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Linear-systems/185321: This question is from textbook Supplementary Angles. Two supplementary angles are such that one is 8 degrees less than three times that other. Find the angles. 1 solutions Answer 139006 by solver91311(16897)   on 2009-03-06 13:32:15 (Show Source): You can put this solution on YOUR website! Supplementary angles are two angles whose measures sum to 180 degrees (or radians if you would rather). Since the other relationship between the angles is given in terms of degrees, we'll use 180. Let the measure of the second angle be x degrees. Then the measure of the first angle must be 3x - 8 degrees. Adding them: Solve for x to give you the measure of one of the angles, then subtract that measure value from 180 to get the other. Then multiply x by 3 and then subtract 8 to check your answer. John

Rational-functions/185325: solve. 1/2+1/5=1/t 1 solutions Answer 139005 by solver91311(16897)   on 2009-03-06 13:21:21 (Show Source): You can put this solution on YOUR website! Just add , and then invert that answer. John

Inequalities/185331: Detremine whether the given number satisfies the inequality of the following -5,-3<-3x-7<8 1 solutions Answer 139003 by solver91311(16897)   on 2009-03-06 13:16:37 (Show Source): You can put this solution on YOUR website! Substitute the value given in place of x and then do the arithmetic. If the inequality is then a true statement, the value satisfies the inequality. If it is a false statement, then the value does not satisfy the inequality. In this case, if the derived value is equal to either end point, then the statement is false because you have < signs and not signs. John

absolute-value/185326: Solve. Absolute value sign /2x =7/ <19 1 solutions Answer 139002 by solver91311(16897)   on 2009-03-06 13:08:08 (Show Source): You can put this solution on YOUR website! I presume that your = sign is a typo and you really meant: This means that: or Now you need to multiply by , but remember that when multiplying an inequality by a negative number, you must reverse the sense of the inequality: And your solution set interval is then: John

Systems-of-equations/185259: Differentiate (find the derivative) of the function 2/(√x) + x/(√3) + 6(3√x <-- cube root over x), the answer should be 1/(√3) - 1/√(x^3) - 2/(3√x^2) <-- cube root over x^2). Please show your steps. 1 solutions Answer 139001 by solver91311(16897)   on 2009-03-06 12:53:17 (Show Source): You can put this solution on YOUR website! Since we know that: We can take the derivitive of each term of your function and just add them. First thing to do is put your functions in terms of fractional exponents using the rules: and Now take the derivitive using the Power Rule: Look at the next term: And then the last term: Then put it all back together: However, I would rationalize all the denominators: John

Linear_Equations_And_Systems_Word_Problems/185238: I need to solve the following word problem, I have to show the equation I use for the solution. One number is 7 less than another. If 4 times the smaller number plus 2 times the larger number is 62, find the two numbers. I just don't get these at all. Thanks, Dawn 1 solutions Answer 138945 by solver91311(16897)   on 2009-03-05 19:03:19 (Show Source): You can put this solution on YOUR website! x is the large number x - 7 is the smaller number Four times the smaller number: 4(x - 7). Two times the larger number: 2x. So: Solve for x to get one of the numbers, and then subtract 7 to get the other one. John

Geometry_Word_Problems/185187: ``I have a circular diagramme. I draw the first sector,then the second one, which is 2 times bigger than the fist one ,and so on, to finally divide the whole diagramme. If we double the previous sector 6 times, find the value of the angle at the middle of the inital sector. 1 solutions Answer 138939 by solver91311(16897)   on 2009-03-05 18:09:14 (Show Source): You can put this solution on YOUR website! I'm presuming that the six partitions add up to one complete circle. Given that a circle is 360 degrees, the last segment must be half of that, or 180. The one before that, 90, before that 45, 22.5, 11.25, and finally, the first one must have been 5.625. Symbolically: John

