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# Recent problems solved by 'josmiceli'

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 Average/587371: Gina earns score of 65,78,85, and 82 on four tests. What grade must she earn on the next to have an average of 80? 1 solutions Answer 374086 by josmiceli(9645)   on 2012-03-15 15:59:39 (Show Source): You can put this solution on YOUR website!Let = her grade on the next test From the definition of an average: She needs a 90 on the next test to average 80
 Geometry_Word_Problems/587367: What number between 20 and 30 is four times the sum of it's two digits?1 solutions Answer 374083 by josmiceli(9645)   on 2012-03-15 15:55:52 (Show Source): You can put this solution on YOUR website!The number has to begin with Let the units digit = The value of the number is given: The number is 24 check: OK
 Age_Word_Problems/587364: Holly is 6yrs younger than her sister. Holly's mother is 44 twice the sum of the age of her two children how old is holy 2x-6=441 solutions Answer 374081 by josmiceli(9645)   on 2012-03-15 15:47:24 (Show Source): You can put this solution on YOUR website!Let = Holly's age Let = Sister's age Let = Mother's age given: (1) (2) (3) ------------------ Substitute (2) into (3) (3) Substitute (1) into (3) (3) (3) (3) (3) (3) and (1) (1) (1) and (3) (3) (3) (3) OK Holly is 8
 Linear-equations/587363: write an equation in slope intercept form for a line that passes through the given point and that is perpendicular to the given line. x= -7; (0,2)1 solutions Answer 374080 by josmiceli(9645)   on 2012-03-15 15:38:42 (Show Source): You can put this solution on YOUR website! is a vertical line through (-7,0) Think of the equation as saying: " I am a line that always sees on the x-axis, and I don't care what is." Any line perpendicular to this line will be a horizontal line which means it has slope = . If the general form of an equation is , where = slope, then I have The line goes through (0,2), which is on the y-axis It intersects the given vertical line at (-7,2). Both these points tell me that the equation is
 Linear-systems/587193: The point (3, 2) lies on the line 11x – 6y = 21. Determine if this point is a solution of the system 11x – 6y = 21 9x + 8y = 43 1 solutions Answer 374026 by josmiceli(9645)   on 2012-03-15 06:21:03 (Show Source): You can put this solution on YOUR website!Does (3,2) also lie on ? Yes, it solves this system
 Age_Word_Problems/587199: If a father is now 5 times as old as his son, how many years ago was the son 2 years old and the father 34 years old?1 solutions Answer 374024 by josmiceli(9645)   on 2012-03-15 06:16:31 (Show Source): You can put this solution on YOUR website!Start when Son was 2 and Father was 34 Add the same number of years, , to each one's age Let that be when Father is 5 times Son's age, and find 6 years ago the Son was 2 and the Father was 34 check: The Son is now The Father is now That is correct
 test/587200: Good day to you all. Please determine the nature of the solutions to each equation without solving it. 1.) 25x^2 - 10x + 1 = 0 2.) x^2 + x +2 = 0 3.) 5x^2 - x = 0 Thank You. 1 solutions Answer 374023 by josmiceli(9645)   on 2012-03-15 06:06:34 (Show Source): You can put this solution on YOUR website!Look at where the equation has the form (1) This means there is 1 real solution It is called a double root --------------------------------- (2) This is minus, so there are 2 imaginary roots ( look like and ) ----------------------------------- (3) This is plus, so there are 2 real roots ------------------------------------- Here's plots of the 3 equations. Touching the x-axis: 1 solution Not touching at all: 2 imaginary solutions Touching twice: 2 real solutions
