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logarithm/166689: log3(x-2)+log3(x+4)=3
1 solutions

Answer 122882 by nerdybill(6962)   on 2008-11-09 21:23:50 (Show Source):
You can put this solution on YOUR website!
log3(x-2)+log3(x+4)=3
log3[(x-2)(x+4)]=3
(x-2)(x+4)=3^3
x^2+4x-2x-8 = 9
x^2+2x-8 = 9
x^2+2x-17 = 0
.
Since we can't factor, we must use the quadratic equation.
Do so will yield:
x = {3.243, -5.243}
.
Details here:
 Solved by pluggable solver: SOLVE quadratic equation with variable Quadratic equation (in our case ) has the following solutons: For these solutions to exist, the discriminant should not be a negative number. First, we need to compute the discriminant : . Discriminant d=72 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 3.24264068711928, -5.24264068711928. Here's your graph:

 logarithm/166757: 5(5)^(-0.08x)=4 please solve for x1 solutions Answer 122879 by nerdybill(6962)   on 2008-11-09 21:06:42 (Show Source): You can put this solution on YOUR website!5(5)^(-0.08x)=4 If so, start by dividing both sides by 5: (5)^(-0.08x)=4/5 (5)^(-0.08x)=.8 Take the LOG5 of both sides: -0.08x = LOG5(.8) -0.08x = LOG(.8)/LOG(5) -0.08x = -.0969/.6990 -0.08x = -.1386 x = 1.733
 logarithm/166748: 5(5)^-.08x=61 solutions Answer 122878 by nerdybill(6962)   on 2008-11-09 21:00:31 (Show Source): You can put this solution on YOUR website!Hey, this sounds familiar... . When you posted: 5(5)^-0.08x=6 I assume you mean: 5(5)^(-0.08x)=6 This means 5 is raised to the power of (-0.08x) If this is incorrect, please write back . If so, start by dividing both sides by 5: (5)^(-0.08x)=6/5 (5)^(-0.08x)=1.2 Take the LOG5 of both sides: -0.08x = LOG5(1.2) -0.08x = LOG(1.2)/LOG(5) -0.08x = .0792/.6990 -0.08x = .1133 x = -1.416
 Polygons/166749: The circumference of the circle is 30.2 cm. Find the radius.1 solutions Answer 122871 by nerdybill(6962)   on 2008-11-09 19:42:20 (Show Source): You can put this solution on YOUR website!circumference of a circle: 2(pi)r . where pi is 3.14 . 30.2 = 2(3.14)r 15.1 = 3.14r 4.81 cm = r (radius)
 Polygons/166750: The area of the circle is 547 m 2. Find the radius.1 solutions Answer 122870 by nerdybill(6962)   on 2008-11-09 19:38:58 (Show Source): You can put this solution on YOUR website!Area of any circle is: (pi)r^2 . They gave you the area as 547 and pi is 3.14. Plug and solve: 547 = (pi)r^2 547 = (3.14)r^2 174.2 = r^2 13.2 m = r (radius)
 logarithm/166740: log(x^2-x-5)= 0 I canot figure out the way to solve this. I looked at the example in my book and it was not clear. Solve for x my guess is to complete the square, but i am not sure how to do this 1 solutions Answer 122869 by nerdybill(6962)   on 2008-11-09 19:36:03 (Show Source): You can put this solution on YOUR website!log(x^2-x-5)= 0 x^2-x-5= 10^0 x^2-x-5= 1 x^2-x-6= 0 (x-3)(x+2)=0 . x = {-2, 3}
 logarithm/166741: 5(5)^-0.08x=6 Please!!! solve for x1 solutions Answer 122868 by nerdybill(6962)   on 2008-11-09 19:33:05 (Show Source): You can put this solution on YOUR website!When you posted: 5(5)^-0.08x=6 I assume you mean: 5(5)^(-0.08x)=6 . If so, start by dividing both sides by 5: (5)^(-0.08x)=6/5 (5)^(-0.08x)=1.2 Take the LOG5 of both sides: -0.08x = LOG5(1.2) -0.08x = LOG(1.2)/LOG(5) -0.08x = .0792/.6990 -0.08x = .1133 x = -1.416
 logarithm/166735: 4log(2x+6)=8 Solve for X. Please1 solutions Answer 122866 by nerdybill(6962)   on 2008-11-09 19:06:32 (Show Source): You can put this solution on YOUR website!4log(2x+6)=8 log(2x+6)=2 2x+6=10^2 2x+6=100 2x=94 x = 47
 Proportions/166699: There is a class. The ratio is 5 boys to 4 girls. There are 65 boys. How many girls are there?1 solutions Answer 122865 by nerdybill(6962)   on 2008-11-09 19:04:47 (Show Source): You can put this solution on YOUR website! There is a class. The ratio is 5 boys to 4 girls. There are 65 boys. How many girls are there? . Let g = number of girls in the class . 4:5 = g:65 or 4/5 = g/65 g = (4*65)/5 g = 260/5 g = 52 (girls in the class)
 Polynomials-and-rational-expressions/166719: how do you simplify this rational expression? (2/k-3)+ (4/k+3)= i was out sick for 3 days and i dont know how to do this.1 solutions Answer 122864 by nerdybill(6962)   on 2008-11-09 19:02:06 (Show Source): You can put this solution on YOUR website! . Common denominator is:(k-3)(k+3) .