Money_Word_Problems/185214: 1.It is 12pm.2 people are fishing.If Benoit gives 2 of his fishes to Amelie,she will have 2 times more fishes than him. If Amelie gives 4 fishes to Benoit,he will have the same amount of fishes.How many fishes does each have ?? 2.It is 4pm.If benoit gives 8 of his fishes to Amelie,she will have 3 times more fishes than him.If Amelie gives the 1/5 of her fishes to Benoit,they willhave the same amount.Howmany fishes do the have?? PLESEEEEEEEEEEEEEE HELPPPPPPPPPPPPPPPPPP WITH THIS ONE !!!!!!!!!!!!!!!!!!!!!!!!! THANK YOU SOOOOOOOOOOOOOOOO MUCHHHHHHHHHHHHHHH !!!!!!!!!!!!!!!! OH GOD !!!!!!!!!!!! 1 solutions Answer 138932 by solver91311(16897)   on 2009-03-05 17:07:52 (Show Source): You can put this solution on YOUR website! Let A be the number of Amelie's fish. Let B be the number of If Benoit's fish. If B gives up 2 fish he will have B - 2 fish. And if A gets 2 fish, she will have A + 2 fish. And we know that A now has 2 times as many fish as B, so: If A gives up 4 fish, she will have A - 4 fish. If B gets 4 fish he will have B + 4 fish. The problem tells us that these two quantities are equal, so: Since you have been given a word problem that requires solving simultaneous linear equations, you must already know how to find the solution set of a system. Solve the above system for A and B. I suggest you use the substitution method. Later that day... and This will be somewhat simpler if you first multiply the 2nd equation by 5 before you collect like terms and solve for A. Again, use the substitution method. And please stop asking God for help with your mathematics. The only thing you will get from God is an opportunity to study, and you have lots of those already. And while you are at it, stop screaming at us by using ALL CAPS. It is the electronic equivalent of shouting and is both rude and annoying. John

Geometric_formulas/185204: CAN YOU HELP A GRADE FIVE KId UNDERSTAND. Susan wanted to frame a nuce picture of herself. The length of the picture was 20 cm and the width was 10 cm. The perimeter was 60 cm. If she wants a 2 cm border around the picture, what will the perimeter of the entire frame be\/ God Please explain 1 solutions Answer 138923 by solver91311(16897)   on 2009-03-05 15:50:45 (Show Source): You can put this solution on YOUR website! I've never seen where God responded to a question on this site, and I would think it rather unlikely. However, if a lesser being such as myself will be sufficient, I would be delighted to give it a try. I'm also a little curious about what a 'nuce' picture is. If the picture is 10cm by 20cm and you want a 2cm border all the way around it, the outside of the border adds 2cm to the top, 2cm to the bottom, 2cm to the left, AND 2cm to the right, so the length becomes 20 + 2 + 2 = 24cm, and the width becomes 10 + 2 + 2 = 14 cm. The perimeter is given by: Substitute your values: Just do the indicated arithmetic. John

Money_Word_Problems/185198: We are standing on a roof and we throw a ball from a certain height.The height of the bounce of the ball is equal to 70% of the height from where we threw it. If the height of the third bounce is 10.29m., at what height are we standing>????????????????????????????????? PLZZZZZZZZZZZZZZZ HELPPPPPPPPPPP !!!!!!!!!!!!! I ReALLY NEED HELPPPPPPPPPPPPPPPPPP !!!!!!!!!! 1 solutions Answer 138916 by solver91311(16897)   on 2009-03-05 13:58:37 (Show Source): You can put this solution on YOUR website! Let h be the height you are looking for. Then let be the height after the 1st bounce and be the height after the 2nd bounce. Then 70% of equals 10.29 m, which is then equal to 70% of , which is then equal to 70% of , so: You can do your own arithmetic. John

Polynomials-and-rational-expressions/185194: please someone help me with this word problem please I tried to do it myself but keep getting it wrong.. The members of the flying club plan to share equally the cost of a $200,000 airplane. The members want to find five more people to join the club so that the cost per person will decrease by $2000. How many members are currently in the club? 1 solutions Answer 138913 by solver91311(16897)   on 2009-03-05 12:51:19 (Show Source): You can put this solution on YOUR website! Let represent the current cost per person and let x be the current number of members. Also, for convenience sake, represent the money amounts in thousands, meaning the cost of the airplane is 200 and the savings after recruiting 5 new members is 2. Then: thousand dollars. If you add five new members reducing the cost per person by 2 thousand, then: Add on the left with x as the common denominator: And now we have a proportion: Cross-multiply: Expand, collect terms, put in standard form: Divide by -2: Factor the quadratic and eliminate the negative root because a negative number of members is absurd -- it is an extraneous root introduced by squaring the variable in the process of solving the problem. The positive root is your current number of members. Check your answer by dividing 200 by your result for x and verify that the quotient is 2 larger than the result of dividing 200 by x + 5. John

