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# Recent problems solved by 'jcmtnez'

 Square-cubic-other-roots/46492: can you simplify 5 divided by 4+the square root of 61 solutions Answer 30821 by jcmtnez(53)   on 2006-07-18 22:44:23 (Show Source): You can put this solution on YOUR website!No you can simplify but you can remove de root from the denominator That if you want to delete the root from the denominator it is the same. Good Luck, glad to help you
 Rational-functions/46497: find a polynomial with leading coefficient 1 and degree 3 that has 1,1,and 3 as roots.1 solutions Answer 30820 by jcmtnez(53)   on 2006-07-18 22:37:22 (Show Source): You can put this solution on YOUR website!That polynomial can be expressed as: (x-1)(x-1)(x-3) Now we have to expand this expression (x-1)(x-1)(x-3)=(x^2-2x+1)(x-3)=x^3-2x^2+x-3x^2+6x-3=x^3-5x^2+7x-3 So the polynomial of degree three that have the solution (1,1,3) is x^3-5x^2+7x-3 I'm glad to help you anytime
 Polynomials-and-rational-expressions/38672: Subtract. Write the difference as a complex number in standard form. (-2 -6i) - (6 - i)1 solutions Answer 24225 by jcmtnez(53)   on 2006-05-20 20:26:11 (Show Source): You can put this solution on YOUR website!We substarct the real numbers and the complex number apart: (-2 -6i) - (6 - i) =( -8 -5i)
 Graphs/38678: Express the interval as an inequality in the variable x. (-4.-1)1 solutions Answer 24224 by jcmtnez(53)   on 2006-05-20 20:09:51 (Show Source): You can put this solution on YOUR website!It is an open interval. Then we have to use the following simbols >to expres greatter than, and< to express less than. Then:
 logarithm/38684: Expand using properties of logarithms: log (xy^2) ------ (Y)1 solutions Answer 24223 by jcmtnez(53)   on 2006-05-20 20:00:57 (Show Source): You can put this solution on YOUR website!The logarithm of a product of two number is the sum of the logarithms of both numbers: log(xy)=log(x)+log(y) and otherwise(similary): log(x/y)=log(x)-log(y) Then: log(xy^2)=log(x)+log(y^2) log(xy^2)/log(y)=log(x)+log(y^2)-log(y)
 Rational-functions/38634: This question is from textbook college algebra Write the point -slope form of the line with slope 5 containing the point (3, -2).1 solutions Answer 24187 by jcmtnez(53)   on 2006-05-20 13:10:30 (Show Source): You can put this solution on YOUR website!The slope form is: y=mx+b m is the slope and b is the y-intercept. From the data we know that when x=3, y=-2 Then: -2=3m+b If the slope if five we have: -2=3(5)+b -2=15+b -17=b Finally we get the slope form of the line as follow:
 Rational-functions/38635: This question is from textbook college algebra True of false: A function f is decreasing on an open interval I, if for any choice of x1, and x2 in I, with x1 < x2, we have f(x1) > f(x2).1 solutions Answer 24185 by jcmtnez(53)   on 2006-05-20 12:58:49 (Show Source): You can put this solution on YOUR website!True
 Length-and-distance/38636: The sound of thunder travels away from a lightning flash at 331m/s. Joe sees a lightning flash, & then hears the thunder 12 seconds later. Howfar away is Joe from the lightning flash?1 solutions Answer 24184 by jcmtnez(53)   on 2006-05-20 12:57:16 (Show Source): You can put this solution on YOUR website!Data: v = 331m/s speed of sound t = 12 second time take by the sound to arrive to Joe d = x distance from Joe to the lightning flash. Above we have the data that will be used to find the distance. Formula: This is the formula to find the distance given the speed and the time. Using the data we have: Answer: The lightning flash is 3972 meters away from Joe.
 Angles/37726: The measure of the supplement of an angle is 15 degrees less than four times the measure of the complement. Find the measure of the angle.1 solutions Answer 23303 by jcmtnez(53)   on 2006-05-14 17:43:18 (Show Source): You can put this solution on YOUR website!Let call the angle X Its complement will be 90-x Its supplement will be 180-x (180-x)+15 = 4(90-x) 180-x+15 = 360-4x 4x-x = 360-180-15 3x = 165 x = 55 Prove The complement of 55 is 35 And the supplement of 55 is 125 Now we must see if the relation stated holds 125+15 = 4(35) 125+15 = 140 The measure of the supplement of an angle is 15 degrees less than four times the measure of the complement. 140 = 140 Therefore the solution of the problem is given by an angle of 55 degrees.