 Mixture_Word_Problems/166734: 2/3 divided by x = 1 please help1 solutions Answer 122863 by nerdybill(6962)   on 2008-11-09 18:54:55 (Show Source): You can put this solution on YOUR website!2/3 divided by x = 1 (2/3)/x = 1 multiplying both sides by x: 2/3 = x
 Linear_Equations_And_Systems_Word_Problems/166724: Charlie owns a coffee shop. He wants to create special mixes using 2 coffees,one priced at \$6.40 per pound and the other priced at \$7.28 per pound. How many pounds of the \$7.28 coffee should he mix with 9 pounds of the \$6.40 coffee to sell the mixture for \$6.95 per pound?1 solutions Answer 122862 by nerdybill(6962)   on 2008-11-09 18:53:52 (Show Source): You can put this solution on YOUR website! Charlie owns a coffee shop. He wants to create special mixes using 2 coffees,one priced at \$6.40 per pound and the other priced at \$7.28 per pound. How many pounds of the \$7.28 coffee should he mix with 9 pounds of the \$6.40 coffee to sell the mixture for \$6.95 per pound? . Let x = pounds of \$7.28 per pound coffee added . 7.28x + 6.40(9) = 6.95(x+9) 7.28x + 57.6 = 6.95x + 62.55 0.33x + 57.6 = 62.55 0.33x = 4.95 x = 15 pounds (of \$7.28 coffee)
 Exponential-and-logarithmic-functions/166732: 3+ Log(2x+5)= 2 I have tried this problem and I am not coming up with the correct answer...can you please guide me?1 solutions Answer 122860 by nerdybill(6962)   on 2008-11-09 18:49:42 (Show Source): You can put this solution on YOUR website!3+ Log(2x+5)= 2 Log(2x+5)= -1 2x+5= 10^-1 2x+5= 1/10 20x+50= 1 20x= -49 x = -49/20 x = -2.45
 Linear_Equations_And_Systems_Word_Problems/166716: A high school sold gift wrap. The gift wrap in solid colors sold for \$4.00 per roll and the print gift wrap sold for \$6.00 per roll. The total amount of rolls sold was 480, and the total amount of money collected was \$2,340.00. How many rolls of each kind of gift wrap was sold?1 solutions Answer 122850 by nerdybill(6962)   on 2008-11-09 17:59:06 (Show Source): You can put this solution on YOUR website!A high school sold gift wrap. The gift wrap in solid colors sold for \$4.00 per roll and the print gift wrap sold for \$6.00 per roll. The total amount of rolls sold was 480, and the total amount of money collected was \$2,340.00. How many rolls of each kind of gift wrap was sold? . Let x = number of \$4 rolls sold then 480-x = number of \$6 rolls sold . 4x + 6(480-x) = 2340 4x + 2880 - 6x = 2340 2880 - 2x = 2340 2880 = 2x + 2340 540 = 2x 270 = x (\$4 rolls sold) . 480-x = 480-270 = 210 (\$6 rolls sold)
 test/166710: solve for W in the equation XW + Y = B / 4 show restrictions:1 solutions Answer 122849 by nerdybill(6962)   on 2008-11-09 17:50:25 (Show Source): You can put this solution on YOUR website!Simply isolate W to one side of the equation: XW + Y = B/4 XW = (B/4) - Y W = (B/4X) - (Y/X) . The only restriction is: Except when X=0 . Notice that if X was equal 0, the numerator would be zero and a zero in the denominator would be "undefined".
