky(2189)   on 2007-02-13 10:00:09 (Show Source): You can put this solution on YOUR website! . read this as 2.5 quarts per minute times 1 gallon per 4 quarts times 60 minutes per hour. . If you multiply the numbers in the numerators and then multiply the numbers in the denominators you have: . . Note how the dimensions work. The qts in the numerator cancel with the qts in the denominator, and the min in the numerator cancel with the min in the denominator. All you are left with is gal in the numerator and hr in the denominator. Therefore, the answer is 37.5 gallons per hour.
 Linear_Algebra/70523: Can someone please help me set-up and solve this problem Solve and write in interval notation for the solution set /x+2/ greater than or equal to 4 1 solutions Answer 50314 by bucky(2189)   on 2007-02-13 09:39:11 (Show Source): You can put this solution on YOUR website!This problem is the same as problem 70524. It was answered by answer 50310. Check that out.
 Inequalities/70524: Can someone please help me set-up and solve this problem Solve and write in interval notation for the solution set /x+2/ greater than or equal to 4 1 solutions Answer 50310 by bucky(2189)   on 2007-02-13 09:22:30 (Show Source): You can put this solution on YOUR website! . One method of solving this involves letting the entire quantity within the absolute value signs first have a positive sign and then have a negative sign. Solve these two cases. Perhaps it is best explained by using this problem as a typical example. . The quantity inside the absolute value signs is . First write the inequality equation using +(x+2) for the left side. In this case the inequality becomes. . . Solve this for x just as you would an ordinary equation ... by subtracting +2 from both sides to get the answer as . . But that's only the first part of the solution. The second part says to give the entire quantity inside the absolute value signs a negative sign and solve the inequality again. . So this time the inequality becomes: . . You can remove the parentheses preceded by a negative sign by changing the sign of all the terms inside the parentheses and then just erasing the parentheses. If you do this you get: . . Begin the solution by adding 2 to both sides to eliminate the -2 on the left side. When you do that, the inequality becomes: . . Next comes a tricky part. You want to solve for positive x, so you are going to multiply both sides by -1. However, if you multiply or divide both sides of an inequality by a negative number you must reverse the direction of the inequality sign. No big deal, just something to remember. So in this case after the multiplication and sign reversal the solution for x becomes . . In summary, the regions on the number line that satisfy the original inequality are any value of x equal to or to the left of -6 and any value of x equal to or to the right of +2. . You can do a quick check by returning to the original problem and solve it for x = -7, and x = +3. Or use any convenient value in the two regions ... for example x = - 10 and x = + 10. You should see that the inequality is satisfied. Plus you can use any value of x between -6 and +2 to prove to yourself that the original inequality is not satisfied by values of x in that region. Usually x = 0 works well for this check because all the terms containing x just disappear. It's usually a good idea to check the points you found on the number line also. If you let x = -6 and then let x = +2, you should find that in both cases the inequality of this problem is true only because of the equal sign associated with the less than or greater than sign. Therefore, for this inequality x = -6 and x = +2 are included in the solution set. . In summary, solve two problems ... first use the entire quantity inside the absolute value signs with a plus sign and solve the inequality for +x. ... next use the entire quantity inside the absolute value signs with a negative sign and solve the inequality for +x. Don't forget multiplication (or division) of both sides of the inequality by a negative number, requires you to reverse the inequality sign. Finally use numbers in each of the regions that you identify for the answer, and plug them into the original problem just to make sure they work correctly. It also pays to check the end point numbers (in this problem they were -6 and +2) to validate what region they fall into (are they part of the solution set or are they not). [In this problem they were in the solution set because of the equal sign.] . Hope you find this method easy to remember and useful to you.
 Exponential-and-logarithmic-functions/70516: write the logarithmic equation in exponential form: log 3 27 = 3 and log 125 25 = 2/31 solutions Answer 50301 by bucky(2189)   on 2007-02-13 01:27:20 (Show Source): You can put this solution on YOUR website!If the log form is log b (d) = c . (read that as log to the base b of d equals c) . then the corresponding exponential form is . You are given log 3 (27) = 3. By comparing this with the log form (see top line above) you can see that b = 3, d = 27, and c = 3. Putting these numbers in the appropriate places in the exponential form results in: . Note that this equation is true because if you cube 3 you get 27 . You are also given log 125 (25) = 2/3. By again comparing this with the log form in the first line of this reply, you see that b = 125, d = 25, and c = 2/3. Substituting these numbers for their corresponding letters in the exponential form results in: . . You may recognize that the exponent means that you can either square the number and then take the cube root, or you can take the cube root and then square that number. In the case of 125, it is easier to first take the cube root because it is 5, and then you square that to get 25. This means the exponential form is true because the left side of that equation equals the right side. . If you work a number of these, you will see the pattern between the log and exponential forms and the translation back and forth between the two forms will become easier for you. Hope this helps you see your way through this type of problem.