logarithm/185120: I am having trouble with a logarithmic bacteria word problem. A bacterial culture is growing according to the formula y=50,000e^0.8x. In this formula, x is the time in days and y is the number of bacteria. Estimate the number of bacteria after 1 month. (Hint: Assume there are 30 days in a month.) I am the teacher for my son and do not know how to solve this. The answer is y = 1.324456 x 10^15. Please help. 1 solutions Answer 138879 by solver91311(16897)   on 2009-03-05 00:40:51 (Show Source): You can put this solution on YOUR website! Substituting 30 for x makes the exponent 0.8 times 30 = 24, so: e is the base of the natural logarithms, approximately 2.718. So, unless you are some sort of arithmetic masochist, and want to multiply 2.718 times itself 24 times, it is time to get out the calculator. Using the Windows built-in calculator in Scientific mode, enter 24, click the Inv check box in the upper left corner, then click the 'ln' button (e raised to a power is the inverse of taking the natural logarithm, ln). Then click '*', enter 50000, and click '='. If you have Excel on your computer, open a sheet and enter the following in a cell: =50000*exp(24) Then press enter. John

Travel_Word_Problems/185118: A certain plane flying with the wind travels 540 mi in 2 hours. Later, flying against the same wind, the plane travels 690 mi in 3 hours. Find the speed of the plane in still air and the speed of the wind. 1 solutions Answer 138877 by solver91311(16897)   on 2009-03-05 00:20:49 (Show Source): You can put this solution on YOUR website! Distance equals rate times time. When the plane is going with the wind, ground speed is air speed plus wind speed. Against the wind, ground speed is air speed minus wind speed. Add the equations: John

Angles/185063: find two angles such that the angles are supplementary and the larger is twice the smaller. 1 solutions Answer 138876 by solver91311(16897)   on 2009-03-05 00:13:03 (Show Source): You can put this solution on YOUR website! Let be the smaller angle. Then the larger must be . Angles are supplementary if the sum of their measures is 180. Solve for John

Rate-of-work-word-problems/185031: A park has two sprinklers that are used to fill a foutain. One sprinkler can fill the foutain in 3 hours, where as the other sprinkler can fill up the foutain in 6 hours. How long will it take to fill the foutain with both sprinklers operating? 1 solutions Answer 138873 by solver91311(16897)   on 2009-03-05 00:04:08 (Show Source): You can put this solution on YOUR website! If A can do a job in x time periods, then A can do of the job in 1 time period. Likewise, if B can do the same job in y time periods, then B can do of the job in 1 time period. So, working together, they can do of the job in 1 time period. Therefore, they can do the whole job in: time periods. John

Geometry_Word_Problems/185049: Find the dimensions of a rectangle if the area is 200 feet squared and the length is 8 feet longer than the width? 1 solutions Answer 138872 by solver91311(16897)   on 2009-03-05 00:00:49 (Show Source): You can put this solution on YOUR website! Let w be the width, then w + 8 is the length. So the area is: In standard form: Solve using the quadratic formula, discarding the negative root giving you the width. Then add 8 to get the length. John

Graphs/185077: This question is from textbook How do you graph the inequalities y>3 and x<-2? 1 solutions Answer 138871 by solver91311(16897)   on 2009-03-04 23:44:15 (Show Source): You can put this solution on YOUR website! For Draw a number line. Draw a little circle at the 3 point. Make a heavy line on your number line starting at your little circle and continuing as far as you can to the right, putting an arrow at the end to indicate that the line goes on forever. For Do the same thing except your little circle is at -2 and the heavy line goes to the left. John

Equations/185111: Hi. I need some help with the following problem. find all x that will make f(x)=0 f(x)=x^4-26x^2+25 thanks! 1 solutions Answer 138866 by solver91311(16897)   on 2009-03-04 23:20:57 (Show Source): You can put this solution on YOUR website! Let then: So for f(u) = 0: Which factors: Hence, or But so: or John

Money_Word_Problems/185107: This question is from textbook Experiencing Introductory & Intermediate Algebra E-Z-R Loan Agency writes a loan agreement stipulating that $1308 is to be paid for a simple-interest loan for one year at 9%. How much is being borrowed? How much interest is being paid on the loan? 1 solutions Answer 138864 by solver91311(16897)   on 2009-03-04 23:12:00 (Show Source): You can put this solution on YOUR website! Let x be the amount of the loan. Then the customer has to pay the amount of the loan plus 9% of the loan as interest. You can do your own arithmetic. The interest amount is John

Radicals/185109: √2x+3=-5 1 solutions Answer 138862 by solver91311(16897)   on 2009-03-04 23:03:33 (Show Source): You can put this solution on YOUR website! It depends. Did you mean or or ? Repost using parentheses to make your intentions clear. John