 Miscellaneous_Word_Problems/37750: The width of a rectangle is one-fourth the length. The perimeter of the rectangle is one hundred thirty feet. What is the width of the rectangle?1 solutions Answer 23301 by jcmtnez(53)   on 2006-05-14 17:29:09 (Show Source): You can put this solution on YOUR website!Perimeter P=130 feet Width w=x Length l=4x Perimeter P=2(w+l) Applying the fromula P = 2(x+4x) P = 2(5x) P = 10x 130 = 10x 130/10 = x 13 = x ,therfore the width is 13 feet
 Numeric_Fractions/37544: How do I multiply and write the result in simplest form of 2 over 9 . 4 over 5? 1 solutions Answer 23170 by jcmtnez(53)   on 2006-05-12 18:31:44 (Show Source): You can put this solution on YOUR website! 2/4=1/2 Dived by the common divisor or commmon factor. 4/5 Can not be simplified because 4 and 5 have not common factors.
 logarithm/37531: the natural base e is also referred to as the ________ number.1 solutions Answer 23169 by jcmtnez(53)   on 2006-05-12 18:29:15 (Show Source): You can put this solution on YOUR website!Is also referred as the Euler's number.
 Polynomials-and-rational-expressions/37552: If the first side of a triangle is 3/4x, the second side is 1/x^2 and the third side is 5/x^2, find an expression that represents its perimeter.1 solutions Answer 23168 by jcmtnez(53)   on 2006-05-12 18:26:55 (Show Source): You can put this solution on YOUR website!The perimeter is describe as the sum of the measures of all sides in a geometrical figure. Then:
 Signed-numbers/37300: 8.38 x 10^7 feet - 5.84 x 10^7 feet 1 solutions Answer 22963 by jcmtnez(53)   on 2006-05-10 22:33:54 (Show Source): You can put this solution on YOUR website!8.38 x 10^7 feet - 5.84 x 10^7 feet = 2.54 x 10^7 feet Explanation: If the exponent of ten are equals(in this case 7) we only have to substract the coefficients. Generally: With the sums is the same: With multiplication and division change a little: For multiplication For division
 Inverses/37297: This question is from textbook Intermediate Algebra the question is the sum of a number and 6 times it's receiprocal is -5. How do I solve this?1 solutions Answer 22962 by jcmtnez(53)   on 2006-05-10 22:24:39 (Show Source): You can put this solution on YOUR website!Given a number x, the reciprocal of x is 1/x. 6 times the reciprocal of x, is 6/x and the problem says that the sum of x and its reciprocal is equal to -5,then: x+6/x=-5 Now we have to eliminate the denominator by multiplying the entire expression by x x(x)+x(6/x)=x(-5) x^2+6=-5x x^2+5x+6=0 Now we have to solve the equation to solve the problem and find the solutions. The solution is given using the general formula for quadratic equations: Solutions: x1=-2,x2=-3 We have to solutions and therefore two pair of number for which the stated condition hold. Those numbers are: -2 and -1/2 , -3 and -1/3 Proof: -2+6(-1/2) = -2-3=-5 -3+6(-1/3) = -3-2=-5 Then the solutions are true. Any doubt?:)
 Exponential-and-logarithmic-functions/37295: Expand each logarithmic expression as much as possible: log sub b (x^3y/z^2) I've been trying to work at this and another all day but can't figure it out to save my algebra butt. final is tomorrow and she said to expect ones like this. Any help would be just so wonderful.1 solutions Answer 22961 by jcmtnez(53)   on 2006-05-10 22:16:25 (Show Source): You can put this solution on YOUR website! log (x^3y/z^2) = 3log(x)+log(y)-2log(z) Explanation The logarithm of the product of two number is equal to the sum of the logarithm of each number. log(xy)=log(x)+log(y) The logarithm of the division of two numbers is equal to the substraction of the logarithm of each number. log(x/y)=log(x)-log(y) Remember that the base does not change. You may use this properties to solve any problem like the above.
 logarithm/37289: use the properties of logarithms to expand the following expressions: 1) log(base10)7x^4 2) log(base7)x^1/2 / x 3) ln 3xy^21 solutions Answer 22960 by jcmtnez(53)   on 2006-05-10 22:11:27 (Show Source): You can put this solution on YOUR website!Solution 1) log(base10)7x^4 log(7)+4log(x), remember log in base 10 2) log(base7)x^1/2 / x 1/2log(x)-log(x), know in base 7 3) ln 3xy^2 Ln(3)+Ln(x)+2Ln(y), I suppose that this is in base e
 logarithm/37287: use the properties of logarithms to condense the following expression: 1) 3 ln x + 2 ln (x+1)1 solutions Answer 22959 by jcmtnez(53)   on 2006-05-10 22:05:37 (Show Source): You can put this solution on YOUR website! 3 ln x + 2 ln (x+1) = ln x^3+ln(x+1)^2 = ln (x^3(x+1)^2 If you need something more please let me know.
