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# Recent problems solved by 'chriswen'

 Linear-systems/658154: After your 528 mile trip to Escondido you fill your car with gas. The car was full of gas when you left home. It takes 16 gallons top fill your car in Escondido. What gas mileage did you get on the trip?1 solutions Answer 410185 by chriswen(106)   on 2012-09-27 16:40:21 (Show Source): You can put this solution on YOUR website!Your gas tank was full when you left the town. Now it needs 16 gallons to fill up. That means you used 16 gallons during the trip. You also drove for 528 miles during that time. Gas mileage = miles / gas used = 528 / 16 = 33 Your gas mileage is 33 miles per gallon.
 Numbers_Word_Problems/658152: one number is 6 more than twice a second number. Their sum is 54. How do I find the numbers?1 solutions Answer 410184 by chriswen(106)   on 2012-09-27 16:36:45 (Show Source): You can put this solution on YOUR website!let x be the first number let 54-x be the second number (second statement) x - 6 = 2(54-x) x - 6 = 108 - 2x 3x = 114 x = 38 54-x=16 The first number is 38 and the second number is 16.
 Money_Word_Problems/658151: Teresa makes an investment at % simple interest. At the end of 1 year, the total value of the investment is . How much did she originally invest?1 solutions Answer 410182 by chriswen(106)   on 2012-09-27 16:30:39 (Show Source): You can put this solution on YOUR website!So you have no numbers. I'm assuming you're using variables then. Let x be the yearly interest rate. Let \$y be the investment after 1 year. This is the equation for simple interest for 1 year. Original Investment*(1+x)=y So if you have y and want to know the original investment, Original Investment = y/(1+x)
 absolute-value/658150: My problem is Absolute Value Equations- Variables on Both Sides.I don't know how to solve the equation. Here is my problem: |x-2|=3x+1. -Thank You 1 solutions Answer 410180 by chriswen(106)   on 2012-09-27 16:27:03 (Show Source): You can put this solution on YOUR website!|x-2|=3x+1 The first stop of finding absolute value functions is by finding the breakpoints. This is when the function changes in normal terms. The break point is basically just the zero of the absolute function. x-2=0 x=2 The breakpoint is at 2. So when x is greater than 2, |x-2| will behave just like x-2. But, when x-2 is less than 2, |x-2| will behave like -(x-2). SO, to the solving part. CASE 1: (Assume x is greater or equal to 2) x-2 = 3x + 1 -3 = 2x x = -3/2 This doesn't follow with our assumption. We can conclude that x isn't >= 2. CASE 2: (Assume x is less than 2) -(x-2) = 3x + 1 -x + 2 = 3x + 1 1 = 4x x = 1/4 This agrees with our assumption. After studying both cases we can conclude that x is equal to 1/4.
 Radicals/657754: given: f(x)= 4x^2/x^2-9 a)find the vertical asymptote if any b) find the vertical asymptote if any 1 solutions Answer 409992 by chriswen(106)   on 2012-09-26 21:40:17 (Show Source): You can put this solution on YOUR website!f(x) = 4x^2/x^2-9 I'm assuming you're asking for Vertical and Horizontal asymptote. The Vertical Asymptote occurs when the denominator is equal to zero. x^2-9=0 (x+3)(x-3)=0 x= 3, -3 So the vertical Asymptotes occur at x=3 and x=-3. To find the asymptote the method I learned was to divide the top and bottom by 1/x^2. You divide top and bottom by 1/x^n(highest power in numerator).This is basically multiplying by 1 but it helps you out. (4x^2/x^2)/(x^2/x^2 - 9/x^2) =4/(1-9/x^2) Now we take the limit of the as x-> infinity and negative infinity. This will mean that 9/x^2 becomes practically zero. so we get 4/1 or 4. The graph will approach 4 when the x values approach positive or negative infinity. This means the horizontal Asymptote is at y=4.
Equations/657728: how to find the value of y?
4^y+4^(2*y+1)=1

1 solutions

Answer 409991 by chriswen(106)   on 2012-09-26 21:25:17 (Show Source):
You can put this solution on YOUR website!
4^y+4^(2*y+1)=1
Simplify the question by making a substitution.
Let x = 4^y