 Inequalities/70474: This question is from textbook Solve the inequality x2-2x-3>01 solutions Answer 50300 by bucky(2189)   on 2007-02-13 00:27:24 (Show Source): You can put this solution on YOUR website!Temporarily replace the inequality sign with an equal sign ... just because you are probably more familiar with working on equations. This temporary maneuver results in: . . This is a typical quadratic equation. This particular equation can be factored so that the equation can be broken down to: . . This equation will be true if either of the factors on the left side is zero, because that would make the left side of the equation equal 0 ... the same value that is on the right side. So, one at a time set the two factors equal to zero and solve for x: . First and by adding 3 to both sides this becomes . Then and by subtracting 1 from both sides this becomes . This tells us that for this problem you have critical points on the number line at and . Draw a horizontal number line and mark the points +3 and -1 on that line. There are three important regions on this number line ... the region extending to the left from the point -1, the region between the points -1 and +3, and the region extending to the right from the point x = +3. You need to examine just these three regions to tell which of them satisfy the inequality equation. . Return now to the original inequality equation as given in the problem statement: . . Now pick any convenient number that is in the first region to the left of x=-1. Suppose that you choose x = -10. Plug that value in for x in the inequality equation and simplify the results. The substitution of -10 leads to: . . . You can already see that this equation is true because 117 > 0. Now you know that numbers in the region from -1 all the way down to negative infinity (but not including -1) will satisfy the inequality equation. . Next examine the region with -1 on one end and +3 on the other end. Select a convenient value of x between these two end points and see what happens to the inequality equation. A convenient value is x = 0 because when it is substituted in for x, it cause terms that have an x in them to become zero. The substitution is: . and this simplifies to: . . This is obviously not true. So all the points from -1 to +3 will not make the inequality equation true. Therefore, x cannot be from -1 to +3 including the end points. (Plug -1 and +3 into the inequality equation and see if the result is GREATER than zero.) . Finally do the same exercise for a single convenient value in the region where x is greater than +3. It might be convenient to use x = +10, but you can use any value greater than +3. If you do this you will find that it does satisfy the inequality equation, so all values in that region of x greater than +3 all the way out to + infinity will satisfy the equation. . In summary the inequality equation is satisfied if x < -1 or x > +3. . Hopefully this refreshes your memory on problems such as these.
 Equations/70479: The solution of the system 4x+5y =2 and 6x-2y=b is (3,a). Find the values of a and b. Helpp1 solutions Answer 50299 by bucky(2189)   on 2007-02-12 23:39:55 (Show Source): You can put this solution on YOUR website!Start with . The fact that the point (3,a) satisfies the system of equations (that means it satisfies both equations), tells you that when x = 3 and y = a, the equation is satisfied. So plug in 3 for x and a for y. When you do, the equation becomes: . . This simplifies to: . . Subtract 12 from each side of this equation to get: . . Finally, divide both sides by 5 to get: . . So now you know that a = -2 and that is one of the things you had to find. You can substitute this into the point (3,a) which is known to work in both equations because it is the solution to the system of equations. By substituting -2 for a you know that the point (3, -2) satisfies both equations. . The second equation of the system of equations is: . . Since you know this equation is satisfied by x = 3 , y = -2 you substitute these values into the equation and both sides should be equal. By substitution the equation becomes: . . Multiplying out the terms on the left side results in: . . and adding the two terms on the left side tells you that b = 22. That is the second quantity that you were supposed to find. . Hope this helps you to see your way through this word problem OK.
 Equations/70487: (2x – 5)/3 – 3/2 = (x + 4)/5 Solve for x1 solutions Answer 50272 by bucky(2189)   on 2007-02-12 21:31:48 (Show Source): You can put this solution on YOUR website! . You cannot add or subtract fractions unless they have a common denominator. In this problem we can use a common denominator of 30 because all the denominators in the problem are factors of 30. There are 3 terms in this problem and we need to get each term so it has a denominator of 30. . The first term is . We could multiply this fraction by and it would not change the value of the fraction because equals 1, so we are multiplying the original fraction by 1. When we multiply the fraction by , the result is and this simplifies to . . The second term is and to get the denominator to equal 30, we multiply the fraction by . The result of this multiplication is that the denominator becomes 30, and the numerator becomes . So the term is now converted to . The last term is . To give this a denominator of 30 we multiply the fraction by . The denominator becomes 30 and the numerator becomes which simplifies to . So the fraction is converted to . . Substituting these three results into the original equation converts the problem to: . . Since the denominator 30 is common to all terms we can eliminate it by multiplying all the terms in the equation by 30. The result is that the multiplier of 30 cancels with the denominator of 30 in all terms and the problem now involves dealing with only the numerators as follows: . . Combine the -50 and the - 45 on the left side to get: . . Add 95 to both sides to cancel the -95 on the left side. This results in: . . Subtract 6x from both sides to eliminate it on the right side. . . And finally, divide both sides by 14 to get: . . That's the answer to the problem. Hope this helps you to see a way of solving fractional problems such as these.