 Numbers_Word_Problems/587059: the sum of two numbers is 19. if 5 times the smaller number is 3 less than twice the larger number, what are the two numbers? thanks God bless.1 solutions Answer 373968 by josmiceli(9645)   on 2012-03-14 21:21:17 (Show Source): You can put this solution on YOUR website!Let the numbers be and given: (1) Let = the smaller number (2) (2) Substitute (2) into (1) (1) (1) (1) (1) (1) and, since (1) (1) (1) The numbers are 5 and 14 check: (2) (2) (2) (2) OK
 Matrices-and-determiminant/586997: How can you translate the graph of y=|x| to obtain the graph of y=|x-4|+2? a.)4 units left and 2 units up b.)4 units left and 2 units down c.)4 units right and 2 units up d.)4 units right and 2 units down1 solutions Answer 373957 by josmiceli(9645)   on 2012-03-14 19:15:27 (Show Source): You can put this solution on YOUR website!I notice 2 things: (1) can never be negative (2) the smallest value of is when , ------------------------ has a minimum at , The translation is (c) 4 units right and 2 units up Here's the plot of :
 Inverses/586443: I am trying to refresh my mind. Please show me how to work this problem. 1/2+(2/3 divided 3/4)-(4/5 times 5/6)=1 solutions Answer 373753 by josmiceli(9645)   on 2012-03-13 18:18:01 (Show Source): You can put this solution on YOUR website! Separate ou the 2nd term and multiply the top and bottom by ----------- So far I have The common denominator is answer I like to check using decimals and I think the error is due to rounding off
 Linear-systems/586442: what is 4(x+7)=7+x??1 solutions Answer 373749 by josmiceli(9645)   on 2012-03-13 17:58:24 (Show Source): You can put this solution on YOUR website! Subtract from both sides Subtract from both sides Divide both sides by check answer: OK
 Money_Word_Problems/586013: In the cash drawer at a bank, the ratio of the number of \$1 bills to the number of \$5 bills is 5 to 4, and the ratio of \$10 bills to \$20 bills is 2 to 1. These bills represent the total amount of money in the drawer: \$6795. How many \$1 bills are in the drawer? I know how to do basic ratio problems, but being that this one involves money, it just confuses me... Please help! I would /really/ appreciate it. 1 solutions Answer 373611 by josmiceli(9645)   on 2012-03-12 20:59:03 (Show Source): You can put this solution on YOUR website!The way I do it is: Let = number of \$1 bills Let = number of \$5 bills Let = number of \$10 bills Let = number of \$20 bills -------------------------- given: (1) (2) (3) ------------------------------- This is 4 unknowns and only 3 equations, so it isn't completely solvable, but the information can still be there ----------------------- (1) (1) and (2) ------------- The possible combinations of \$1s and \$5s is: 5 \$1s 4 \$5s ----- 10 \$1s 8 \$5s ----- 15 \$1s = \$15 12 \$5s = \$60 ----- Whatever combination I choose, the remainder of the money must be divisible by \$40 ( 1 \$20 and 2 \$10s ) this seems to work 168 \$20s = \$3360 336 \$10s = \$3360 12 \$5s = \$60 15 \$1s = \$15 ------------ sum = \$6795 I don't know if another combination will work. This one seems to.
 Exponents/586023: i need help on scientific notation! if i have a problem like this: (5 x 10 to the 5th) to the negative 2nd ......how do i solve it?1 solutions Answer 373578 by josmiceli(9645)   on 2012-03-12 19:26:03 (Show Source): You can put this solution on YOUR website!Is this the problem: Rewrite this as: ---------------------- You can do this because of general rules: (1) (2) ---------------------- and so far, I have: Now I have: answer
 Numbers_Word_Problems/585870: 50 children bought either chocolate or white milk. Chocolate milk costs \$.30 and white milk costs \$.25. the total cost of milk sold was 13.30.How man chocolate and white milks were sold? Easiest way to solve this.1 solutions Answer 373517 by josmiceli(9645)   on 2012-03-12 14:13:12 (Show Source): You can put this solution on YOUR website!Let = number of white milks sold Let = number of chocolate milks sold given: (1) (2) ( in cents ) ------------------- Multiply both sides of (1) by and subtract (1) from (2) (2) (1) and, since (1) (1) (1) 34 white milks were sold 16 chocolate milks were sold check answer: (2) (2) (2) OK