 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=17 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 0.390388203202208, -0.640388203202208. Here's your graph:

0.390388203202208, -0.640388203202208
sub into x = 4^y
logx = ylog4
y = logx/log4
y1 = -0.6785
y2 = invalid (can't log negative numbers)
The answer is approximately -0.6785. If you want exact formula you'll need to use the quadratic formula to solve and leave in exact numbers.

 test/657732: X^2-6x+9/x^2-91 solutions Answer 409990 by chriswen(106)   on 2012-09-26 21:08:46 (Show Source): You can put this solution on YOUR website!(x^2 - 6x + 9) / (x^2 - 9) factor =(x-3)(x-3)/(x-3)(x+3) FYI a^2 - b^2 = (a+b)(a-b) cancel out (x-3) =(x-3)/(x+3) I think that is fully simplified. You might also have to say that x can not equal positive or negative 3.
 Expressions-with-variables/657727: What is the elimination method for 3x-5y=30 and 5x+7y=41 solutions Answer 409989 by chriswen(106)   on 2012-09-26 21:05:54 (Show Source): You can put this solution on YOUR website!Okay for elimination we need to eliminate something. I'll choose to eliminate x. I need both x's to be equal. So I'll multiply the first equation by 5 and the second equation by 3. 3x-5y=30 ... (i) 15x - 25y = 150 ... (iii) 5x + 7y = 4 ... (ii) 15x + 21y = 12 ... (iv) Now eliminate. I will subtract equation 4 from equation 3. 15x - 25y = 150 -)15x+21y = 12 ________________ 0x -46y = 138 y = -138/46 y = 3 now I will sub y = 3 into equation 1. 3x - 5(3) = 30 3x - 15 = 30 3x = 45 x = 45/3 x = 15 Therefore, x = 15, y = 3. This was solved via elimination method.
 Equations/657724: Solve for x y=w/x-21 solutions Answer 409987 by chriswen(106)   on 2012-09-26 20:57:00 (Show Source): You can put this solution on YOUR website!I'm assuming you mean solve for x in terms of y and w. y = w/x - 2 Add two on both sides y + 2 = w / x Multiply both sides by x x ( y + 2 ) = w Divide both sides by y + 2 x = w / (y + 2)
 Surface-area/657717: The length and width of a rectangular swimming pool are each doubled, while the depth remains the same. Which is true? a) it takes twice as much paint to paint the bottom b) it takes twice as much paint to paint the four walls c) it takes twice as much water to fill the pool d) all of the above e) none of the above 1 solutions Answer 409985 by chriswen(106)   on 2012-09-26 20:48:53 (Show Source): You can put this solution on YOUR website!Lets say the original pool is l*w*h. New pool is 2l*2w*h a) the SA of bottom is the length times width. Original Pool = l*w New pool = 2l*2w = 4*l*w FALSE b) 4 walls is length times base times two. Added with width times base times two. ORiginal Pool = l*b*2 + w*b*2 New Pool = 2l*b*2 + 2w*b*2 = 2(l*b*2 + w*b*2) TRUE c) Area of pool is length times width times base. Original Pool = l*w*b New Pool = 2l*2w*b = 4*l*w*b FALSE The correct answer is b)
 Polynomials-and-rational-expressions/448682: for what values of m is the expression m2-2m+1/2m2+m-3 undefined? 1 solutions Answer 308739 by chriswen(106)   on 2011-05-12 19:08:29 (Show Source): You can put this solution on YOUR website!The expression is undefined if the bottom of denominator is 0 as you can't /0. So, we want to see when the bottom is 0. ... or or Therefore, if m is equal to 1 or -3/2 than the expression is undefined.
Quadratic_Equations/448678: The length of the table top is 5m greater than the width. The area is 66m2. Find the Dimensions of the table top
1 solutions

Answer 308736 by chriswen(106)   on 2011-05-12 19:02:07 (Show Source):
You can put this solution on YOUR website!
Let x m be the width of the table top.
Let x+5 m be the length of the table top.
...
A=l*w
66=(x)(x+5)
66=x^2+5x
0=x^2+5x-66
 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=289 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 6, -11. Here's your graph:

The answer must be positive so,
x=6
x+5=11
...
Therefore, the dimensions of the table top is 6m by 11m.

