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# Recent problems solved by 'nic0le116'

 Complex_Numbers/571340: 7x - 3x = 80 1 solutions Answer 368053 by nic0le116(25)   on 2012-02-11 17:29:42 (Show Source): You can put this solution on YOUR website!Combine like terms. Since 7x and -3x both contain an x, you can subtract them normally. 7x-3x=4x You're then left with 4x=80 You want want to get x alone. Divide each side by 4. You're left with x=20.
 Word_Problems_With_Coins/507678: Your piggy bank contains only dimes and quarters. If there are 73 coins in your piggy bank and the total of the coins is \$14.50, how many dimes are ther in the bank?1 solutions Answer 340792 by nic0le116(25)   on 2011-10-02 13:31:23 (Show Source): You can put this solution on YOUR website!What can we use for the value of of dimes? .10x (since times are worth .10 and we don't know how many we have, so we multiply x amount of times. ------------------------------------------------------------- What can we use for the value of quarters? .25(73-x) (since we know quarters are worth .25 and all we know about how many we have is that there is 73 minus however many dimes we have. since we used x for the amount of dimes, we subtract x) Now we set it all equal to the total amount .10x+.25(73-x)=14.50 (We add just like if we're trying to find the value of 10 times and 10 quarters. We would do .10*10+.25*10=___) ---------------------------------- Solve for x. Remember what did we decide x was? the amount of dimes. .10x+.25(73-x)=14.50 (distribute .25 to the numbers inside of parenthesis) .10x+18.25-.25x=14.50 (combine like terms on each side) -.15x+18.25=14.50 (subtract 18.25 from each side) -.15x=-3.75 (divide each side by -.15 to get x alone) x=25 --------------------------------- There are 25 dimes. If you're unsure subtract 25 from 73 to get the amount of quarters. Multiply the values out and add them up to see if they equal 14.50 73-48=48 quarters 25*.10+.25*48= 14.50 CHECK! --------------------------------- answer=25 dimes
 Circles/504405: Find the area of a circle with radius 5 mm, rounded to the nearest tenth. 1 solutions Answer 339593 by nic0le116(25)   on 2011-09-25 23:55:27 (Show Source): You can put this solution on YOUR website!Area of a circle= 3.14(radius^2) (3.14)(5^2) (3.14)(25)= 78.5mm
 Average/504399: I am very confused please help. Find three consecutive integers whose sum is -114?1 solutions Answer 339591 by nic0le116(25)   on 2011-09-25 23:53:11 (Show Source): You can put this solution on YOUR website!x+(x+1)+(x+2) x= the first number, and since we need consecutive integers, the next number will be x+1, and the next x+2. So set this equation=-114 x+x+1+x+2=-114 (combine like terms) 3x+3=-114 (subtract 3 from each side) 3x=-117 (divide each side by 3) x=-39 (now add one to this to get our 2nd number, and 1 more to get our third) -39+1=-38 -38+1=-37 Now check to make sure it works! -39+(-38)+(-37)=-114 CHECK! ANSWER=-39,-38,-37
 Equations/504359: (2t - 7) - (3t + 5) 1 solutions Answer 339587 by nic0le116(25)   on 2011-09-25 23:39:17 (Show Source): You can put this solution on YOUR website!Subtraction in this case means distribute the negative. So we now have 2t-7-3t-5 Combine like terms -t-12
 Average/504393: Please help me solve this i am confused. The sum of 6 and twice a number is equal to 7 less than a number. find the number1 solutions Answer 339586 by nic0le116(25)   on 2011-09-25 23:29:17 (Show Source): You can put this solution on YOUR website!Read carefully and set up an equation. sum of 6 and twice a number= 6+2x 7 less than a number = x-7 Since these two are said to be equal, set them equal to each other and solve for x -------------------------------------- 6+2x=x-7 (subtract x from each side) 6+x=-7 (subtract 6 from each side) x=-13 -------------- ---------------------- Now that we have the value of x, replace x in the original equation and solve.\ 6+2x=x-7 6+2(-13)=-13-7 6-26 =-20 -20=-20 CHECK! ------------------------------- answer=-20
 Inequalities/504366: I have an absolute value question.... 5(5x+7)+2<=21...the parenthesis are the absolute value symbols....ive tried every step at different points in the equation, and i always end up with the wrong answer....(-56/25,-26/25) i thought for sure was it but i was wrong....ive spent the last hour on this one. I know set the left side to -21 and commence the solving, isolate the absolue value and divide by 5 but every time i try, my math comes up short.1 solutions Answer 339579 by nic0le116(25)   on 2011-09-25 23:09:28 (Show Source): You can put this solution on YOUR website!We want to get the absolute value by itself 5(5x+7)+2<=21 (Subtract 2 from both sides) 5(5x+7) <=19 (Divide each side by 5) 5x+7 <=19/5 (Now we need to solve for both 19/5 and -19/5 -19/5<=5x+7<=19/5 (You can either set up two separate problems or build a 3 part problem.) We need to get x alone. Whatever you do to the middle to get x by itself, needs to be done to each side as well. -19/5<=5x+7<=19/5 (subtract 7 from each side. Be sure to multiply 7/1 by 5 so you can get a common denominator and be able to subtract properly) -54/5<=5x<=-16/5 (Now we need to divide each side by 5 to get x alone. Remember to divide by fractions, take the reciprocal and multiply- So we will be multiplying the left and right side by 1/5) -54/25<=x<=-16/25 X is greater than or equal to -54/25 X is less than or equal to -16/25
 Polynomials-and-rational-expressions/504339: multiply polynomials (2x-3)(x+10)1 solutions Answer 339569 by nic0le116(25)   on 2011-09-25 22:26:10 (Show Source): You can put this solution on YOUR website!distribute. 2x (x+10) = 2x^2+20x -3 (x+10) = -3x-30 Then put it all together,combining like terms in descending order. ANSWER= 2x^2+17x-30