 Age_Word_Problems/166624: If Leah is 6 years older than her sister, Sue, and John is 5 years older than Leah, and the total of their ages is 41. Then how old is Sue? 1 solutions Answer 122800 by nerdybill(6962)   on 2008-11-09 11:06:42 (Show Source): You can put this solution on YOUR website! If Leah is 6 years older than her sister, Sue, and John is 5 years older than Leah, and the total of their ages is 41. Then how old is Sue? . Let x = Sue's age then x+6 = Leah's age x+6+5 = John's age . x + x+6 + x+6+5 = 41 3x + 17 = 41 3x = 24 x = 8 years (Sue's age)
 Polynomials-and-rational-expressions/166619: Please help me solve this question: (x+2)/(x-6) less than or equal to 41 solutions Answer 122799 by nerdybill(6962)   on 2008-11-09 11:04:24 (Show Source): You can put this solution on YOUR website! Multiplying both sides by (x-6):
 Percentage-and-ratio-word-problems/166606: The Krunch Cereal Co. changed the size of its box. The old box was 3 by 8 by 10. The new box is 4 by 8 by 12. Find the percent of change in the volume of the box.1 solutions Answer 122795 by nerdybill(6962)   on 2008-11-09 09:48:25 (Show Source): You can put this solution on YOUR website! The Krunch Cereal Co. changed the size of its box. The old box was 3 by 8 by 10. The new box is 4 by 8 by 12. Find the percent of change in the volume of the box. . Old box volume: 3*8*10 = 240 . New box volume: 4*8*12 = 384 . Volume change: 384/240 * 100 = 160%
 Rational-functions/166613: Please help with: For f(x)=-2x^5+3x^4-6x^2+1, what does Descartes rule of signs tell you about: (a) the number of positive real zeros? (b) the number of negative real zeros? Thank you. 1 solutions Answer 122794 by nerdybill(6962)   on 2008-11-09 09:41:21 (Show Source): You can put this solution on YOUR website!Refer to this site for a good explanation: http://www.purplemath.com/modules/drofsign.htm . f(x)=-2x^5+3x^4-6x^2+1 There are three sign changes. So, 3 or 1 positive roots . f(-x)=-2(-x)^5+3(-x)^4-6(-x)^2+1 f(-x)=2(x)^5+3(x)^4-6(x)^2+1 There are two sign changes. So, 2 or 0 negative roots .
 Quadratic_Equations/166604: Write the equation of a quadratic that has zeros of 5 and 1 with F(0)=1. I understand you need to multiply (x-5)(x-1) to get the polynomial, but f(0) wouldnt equal 1. PLEASE HELP ME OUT!!!1 solutions Answer 122788 by nerdybill(6962)   on 2008-11-09 08:44:33 (Show Source): You can put this solution on YOUR website!As you say: (x-5)(x-1) x^2 - x - 5x + 5 x^2 - 6x + 5 . So, F(x) = x^2 - 6x + 5 . F(1) = 1^2 - 6(1) + 5 F(1) = 1 - 6 + 5 F(1) = 0 .
 Linear-systems/166603: A credit manager rates each applicant for a car loan on a scale of 1 through 5 and then determines the interest rate from the accompanying table FIND THE EQUATION of the linear in slope-intercept form that goes through these points: (1,24)(2,20)(3,16)(4,12)(5,8)1 solutions Answer 122786 by nerdybill(6962)   on 2008-11-09 08:41:34 (Show Source): You can put this solution on YOUR website!. Slope between two points, can be found by: m = (y2-y1)/(x2-x1) . We can pick any two points but we'll pick 1 and 2 to determine the slope: m = (y2-y1)/(x2-x1) m = (20-24)/(2-1) m = (-4)/(1) m = -4 . Now, we can plug any point, say (5,8), and the slope (-4) and plug it into the "point-slope" form: y-y1 = m(x-x1) y-8 = -4(x-5) y-8 = -4x + 20 y = -4x + 28 (this is what they're looking for)
 Travel_Word_Problems/166586: The equations S =5000 + 200x and D =9500 - 100x express the supply S and the demand D, respectively, for a popular music in terms of its price x (in dollars).1 solutions Answer 122784 by nerdybill(6962)   on 2008-11-09 08:32:02 (Show Source): You can put this solution on YOUR website!You don't say what the problem is asking for, but I suspect they want to know the amount (x) when supply equals demand. . If so, set the two given equations equal to each other and solve for 'x': 5000 + 200x = 9500 - 100x 5000 + 300x = 9500 300x = 4500 x = \$15
 Polynomials-and-rational-expressions/166602: Please help me with the following: Use long division to find the quotient Q(x) and the remainder R(x) when P(x) is divided by d(x). P(x)=x^4+2x^3-2x+4 d(x)=x-2 Thank you.1 solutions Answer 122783 by nerdybill(6962)   on 2008-11-09 08:15:35 (Show Source): You can put this solution on YOUR website!Use long division to find the quotient Q(x) and the remainder R(x) when P(x) is divided by d(x). P(x)=x^4+2x^3-2x+4 d(x)=x-2 . NOTE: it will be easier to see the solution (because of the spacing) below if you view the "source"! . x^3+5x^2+2x+2 _______________ x-2 |x^4+2x^3+0x^2-2x+4 x^4-3x^3 --------- 5x^3+0x^2-2x+4 5x^3-2x^2 -------------- 2x^2-2x+4 2x^2-4x --------- 2x+4 2x-4 ---- 8 . Therefore: Q(x) = x^3+5x^2+2x+2 R(x) = 8/(x^4+2x^3+0x^2-2x+4)