 Systems-of-equations/37232: This question is from textbook solve the following systems of equation x-y=3 2x-y=-11 solutions Answer 22915 by jcmtnez(53)   on 2006-05-10 19:54:02 (Show Source): You can put this solution on YOUR website!We can solve this system by substitution: x-y=3, From this equation we get x=3+y 2x-y=-1, Substituting in the second equation we get 2(3+y)-y=-1, solving 6+2y-y=-1, y=-1-6, y=-7, And replacing the obtained value in the equation x=3+y, we obtain x=3+(-7), x=-4 The solutions to the system are x=-4, y=-7.
 Systems-of-equations/37235: This question is from textbook 2x+4y=10 3x-2y=-91 solutions Answer 22914 by jcmtnez(53)   on 2006-05-10 19:46:57 (Show Source): You can put this solution on YOUR website!System. 2x+4y=10 3x-2y=-9 We can easily solve this system by reduction: 2x+4y=10 2(3x-2y)=2(-9) We multiply the second equation by two getting a similar equation. 2x+4y=10 6x-4y=-18 We have the same system, now we only have to sum the corresponding parts. 2x+4y=10 +6x-4y=-18 Result:8x =-8 Solving for x, 8x=-8, x=-1 Substitution of x by its value, 2(-1)+4y=10 -2+4y=10 4y=12 y=3 The solutions to the system are, x=-1 and y=3
 Linear_Equations_And_Systems_Word_Problems/37227: The sum of two consectutive positive integers is 11 less than their product. find the integers.1 solutions Answer 22911 by jcmtnez(53)   on 2006-05-10 19:37:05 (Show Source): You can put this solution on YOUR website!Let call those integers x and y, if they are consecutives y=x+1. x+(x+1)=x(x+1)-11 The sum of two consectutive positive integers is 11 less than their product. 2x+1=x^2+x-11 0=x^2-x-12 Using the general formula for solving quadratic equations we get x1=4,x2=-3 Then if the integers are positive they are 4 and 5, 4+5=9, 4*5=20, 20-9=11, And if they are negative they are -3 and -2, -3+(-2)=-5, -3*(-2)=6, 6-(-5)=11.
 Graphs/37228: Where on the graph of 3x-y = 12 are the x and y coordinates opposites of each other? I started out by y = mx + b and changed the equation to y = 3x - 12 but i am stuck from there 1 solutions Answer 22910 by jcmtnez(53)   on 2006-05-10 19:30:58 (Show Source): You can put this solution on YOUR website!If you want a point in which the x is opposite to y the point is (x,-x), To find such point we have to solve the equation for y=-x 3x-y = 12, y=3x-12, (-3)=3x-12, -3+12=3x, then 9=3x, finally we get x=3 Therefore the point is (3,-3), In wich the x and the y are opposites.
 Linear_Equations_And_Systems_Word_Problems/37229: What is the value of y^3+y^3 ? is it 2y^3 or y^6?1 solutions Answer 22909 by jcmtnez(53)   on 2006-05-10 19:25:04 (Show Source): You can put this solution on YOUR website!Sum: and, Product:
 Equations/37224: SOLVE THE FOLLOWING EQUATIONS 15+20=2x+2x 6x+2x=20-4 5x-17=30x+3 3(x+2-3x)=20+2(x-2) 10(x+5-3)=5x-3 4x-10+30=4x+7x-8 5x-10+2(3+x-2x)=8x 3x-2=4(-2+3x)+201 solutions Answer 22908 by jcmtnez(53)   on 2006-05-10 19:20:51 (Show Source): You can put this solution on YOUR website!Solving 15+20=2x+2x, 35=4x, x=35/4 6x+2x=20-4, 8x=16, x=2 5x-17=30x+3, -20=25x, x=-4/5 3(x+2-3x)=20+2(x-2), 3x+6-9x=20+2x-4, -10=8x, -5/4=x 10(x+5-3)=5x-3, 10x+50-30=5x-3, 5x=-23, x=-23/5 4x-10+30=4x+7x-8, 28=7x, 4=x 5x-10+2(3+x-2x)=8x, 5x-10+6+2x-4x=8x, -4=5x, -4/5=x 3x-2=4(-2+3x)+20, 3x-2=-8+12x+20, -14=9x, x=-14/9
 Complex_Numbers/37223: 1/(x-1)- 1/(x+2)= 1/2 I've been trying to figure this problem out for a while now. Help please!1 solutions Answer 22907 by jcmtnez(53)   on 2006-05-10 19:11:21 (Show Source): You can put this solution on YOUR website!To eliminate the denominator you have to multiply all the expression by (x-1)(x-2)(2). 1(x-1)(x-2)(2)/(x-1)-1(x-1)(x-2)(2)/(x+2)=1(x-1)(x-2)(2)/2 Reducing common factors we get: 2(x-2)-2(x-1)=(x-1)(x-2) Now we have to expand and reduce. 2x-4-2x+2=x^2-2x-x+2 Expanding 0=x^2-2x-x+2x-2x+4-2 Reducing 0=x^2-3x+2 Final equation Know we have to solve this problem, you can use the general formula. You will get as solutions x=1,x=2
 Quadratic_Equations/37220: Need to solve this by using square root property: 4x^2 -48 = 0 Please help and show me how you get the answer1 solutions Answer 22906 by jcmtnez(53)   on 2006-05-10 19:04:34 (Show Source): You can put this solution on YOUR website!At first you must put the last number in the other side of the equation, so we get: 4x^2-48=0, 4x^2=48 Now we divide by 4 in both side of the equations and we get: 4x^/4=48/4, and then we get, x^2=12, now and to finish we have to get the square root of 12. And now taking out the for of the square root we get The solution of the equation.