 percentage/585869: Twice the difference of a number and seven is tripled, the result is eight times a number1 solutions Answer 373516 by josmiceli(9645)   on 2012-03-12 14:02:49 (Show Source): You can put this solution on YOUR website!given: The number is 3
 Travel_Word_Problems/585862: it takes me about 30 minute to travel 25 miles. What is my average speed?1 solutions Answer 373515 by josmiceli(9645)   on 2012-03-12 13:57:48 (Show Source): You can put this solution on YOUR website!In 1 hour you could go twice as far, or 50 miles Your average speed is 50 mi/hr
 Equations/585857: write the equation in slope intercept form. (-1,2) (1,-4), and (0,0) (-3,-2)1 solutions Answer 373512 by josmiceli(9645)   on 2012-03-12 13:54:59 (Show Source): You can put this solution on YOUR website! here's the plot:
 test/585858: A+a+a1 solutions Answer 373502 by josmiceli(9645)   on 2012-03-12 13:21:26 (Show Source): You can put this solution on YOUR website!A + a + a = A + 2a
 logarithm/585855: Write these expressions as a single logarithm: 1. log3 24 + log3 2 2. 3 logx + 5 log y1 solutions Answer 373501 by josmiceli(9645)   on 2012-03-12 13:20:44 (Show Source): You can put this solution on YOUR website!(1) Use the general rule: (1) ------------------- (2) Use the previous rule and also: (2) (2)
 Mixture_Word_Problems/585850: How many liters of pure alcohol must be added to 10 liters of a 70% solution to obtain a 90% solution? I know the answer is 20 liters, but I need help with the equation I would use to figure this out on my own please.1 solutions Answer 373498 by josmiceli(9645)   on 2012-03-12 13:11:48 (Show Source): You can put this solution on YOUR website!Let = liters of pure alcohol to be added liters of alcohol in 70% solution In words: ( liters of alcohol you end up with ) / ( total liters of solution ) = 90% 20 liters of pure alcohol must be added
 Rate-of-work-word-problems/585848: A mowed 3/4 at his lawn in 5/4 hours.B who works twice as fast finished the job.how many minutes did B work?1 solutions Answer 373497 by josmiceli(9645)   on 2012-03-12 13:04:11 (Show Source): You can put this solution on YOUR website!If A mowed 3/4 of his lawn, there is 1/4 left for B to mow ------------- If A mowed a lawn 4 times as large, it would take him 4 times longer, so lawns take him hrs 1 lawn would take him 1/3 of that time, or hrs ------------- If B works twice as fast, he can mow 1 lawn in hrs But B only has to mow 1/4 of a lawn, so B can mow it in hrs hrs x min/hr = 12.5 minutes
 Money_Word_Problems/585812: Rick and sandy bought some raffle tickets together and won the prize of \$3,600. if rick and sandy agreed to split the winnings at a ratio of 8 to 7 (ricks winnings to sandys winnings) how much did each of them receive?1 solutions Answer 373496 by josmiceli(9645)   on 2012-03-12 12:51:21 (Show Source): You can put this solution on YOUR website!Let = Rick's share Let = Sandy's share given: (1) (2) ------------- Multiply both sides of (2) by (2) (2) Substitute this into (1) (1) (1) (1) (1) and, since (1) (1) (1) Rick gets \$1,920 Sandy gets \$1,680 check: (2) (2) (2) (2) OK
 logarithm/585822: Find log of -3.7*10^21 solutions Answer 373490 by josmiceli(9645)   on 2012-03-12 11:41:11 (Show Source): You can put this solution on YOUR website!This can't be done. Logs are exponents, and there is no exponent with a positive base that possibly give you a negative number. Note that a negative exponent with a positive base still gives you a positive number. ---------------------------- Look for an error in signs if you are required to find the log of this number.