Equations/448721: m2-5m=0
1 solutions

Answer 308729 by chriswen(106)   on 2011-05-12 18:54:41 (Show Source):
You can put this solution on YOUR website!
 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=25 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 5, 0. Here's your graph:

 logarithm/447643: Express in terms of logarithms of a,b, and c: log (a^1/3 b^1/2) / c 1 solutions Answer 308149 by chriswen(106)   on 2011-05-10 17:20:44 (Show Source): You can put this solution on YOUR website!log (a^1/3 b^1/2) /c = log (a^1/3 b^1/2) - log c = log a^1/3 + log b^1/2 - log c = 1/3*log a + 1/2*log b - log c
1 solutions

Answer 307896 by chriswen(106)   on 2011-05-09 18:44:12 (Show Source):
You can put this solution on YOUR website!
x^2+14x+40=-5
x^2+14x+40+5=0
x^2+14x+45=0
 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=16 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: -5, -9. Here's your graph:

 Systems-of-equations/447133: During the 1998-1999 Little League season, the Tigers played 52 games. They won 12 more games than they lost. How many games did they win that season? I figured if you divided 52 by 2 and you get 26 then add 12 then you get the answer of 38 but not sure how to put it into an equation . Or am I even close ? 1 solutions Answer 307865 by chriswen(106)   on 2011-05-09 17:06:23 (Show Source): You can put this solution on YOUR website!Let x be the number of games they won. Let x-12 be the number of games they lost. ... x+x-12=52 2x-12=52 2x=52+12 2x=64 x=32 Therefore, the Tigers won 32 games that season.
 logarithm/447134: Solve: logx 216=31 solutions Answer 307860 by chriswen(106)   on 2011-05-09 16:59:40 (Show Source): You can put this solution on YOUR website!You mean log root x logx 216 = 3 x^3 = 216 x = +- 6
1 solutions

Answer 307855 by chriswen(106)   on 2011-05-09 16:44:01 (Show Source):
You can put this solution on YOUR website!
n(n+5)=-4
n^2+5n=-4
n^2+5n+4=0
 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=9 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: -1, -4. Here's your graph:

Therefore n = -1 or -4.
3n^2= 3 or 48

Equations/447105: x^2+3x+2=0
1 solutions

Answer 307846 by chriswen(106)   on 2011-05-09 16:02:38 (Show Source):
You can put this solution on YOUR website!
 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=1 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: -1, -2. Here's your graph:

Expressions-with-variables/447077: The length of a rectangle is one foot less then three times the width. Find the length and width of the area is 30 square feet
1 solutions

Answer 307844 by chriswen(106)   on 2011-05-09 16:01:30 (Show Source):
You can put this solution on YOUR website!
Let x ft be the width of the rectangle.
Let 3x-1 ft be the length of the rectangle.
...
l*w=A
(3x-1)(x)=30
3x^2-x=30
3x^2-x-30=0
 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=361 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 3.33333333333333, -3. Here's your graph:

x must be positive.
x=3.33
3x-1=9
Therefore, the rectangle is 3.33 ft by 9 ft.

 Rectangles/447042: A rectangle has a 200 meter perimeter, and its length is 8 times its width. What are the dimensions of the rectangle?1 solutions Answer 307841 by chriswen(106)   on 2011-05-09 15:53:29 (Show Source): You can put this solution on YOUR website!Let x m be the width of the rectangle. Let 8x m be the length of the rectangle. ... P=2(l+w) 200=2(8x+x) 100=9x x=100/9 x=11.1 8x=88.9 Therefore the dimensions of the rectangle are 11.1 m by 88.9 m.
 Polynomials-and-rational-expressions/447096: Solve the equation by factoring. 49w(w)-25=0 (w is squared)1 solutions Answer 307838 by chriswen(106)   on 2011-05-09 15:49:04 (Show Source): You can put this solution on YOUR website! ... difference of squares or or
Pythagorean-theorem/447083: A water pipe runs diagonally under a rectangular garden that is 7 feet longer then it is wide. If the pipe is 13 feet long, what are the dimensions of the garden
1 solutions

Answer 307835 by chriswen(106)   on 2011-05-09 15:45:39 (Show Source):
You can put this solution on YOUR website!
Let x ft be the width of the garden.
Let x+7 ft be the length of the garden.
...
... Pythagorean theorem

 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=289 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 5, -12. Here's your graph:

x must be positive.
x=5
x+7=12
Therefore, the dimensions of the garden is 5 ft by 12 ft.