Polynomials-and-rational-expressions/185108: This question is from textbook A rug 4 meters by 5 meters covers 2/3 of the floor area in a room. The rug touches two walls, leaving a strip of uniform width around the other two walls. How wide is the strip? 1 solutions Answer 138858 by solver91311(16897)   on 2009-03-04 22:53:04 (Show Source): You can put this solution on YOUR website! If the rug is 4 ft by 5 ft, then the area covered by the rug is 20 square feet, which is 2/3 of the unknown total area of the room, so: So the area not covered by the rug is 30 - 20 = 10 square feet. Let the width of the uncovered strip be x. The uncovered strip is an L shaped area that can be divided into three pieces. One piece is 5 ft by x feet, another piece is 4 feet by x feet, and the little piece in the corner is x feet by x feet. The area of the three pieces are 5x, 4x, and . The sum of the areas of these three pieces must be 10 square feet, thus: Put in standard form: Solve the quadratic by factoring and exclude the extraneous negative root. The positive root will be the width of the uncovered strip. John

Equations/185103: Hi. I'm seeing if I solved this equation correctly by factoring. 2y(4y+3)=9 thanks! 1 solutions Answer 138856 by solver91311(16897)   on 2009-03-04 22:39:13 (Show Source): You can put this solution on YOUR website! Post your solution and we'll let you know John

Equations/185105: Hi. I'm seeing if I solved this equation correctly by factoring 2z^3-200z=0 thanks! 1 solutions Answer 138855 by solver91311(16897)   on 2009-03-04 22:20:43 (Show Source): You can put this solution on YOUR website! Tell us what roots you got for the equation and we'll let you know. John

Money_Word_Problems/185098: Sean mows his half of hte yard in 30 minutes. His brother takes 50 minutes. If they each had their own lawn mower and worked together, how long would the job take? 1 solutions Answer 138854 by solver91311(16897)   on 2009-03-04 22:19:19 (Show Source): You can put this solution on YOUR website! If A can do a job in x time periods, then A can do of the job in 1 time period. Likewise, if B can do the same job in y time periods, then B can do of the job in 1 time period. So, working together, they can do of the job in 1 time period. Therefore, they can do the whole job in: time periods. Just substitute your given time values and do the arithmetic. John

Linear_Equations_And_Systems_Word_Problems/185078: please help me solve this word problem thank you. junior's boat will go 15 miles per hour in still water. If he can go 12 miles downstream in the same amount of time as it takes to go 9 miles upstream, then what is the speed of the current.: 1 solutions Answer 138844 by solver91311(16897)   on 2009-03-04 20:57:14 (Show Source): You can put this solution on YOUR website! I already solved this one. Just substitute 9 for m in the final equation and do the arithmetic. Your problem statement left out an important detail: "[J]unior's boat will go 15 miles per hour in still water. If he can go 12 miles downstream in the same amount of time as it takes to go ??? miles upstream, then what is the speed of the current[?]" However, all is not lost. Remember that distance equals rate times time, that is: Which, for this problem, will be convenient to express as: Let the speed of the current be represented by and your missing upstream distance be represented by m. When the boat is going downstream, the boat is actually moving the speed through still water plus the speed of the current. When going upstream, it is the speed in still water minus the speed of the current. For the downstream trip, which we know to be 12 miles, we can write: For the upstream trip, which we are saying is m miles, we can write: Now remembering that the problem said the amount of time for the downstream and upstream trips was the same, we can equate the two right sides of the above equations: Giving us a proportion. Step 1: Cross-multiply: Step 2: Simplify, collect terms, and solve for : Step 3: Once you determine the correct value for m you can substitute and do the arithmetic to determine . John

Exponential-and-logarithmic-functions/185081: I hope someone can explain where I went wrong????? The chemical element strontium has a half-life of 25 years. If 32g were present initially, how long will it take for the amount to be reduced to 2g? Set up an exponential equation and solve algebraically. This is what I did: y=32(1/2)^x/25 2=32(1/2)^x/25 2/32=1/2^x/25 1/16=1/2^x/5 Then I finished it using logs but my teacher said that I was supposed to solve it algebraically !!??!?!? HOW? This is how I finished it: (log(1/16)/ log(1/2))=(log(1/2)^x/5)/(log(1/2)) 4=x/5 20=x 1 solutions Answer 138838 by solver91311(16897)   on 2009-03-04 20:24:56 (Show Source): You can put this solution on YOUR website! You have done everything right. It is just that when you got to the point of saying: You might have noticed that: From which you could then deduce that: I think you should be able to take it from there. The answer you got by using logs would have been correct if you had not, for some inexplicable reason, changed the half-life number from 25 to 5 in the denominator of your fractional exponent. John