 Divisibility_and_Prime_Numbers/503973: 12/(6x-18)1 solutions Answer 339467 by nic0le116(25)   on 2011-09-25 14:30:13 (Show Source): You can put this solution on YOUR website!First check to see if you can factor. You can in the denominator. Take the greatest common factor which is 6 in this case The denominator should then look like this: 6(x-3) If this looks confusing, distribute it back out and you will see that it equals the same thing. Now we have: 12/6(x-3) You can reduce since we have 12 and 6 in the problem. Cancel out the 6 and make the 12 a 2. Final answer= 2/x-3
 Geometry_Word_Problems/503921: What is the formula for the area of a square and circle?1 solutions Answer 339465 by nic0le116(25)   on 2011-09-25 14:25:06 (Show Source): You can put this solution on YOUR website!area of a square= length*width area of a circle= Pi(3.14)*radius^2
 Mixture_Word_Problems/503956: can someone please help me? the perimeter of a rectangle field is 110 feet. the length is 7 feet more than twice the width. what is length of the rectangle?1 solutions Answer 339464 by nic0le116(25)   on 2011-09-25 14:20:10 (Show Source): You can put this solution on YOUR website!What can we use to represent the value of the width at this time? Since we have no numerical value at this time, we'll use "x." And what can we use for the length at this time? Well we know that the length is 7ft longer than 2 times the width. So we can represent this by 2x+7. ---------------------------------- We know that perimeter is the sum of all the sides. In the case of the rectangle we can assume that perimeter equals 2 times the length+ 2 times the width. ---------------------------------- So with this information, let's set up an equation to solve for x 2x + 2(2x+7)=110 <--------- 2WIDTH+2LENGTH=PERIMETER -------------------------------------- Solve for x! 2x+2(2x+7)=110 (Distribute the 2) 2x+4x+14=110 (Combine like terms) 6x+14=110 (Subtract 14 from each side) 6x=96 (Divide each side by 6) x=16 <-------What does this x represent? The value of the width! --------------------------------------- Now remember to always check what specifically the word problem is asking of you. We want to know the value of the length, so we're not done yet. So now we need to plug in the value of x into what we originally represented length to equal which was (2x+7) ------------------------------------ 2(16)+7 32+7 39<------------------the value of the length! --------------------------------------- Not sure if this is right? Check by adding up all the side of the values of width and length and see if they equal the given perimeter value. 39+39+16+16=110 CHECK! ANSWER= LENGTH=39ft
 Rectangles/503953: The length of a rectangular garden is 8 feet longer than its width. If the garden's perimeter is 184 feet, what is the area of the garden in square feet? 1 solutions Answer 339462 by nic0le116(25)   on 2011-09-25 14:01:11 (Show Source): You can put this solution on YOUR website!I always recommend drawing a picture for problems like these. -------------------------- What can we use to represent the value of the width right now? Since we can not answer with a numerical value at this time, it is "x." -------------------------- What can we use to represent the value of the length at this time? Since all we now is that it is 8 ft longer then the width, we can represent it as "x+8" -------------------------- Since we also know the value of the perimeter...how can we solve to find the value x to solve for length and width? Since we know Perimeter is the value of all the sides added up, we can conclude in the case of a rectangle that the value is 2 times the width +2 times the length. ------------------------- Now, set up a problem to determine x using all the information we currently have. What did we use for width- x and length?- x+8 _--------------------------- Now lets use that 2 times length + 2times width= perimeter to figure out what x is! 2x+ 2(x+8)= 184 (distribute the 2) 2x+2x+16=184 (combine like terms) 4x+16=184 (subtract 16 from both sides) 4x=168 (divide by 4) x=42 Now what does this x represent? The value of the width! --------------------------- Now how do we know what the length is? Plug the value of x (42) into what we originally represented the length by which was(x+8) 42+8= 50 ---------------------------- Not sure if this is right? add it all up to see if it equals the perimeter. 42+42+50+50=184. CHECK! ------------------------------- Now remember with word problems, sometimes you have to do some extra work. Always make sure you answered what was originally asked. So we're not done yet! We want to know the area, and now that we know the value of the length and width, we can do that. ------------------------------- Area= L*W 42*50=2100
 Complex_Numbers/503933: 3-9i/6-9i in complex form1 solutions Answer 339459 by nic0le116(25)   on 2011-09-25 13:41:28 (Show Source): You can put this solution on YOUR website!We need to get rid of the i's in the denominator. You do this by multiplying the top and bottom by the conjugate of the denominator. The conjugate of 6-9i is 6+9i. You just need to change the sign of the second number. ------------------------------------ So lets multiply the numerator first. (3-9i)(6+9i)= 18+27i-54i+81i^2 REMEMBER- i^2 is equal to -1. So replace the i^2 with -1 Multiply 81 by -1 = 18-27i-81 -63-27i <----------THIS IS OUR NUMERATOR FOR NOW ------------------------------------- Now, lets multiply the conjugate by the denominator Remember the goal is to get rid of all i's in the denominator. (6-9i)(6+9i) =36+54i-54i-81i^2 (i's cancel and we're left with only an i^2 which we now know needs to be replaced with negative 1) =36-(81*-1) =36+81 =117 <-----------------THIS IS OUR DENOMINATOR FOR NOW. ---------------------------------------- Now let's put them together in complex form which is a+bi. This simply means numbers on one side and all numbers attatched to an i on the other NOT IN COMPLEX FORM ANSWER= -63-27i/117 Since out denominator is 117, all numbers need to be over 117, but broken up so i's are to the right. ANSWER IN COMPLEX FORM= (-63/117)-(27i/117)