 Surface-area/447036: Find the area of a parallelogram if a base and corresponding altitude have the indicated lengths. Base 1 feet, altitude 6 inches. 1 solutions Answer 307829 by chriswen(106)   on 2011-05-09 15:38:31 (Show Source): You can put this solution on YOUR website!A=b*h A=12*6 A=72 Therefore the area of the parallelogram is 72 inches squared.
 Exponential-and-logarithmic-functions/446792: I need help solving this problem: 1n (x+7) + 1n (x+3) = 1n771 solutions Answer 307726 by chriswen(106)   on 2011-05-09 06:18:53 (Show Source): You can put this solution on YOUR website!1n (x+7) + 1n (x+3) = 1n77 ln x + ln 7 + ln x + ln 3 = ln 77 ****** Problem here --------------------- 2 ln x + ln 7*3 = ln77 2 ln x = ln 77 - ln 21 ln x^2 = ln 77/21 x^2 = 77/21 x = sqrt (77/21) x = 1.915 x must be positive as you can't have negative ln.
logarithm/446837: log 3=2 with log base x-1

1 solutions

Answer 307725 by chriswen(106)   on 2011-05-09 06:08:42 (Show Source):
You can put this solution on YOUR website!
log 3=2 with log base x-1

 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=12 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 2.73205080756888, -0.732050807568877. Here's your graph:

 Complex_Numbers/446614: how do you write 3+2i/2+i in standard form1 solutions Answer 307716 by chriswen(106)   on 2011-05-09 05:47:55 (Show Source): You can put this solution on YOUR website!Division of complex numbers is if you need more info or proof search complex numbers on Wikipedia. ... = =
Quadratic_Equations/446744: for the following equation, state the value of the discriminant and then describve the nature of the solution -8x^2+5x+13=0
1 solutions

Answer 307639 by chriswen(106)   on 2011-05-08 21:07:05 (Show Source):
You can put this solution on YOUR website!
 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=441 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: -1, 1.625. Here's your graph:

 Exponents/446720: How do you solve this problem for the variable a? 36 to the a equals 216 to the 2a + 3?1 solutions Answer 307630 by chriswen(106)   on 2011-05-08 20:43:28 (Show Source): You can put this solution on YOUR website!Convert them both to the same base. ... Therefore, since, therefore gloop=junk.
 Problems-with-consecutive-odd-even-integers/446717: The product of two consecutive positive integers is 62 more than the third consecutive integer. What is the largest of the three integers? a. 5 b. 8 c. 6 d. 10 Please show me the work so I understand it. Thank you.1 solutions Answer 307625 by chriswen(106)   on 2011-05-08 20:31:14 (Show Source): You can put this solution on YOUR website!Let x be the first integer. Let x+1 be the second integer. Let x+2 be the third integer. ... (x)(x+1)=x+2+62 x^2+x=x+2+62 x^2+x-x-64=0 x^2-64=0 x^2-(8)^2=0 (x+8)(x-8)=0 x=-8 or x=8 x+2= -6 or 10 ... x=10 as that is the the forth choice d.
 Linear_Equations_And_Systems_Word_Problems/446700: Please Help!!! The difference if two numbers is 4. The larger number is 5 less than four times the smaller number. Find the two numbers?1 solutions Answer 307621 by chriswen(106)   on 2011-05-08 20:22:08 (Show Source): You can put this solution on YOUR website!Let x be the smaller number. Let x+4 be the larger number. ... (x+4)+5=4x x+4+5=4x 9=4x-x 9=3x x=9/3 x=3 x+4=7 Therefore, the two numbers are 3 and 7.