Age_Word_Problems/185082: seven years ago, my son was one third my age at the time. seven years from now, he will be one half my age at that time. How old is my son? 1 solutions Answer 138836 by solver91311(16897)   on 2009-03-04 20:09:14 (Show Source): You can put this solution on YOUR website! Son's age now: s, and 7 years ago: s - 7, and 7 years from now: s + 7. Father's age now: f, and 7 years ago: f - 7, and 7 years from now: f + 7. and Put the equations into standard form, i.e. or slope intercept form, i.e., and then solve the system either by elimination or substitution. John

Graphs/185079: This question is from textbook Algebra 2: Applications, Equations, Graphs 5x-2y=10 graph 1 solutions Answer 138835 by solver91311(16897)   on 2009-03-04 20:01:08 (Show Source): You can put this solution on YOUR website! Pick a value, any value, for x. Substitute that value in place of x in the equation. Do the arithmetic to determine the resulting value of y. With the value of x and the value of y form an ordered pair (x,y). Plot this point on your graph. Pick a different value for x and repeat the above process. Draw a line all the way across your graph through the two plotted points. Hint: Pick values for x like 0 or 1 to make the arithmetic easier. John

Angles/185067: find two angles such that the angles are adjacent and form an angle of 120 degress. the larger is 20 degrees less than three times the smaller. 1 solutions Answer 138834 by solver91311(16897)   on 2009-03-04 19:55:52 (Show Source): You can put this solution on YOUR website! Let the measure of the smaller angle be x. Then the measure of the larger angle must be 3x - 20. The sum of the measures of these two angles must be 120, thus: Solve for x to get the measure of the smaller angle, and subtract that value from 120 to get the measure of the larger. Check your answer by multiplying the measure of the smaller angle by 3 and subtracting 20 to see if the result is what you got for the larger angle. John

Linear_Equations_And_Systems_Word_Problems/185061: please help me solve this word problem thank you. junior's boat will go 15 miles per hour in still water. If he can go 12 miles downstream in the same amount of time as it takes to go miles upstream, then what is the speed of the current. 1 solutions Answer 138832 by solver91311(16897)   on 2009-03-04 19:41:20 (Show Source): You can put this solution on YOUR website! Your problem statement left out an important detail: "[J]unior's boat will go 15 miles per hour in still water. If he can go 12 miles downstream in the same amount of time as it takes to go ??? miles upstream, then what is the speed of the current[?]" However, all is not lost. Remember that distance equals rate times time, that is: Which, for this problem, will be convenient to express as: Let the speed of the current be represented by and your missing upstream distance be represented by m. When the boat is going downstream, the boat is actually moving the speed through still water plus the speed of the current. When going upstream, it is the speed in still water minus the speed of the current. For the downstream trip, which we know to be 12 miles, we can write: For the upstream trip, which we are saying is m miles, we can write: Now remembering that the problem said the amount of time for the downstream and upstream trips was the same, we can equate the two right sides of the above equations: Giving us a proportion. Step 1: Cross-multiply: Step 2: Simplify, collect terms, and solve for : Step 3: Once you determine the correct value for m you can substitute and do the arithmetic to determine . John

Linear_Equations_And_Systems_Word_Problems/185058: Different weights. Professor Williamson counts his midterm as 2/3 of the grade and his final as 1/3 of the grade. Wendy scored only 48 on the midterm. What range of scores on the final exam would put Wendy’s average between 70 and 79 inclusive? Compare to the previous exercise which is (Going for a C.) Prof gives only a midterm and final. The semester avg is computed by taking 1/3 of the midterm exam score plus 2/3 of the final exam score, to get a C Stacy must have a sem avg between 70 and 79 inclusive. If Stacy scored only 48 on the midterm then for what range of scores on the final exam will Stacy get a C? I cannot understand thie word problem at all ... can anyone help shed some light on the subject for me? Thanks so much for your help 1 solutions Answer 138823 by solver91311(16897)   on 2009-03-04 19:16:10 (Show Source): You can put this solution on YOUR website! If m is the mid-term score and f is the score on the final exam, then Professor Williamson will give a final grade, g, of: But we are given that m = 48 and the minimum g we are looking for is 70, then: Just solve for f to get the lowest score that will put you in the stated range, then: Solve for f again to get the highest score that will keep the final grade in the stated range. I think you will find that, unless the good Professor gives a final with more than 100 as a possible score, you can't get there from here. If the maximum possible score on the final is 100, the best Wendy can do is a 65.33 -- and the moral of the story is study hard; study early. If you are also asking about the previous problem, the equations are the same if you reverse the fractional coefficients. John