 Travel_Word_Problems/585813: if David does a job in 78 hours and with the help of Jacqueline they can do it together in 26 hours, how long would it take Jacqueline to do it alone?1 solutions Answer 373489 by josmiceli(9645)   on 2012-03-12 11:36:15 (Show Source): You can put this solution on YOUR website!Add their rates of working to get their rate working together. David's rate: ( 1 job ) / ( 78 hrs ) Let J's rate = ( 1 job ) / ( t hrs ) Rate working together: ( i job ) / ( 26 hrs ) -------------------------------- Note that Multiply both sides by Jacqueline working alone can do the job in 39 hrs
 Angles/585807: Joe has a collection of nickles and dimes that is worth \$7.05. If the number of dimes were doubled and the number of nickels were increased by 7, the value of the coins would be \$13.30. How many dimes does he have?1 solutions Answer 373488 by josmiceli(9645)   on 2012-03-12 11:28:49 (Show Source): You can put this solution on YOUR website!Let = number of nickels Let = number of dimes given: (1) ( in cents ) (2) -------- (2) (2) Subtract (1) from (2) (2) (1) and, since (1) (1) (1) (1) (1) He has 23 nickels and 59 dimes check: (2) (2) (2) (2) OK
 Complex_Numbers/585798: When simplifying expressions that involve complex numbers, How do I determine what the values of the numbers will be? I need help with solving expressions containing these. Ex: (4-5i) (1-i) (3-4i)/(4-3i)1 solutions Answer 373487 by josmiceli(9645)   on 2012-03-12 11:09:31 (Show Source): You can put this solution on YOUR website! Combine like terms. Note that --------------- Combine like terms, again, ---------
 Probability-and-statistics/585802: Find the common denominator and smallest number that has both denominator as a factor. Write these pairs of fractions with common denominators. 1. 5/8 and 1/2 2. 3/4 and 1/8 3. 1/4 and 1/2 4. 1/2 and 3/8 5. 3/4 and 5/8 6. 7/8 and 1/41 solutions Answer 373486 by josmiceli(9645)   on 2012-03-12 10:58:33 (Show Source): You can put this solution on YOUR website!1. 5/8 and 4/8 2. 6/8 and 1/8 3. 1/4 and 2/4 4. 4/8 and 3/8 5. 6/8 and 5/8 6. 7/8 and 2/8
 Money_Word_Problems/585730: Can you please help me on this equation: How many liters of water are needed to dilate 20 liters of a 5% salt solution to a 1% solution?1 solutions Answer 373451 by josmiceli(9645)   on 2012-03-12 01:32:26 (Show Source): You can put this solution on YOUR website!Let = liters of water needed given: liter of salt in 5% solution 80 liters of water are needed check: OK
 Rectangles/585620: Two cars start from the same place traveling in opposite directions one car travels 5 miles per hour faster than the other car.find the speeds of the two cars if after 6 hours they are 570 miles apart?1 solutions Answer 373428 by josmiceli(9645)   on 2012-03-11 20:51:54 (Show Source): You can put this solution on YOUR website!They are moving apart at the sum of their speeds Let = the speed of the slower car The speeds of the cars are 45 mi/hr and 50 mi/hr
 Mixture_Word_Problems/585605: A solution of 75% pesticide is to be mixed with a solution of 35% pesticide to form 440 liters of a 43% solution. How many liters of the 75% solution must be used?1 solutions Answer 373426 by josmiceli(9645)   on 2012-03-11 20:48:04 (Show Source): You can put this solution on YOUR website!Let = liters of 75% pesticide needed Let = liters of 35% pesticide needed given: (1) (2) ----------------------------- (2) (2) (2) (2) Multiply both sides of (1) by and subtract (1) from (2) (2) (1) and, since (1) (1) (1) (1) 88 liters of 75% pesticide are needed 352 liters of 35% pesticide are needed check: (2) (2) (2) (2) (2) OK
 Numbers_Word_Problems/585595: Please help me solve this problem: The sum of the reciprocals of two numbers is 7 and the difference of their reciprocals is 3. What are the number? Thanks..1 solutions Answer 373414 by josmiceli(9645)   on 2012-03-11 20:32:30 (Show Source): You can put this solution on YOUR website!Let the numbers be and given: (1) (2) ------------------ Just add the equations and (1) (1) (1) (1) The numbers are 1/5 and 1/2