 Numbers_Word_Problems/70498: Solve the problem: An employee who produces x units per hour earns an hourly wage of y = 0.55x + 7 (in dollars). Find the hourly wage for an employee who produces 13 units per hour. 1 solutions Answer 50258 by bucky(2189)   on 2007-02-12 20:57:04 (Show Source): You can put this solution on YOUR website! . If x = 13, all you do is substitute 13 for x in the equation to get: . . Do the multiplication of and you get an answer of . Substitute this value into the equation in place of the multiplication to get: . . Then do the addition on the right side and you find that the employee makes an hourly wage of: . or \$14.15 per hour. . Hope this helps you see how equations can work for you to solve problems.
 Equations/70368: Divide: x^2 + 2x^2 + x + 12 ------------------- x + 3 Can anyone give me a hand on this, it seems to be so confusing to me! Thank you very much1 solutions Answer 50198 by bucky(2189)   on 2007-02-12 12:05:26 (Show Source): You can put this solution on YOUR website!Please check your numerator and re-post your problem. I think you may have made a mistake in your terms. Thanks
 Evaluation_Word_Problems/70361: The inventor of a new product believes that the cost of producing the product is given by the function: C(x)= 1.75x + 7000 The cost of 2000 units of her invention is \$10,500. If the inventor charges \$4 per unit, then her profit for producing and selling x units is given by the function: P(x)= 2.25x - 7000 (a) What is her profit if she sells 2000 units? (b) What is her profit if she sells 5000 units? (c) What is the break-even point for sales?1 solutions Answer 50192 by bucky(2189)   on 2007-02-12 11:24:29 (Show Source): You can put this solution on YOUR website!From the way this problem is worded, the equation for C(x) is not needed to answer the questions that are asked. The only equation that applies is: . The first question ... What is the profit if she sells 2000 units? Calculate the profit by setting x equal to 2000 units so that the equation becomes: . . The negative sign tells you that overall she loses \$2500 if she sells only 2000 units. . The second question ... What is the profit if she sells 5000 units? Do the same calculation as above, but this time set x equal to 5000 units so that the equation becomes: . . The positive answer tells you that overall she makes \$4,250 if she sells 5000 units. . So somewhere between sales of 2000 units (a loss) and selling 5000 units (a gain) she reach a break-even point. At that break-even point her profit would be zero (neither a loss nor a gain). So this time set the profit equal to zero in the equation and solve the resulting equation for x. . . Add 7000 to both sides and transpose the equation: . . Divide both sides by 2.25 to get: . } . This result tells you that if she sells less than this amount she loses money, but if she sells more than this number of units she makes money. Therefore, you can say that she loses a very small amount of money if she sells 3111 units, and she makes a very small amount of money if she sells 3112 units. . Hope this helps you to see your way through the problem ... especially with regarding the information on the costs involved with production, C(x), and the sales price of \$4.00 per unit. That information was not needed because you were provided with an equation that directly calculates profit based on the number of units sold.
 Equations/70356: Rewrite the equation as a function of x. -3x + 4y = 111 solutions Answer 50187 by bucky(2189)   on 2007-02-12 10:45:20 (Show Source): You can put this solution on YOUR website!Given . To rewrite this as a function of x, you need to do two things ... first solve for y and then replace y by f(x). . First solve for y. You need to move the -3x to the other side of the equation. You can do that by adding 3x to both sides. On the left side the +3x cancels the -3x, and on the right side the +3x appears. You now have: . . You can now solve for just +y by dividing both sides by the coefficient (or multiplier) of y. In this case the coefficient of y is +4, so divide both sides of the equation by +4. The result is: . . This simplifies to: . . As the final step you replace y by f(x) to end up with: . . and this has re-written the original equation (that was in standard form) into the form of a function of x (denoted by f(x)) . Hope this helps you to see how to do problems of this sort. Just follow the two-step process ... first solve in for y in terms of x and then replace y by the notation f(x).
 Distributive-associative-commutative-properties/70362: [(7x^2-9x+4)-(9x^2+3x-2)]-[(5x^2+4x-6)+(-8x^2+6x+1)] Ok I can get all the way to the end and then I'm stuck. Below is what I ended up with: = -9x^2+8x^2+7x^2-5x^2-9x-6x-4x-3x+4+2+6-1 = x^2-4x+11 (<---is that right)1 solutions Answer 50185 by bucky(2189)   on 2007-02-12 10:23:48 (Show Source): You can put this solution on YOUR website!Below is what I ended up with: . = -9x^2+8x^2+7x^2-5x^2-9x-6x-4x-3x+4+2+6-1 <----This is correct! . = x^2-4x+11 (<---is that right. No it's not. Look at -4x. How did you get the -4? The x^2 and the +11 are OK.) . You obviously know how to work these, but just made a minor mistake. Keep up the good work!