 Linear-systems/37221: how can you interpret the solution of a system of equations by the corresponding graph? 1 solutions Answer 22905 by jcmtnez(53)   on 2006-05-10 18:56:59 (Show Source): You can put this solution on YOUR website!You can see the solution of the system when both equation have a common point in the graph. If they do not have a common point, I mean that if they are parallel, then the system do not have any solution. If both graph of the equations are the same then the system have infinite solution. A system with one solution: You can see the solutions in the graph, x=-1,and y=-3. A system without any solution: As you see in this system both lines are parallel, then they do not have any solution. A system with infinite solutions: In this system the graph of both equations is the same and therefore there are infinite solutions, for every point on the line.
 Equations/37164: This question is from textbook mathematics solve x2-5x+6more than 21 solutions Answer 22871 by jcmtnez(53)   on 2006-05-10 15:49:55 (Show Source): You can put this solution on YOUR website!x^2-5x+6>2 Is the same as x^2-5x+4>0 Applying the general formula: We get the solution x=1,x=4. Therefore the solution is the union of two intervals minus the values for which the equation is equal to cero (-inf,1)U(4,+inf)-(1,4)
 Quadratic_Equations/37169: This question is from textbook Algebra 1 Factor. Check by using FOIL or the distributive property. m^3 + 6m^2 + 9m and then a question not from the book, b^2-6b-10, factor this one also please.1 solutions Answer 22867 by jcmtnez(53)   on 2006-05-10 15:40:34 (Show Source): You can put this solution on YOUR website!(1) Here is the first m^3+6m^2+9m=0 , This polynomial of degree 3 is divisible by m, therefore we divede by m and get: m(m^2+6m+9)=0 Now we have to solve the polynomial of degree two, and the solution is m=-3, and is unique. Finally we get m(m+3)(m+3) As the factorization of m^3 + 6m^2 + 9m (2) Here is the second b^2-6b-10=0, First have to solve the equation, find the roots, we can do this using the general formula or using more advance methods. Using the formula we get as a result b=3+sqrt(19), and b=3-sqrt(19). Then the factors will be (b-(3-sqrt(19))(b-(3+(sqrt(19))
 Average/37161: An automobile travels 10km at a speed of 100kph, 40km at 80kph and a 3rd diatance at 50kph. If the average velocity for the trip is 70kph, what is the length of the 3rd distance travelled?1 solutions Answer 22844 by jcmtnez(53)   on 2006-05-10 14:42:22 (Show Source): You can put this solution on YOUR website!Translating this to an equation you get: 1/10+1/2+d/50=70 Solving the equation we get: 5+25+d=70 d=70-30 d=40 It is the 3rd distance travelled
 Numbers_Word_Problems/36086: This question is from textbook Working with Numbers Algebra The sum of 5 and a negative integer is greater than -4 and less than 0. How many possible negative intergers satisfy the information?1 solutions Answer 22843 by jcmtnez(53)   on 2006-05-10 14:34:46 (Show Source): You can put this solution on YOUR website! -4<5+x<0 and x<0 Because it is negative -4=5+x -9=x Therefore x must be greater than -9 5+x=0 x=-5 Therefore x must be less than -5 The solution of the problem is the open interval of the numbers greater than -9 and less than -5, S=(-6,-7,-8) Are the threes negative integers that are solution to the problem.