 Travel_Word_Problems/166580: fran swims at a speed of 2.2 km/h in still water. the lazy river flows at a speed of 0.4 km/h. how long will it take fran to swim 0.9 km upstream?1 solutions Answer 122781 by nerdybill(6962)   on 2008-11-09 08:07:33 (Show Source): You can put this solution on YOUR website! fran swims at a speed of 2.2 km/h in still water. the lazy river flows at a speed of 0.4 km/h. how long will it take fran to swim 0.9 km upstream? . We will need to apply the "distance" formula: d = rt where d is distance r is rate or speed t is time . Reordering the equation, we solve for 't': t = d/r . Fran's rate (r) is: 2.2 - 0.4 = 1.8 km/h . Therefore: .9/1.8 = 0.5 hours
 Money_Word_Problems/166582: Rental Company A charges \$12.00 plus 80 cents per hour to rent a paint sprayer. A competitor, Rental company B rents the same sprayer for \$3.95 plus \$1.50 per hour. Write an algebraic equation for the cost in terms of the number of hours rented for each business. Determine algebraically the number of hours for which the cost of renting a paint sprayer will be the same for company A or B.1 solutions Answer 122767 by nerdybill(6962)   on 2008-11-08 22:30:24 (Show Source): You can put this solution on YOUR website!Rental Company A charges \$12.00 plus 80 cents per hour to rent a paint sprayer. A competitor, Rental company B rents the same sprayer for \$3.95 plus \$1.50 per hour. Write an algebraic equation for the cost in terms of the number of hours rented for each business. Determine algebraically the number of hours for which the cost of renting a paint sprayer will be the same for company A or B . Let h = number of hours rented . Company A: C(h) = 12 + .80h . Company B: C(h) = 3.95 + 1.50h . To find out when the cost will be the same, set it equal to each other and solve for 'h': 12 + .80h = 3.95 + 1.50h 12 = 3.95 + .70h 8.05 = .70h 11.5 hours = h
 Travel_Word_Problems/166563: PLEASE HELP ME ANSWER THIS PROBLEM: If a car travelling 60 mph can stop in 200ft,how far will it take a car to stop if it is travelling at 50 mph?1 solutions Answer 122760 by nerdybill(6962)   on 2008-11-08 20:39:03 (Show Source): You can put this solution on YOUR website!You can find your answer at: http://www.csgnetwork.com/stopdistcalc.html
Geometry_Word_Problems/166560: Hey, I just need help with two word problems.
1st one: A lot is in the shape of a right triangle. The shorter leg measures 180 m. The hypotenuse is 60 m longer than the length of the longer leg. How long is the longer leg??
2nd one: A rectangular piece of cardboard measuring 28 inches by 29 inches is to be made into a box with an open top by cutting equal size squares from each corner and folding up the sides. Let x represent the length of a side of each such square. For what value of x will the volume be a maximum? If necessary, round to 2 decimal places.
Thank u
1 solutions

Answer 122757 by nerdybill(6962)   on 2008-11-08 19:53:54 (Show Source):
You can put this solution on YOUR website!
1st one: A lot is in the shape of a right triangle. The shorter leg measures 180 m. The hypotenuse is 60 m longer than the length of the longer leg. How long is the longer leg??
.
Let x = length of longer leg
then
x+60 = hypotenuse
.
Applying pythagorean's theorem:
180^2 + x^2 = (x+60)^2
180^2 + x^2 = (x+60)^2
32400 + x^2 = x^2 + 120x + 3600
32400 = 120x + 3600
28800 = 120x
240 meters = x (longer leg)
.
2nd one: A rectangular piece of cardboard measuring 28 inches by 29 inches is to be made into a box with an open top by cutting equal size squares from each corner and folding up the sides. Let x represent the length of a side of each such square. For what value of x will the volume be a maximum? If necessary, round to 2 decimal places.
.
Volume = x(28-2x)(29-2x)
Volume = x(812-56x-58x+4x^2)
Volume = x(812-114x+4x^2)
Volume = 812x-114x^2+4x^3
Volume = 4x^3-114x^2+812x
.
Taking the derivative:
4x^3-114x^2+812x
12x^2-228x+812 = 0
6x^2-114x+406 = 0
Solving the above with the quadratic equation we get:
x = {14.25, 4.75}
.
Solution: 4.75 inches
.