 Equations/70360: If f(x)=5x-1, find the following: f(a-2)1 solutions Answer 50177 by bucky(2189)   on 2007-02-12 09:36:16 (Show Source): You can put this solution on YOUR website!If f(x)=5x-1, find the following: f(a-2) Look in the sets of parentheses that follow the "f". The second set of parentheses contains the expression a-2. The first set of parentheses just contains x. So the problem means that there is a correspondence between x and a-2. All you do is go to the expression . f(x) = 5x - 1 . and replace every x by a-2. When you do, the expression becomes: . f(a-2) = 5(a-2) - 1 . Multiply out the right side so that the expression becomes: . f(a-2) = 5a - 10 -1 . Finally, simplify the right side by combining the -10 and -1 to find that: . f(a-2) = 5a - 11 Hope this helps you to understand the basics of this problem.
 absolute-value/70358: If f(x)= 4x -3, find the following: f(-1)1 solutions Answer 50176 by bucky(2189)   on 2007-02-12 09:27:11 (Show Source): You can put this solution on YOUR website!If f(x)= 4x -3, find the following: f(-1) What f(-1) tells you to do is to start with f(x) = 4x - 3, then replace every x you see in it by (-1), and finally compute what the right side equals. . Let's change the problem a little and find f(-4). Go to the expression f(x) = 4x - 3 and replace all the x's by -4. When you do the expression becomes: . f(-4) = 4(-4) - 3 . When you multiply 4 times -4 you get -16. Substitute -16 for 4(-4) and the expression becomes . f(-4) = -16 -3 and the two terms on the right combine so that the expression becomes: . f(-4) = -19 . You can do the work to find f(-1). Follow the same process as the example. . I hope this helps you to understand what the problem really means.
 Circles/70339: This question is from textbook College Algebra Essentials The endpoints of the diameter of a circle are (-3,2) and (5,-6). Find the center and the radius of the circle. Write the general equation of this circle. I had thought maybe to to use the midpoint formula and distance formula, but am not really sure. question 131 from chapter 1 Review Exercises1 solutions Answer 50169 by bucky(2189)   on 2007-02-12 00:36:18 (Show Source): You can put this solution on YOUR website!You have a good plan! The mid-point formula should get you the center of the circle. Then use the distance formula for the length of the line that joins the two points. That will give you the diameter of the circle so you need to divide it by 2 to get the radius. . The points are (-3,2) and (5,-6). The two values of x are -3 and + 5 so the distance between them is 8 units. Divide that by 2 to get 4 units as the half-way point. Then either add 4 units to -3 or subtract the 4 units from 5 to find that the mid-way point is at x = +1. Next the two values of y are +2 and -6 so the distance between them is 8 units. Divide that by 2 to get 4 units. Then either subtract the 4 units from +2 or add 4 units to -6 to find the half-way point is at y = -2. Using that method you get the location of the midpoint along the line joining the given points is at (+1, -2). Since the x-distance between the points is 8 units and the y-distance between the points is also 8 units, the distance between the two points (that is the hypotenuse) is: . . The radius of the circle is half that or 5.65685 units. . You'd better work it yourself and check my answers. I did a lot in my head and it's late at night. I'm prone to making mistakes without a coffee fix.
 Exponential-and-logarithmic-functions/70330: Solve for x: 3^2x = 12 x = ? Round to 2 decimal places.1 solutions Answer 50168 by bucky(2189)   on 2007-02-12 00:12:27 (Show Source): You can put this solution on YOUR website!I interpret your problem to be to solve for x in the equation: . . and I assume you know the use of logarithms and exponents. . By using the power rule of exponents you can re-write the equation in the form: . . so substitute 9 for to reduce the equation to: . . Take the log of both sides to get: . . But by the rules of exponents in logarithms, the exponent becomes a multiplier of the log. x is the exponent, so it becomes the multiplier of log(9) to give: . . To solve for x, divide both sides by log(9) to get: . . Calculator time! log(12) = 1.079181246 and log(9) = 0.954242509. By dividing log(12) by log(9) you find that x = 1.130929754. . That's the answer. By doubling it and raising 3 to that exponent on your calculator you will find that the answer is, as it should be, 12. . And don't forget to round the answer to two decimal places as the problem requests. . Hope that I interpreted the problem correctly and that the approach I used was not beyond where you are in your text.