Algebra ->  Tutoring on algebra.com -> See tutors' answers!      Log On

 Tutoring Home For Students Tools for Tutors Our Tutors Register Recently Solved
 By Tutor
| By Problem Number |

Tutor:

# Recent problems solved by 'actuary'

 Equations/252279: How do I solve this equation? i got two result and both were wrong. I have the correct answer 55, but don't know how they got it [40 + (3 - 8)]÷ -5 * 2 + 6 * 32 - (9 - 24) = Thaks 1 solutions Answer 184120 by actuary(112)   on 2009-12-26 03:42:52 (Show Source): You can put this solution on YOUR website!Are you sure that you wrote dpwn the problem correctly?
 Systems-of-equations/252265: Hello I have a problem that is nonlinear and cramer's rule or Gaussian elimination can't be used for. I'm trying to use substitution and factoring for this one but I'm coming up with the right thing... And I know its something that I'm missing I just can't see it.... it seems like the simplier the problem, I make mistakes. Could you please assist me with solving this problem .. Thanks y=x^2-4x+7 y=x+1 1 solutions Answer 184088 by actuary(112)   on 2009-12-25 17:38:04 (Show Source): You can put this solution on YOUR website!Since x+1 = y AND y=x^2-4x+7, x+1 = x^2-4x+7 This equation can be rewritten as 0 = x^2-5x+6. This equation can be factored into linear expressions so x^2-5x+6=(x-3)*(x-2)=0 So x=3 and x = 2. Next each of values for x can be substituted in either equation to determine the values of y. Using the equation y = x +1. When x = 2, y = 2+1 = 3 When x = 3, y = 3+1 = 4. So, there are two solutions to the system of equations. You may want to graph both equation to "see" the points of intersection of the two graphs.
 Percentage-and-ratio-word-problems/252260: The spaghetti sauce calls for 3 2/3 Tablespoons of parsley. How many tablespoons of parsley will he need if he makes 4 times the recipe?1 solutions Answer 184084 by actuary(112)   on 2009-12-25 17:19:07 (Show Source): You can put this solution on YOUR website!Since you making "4 times" the recipe, you need to multiply 3 2/3 by 4. First convert the mixed number 3 2/3 to an improper fraction. 3 2/3 = 11/3 So 3 2/3 * 4 = (11/3) * 4 = 44/3 (Tablespoons). Now, convert the improper fraction 44/3 to a mixed number. 44 divided by 3 = 14 and remainder of 2. So 44/3 = 14 2/3 (Tablespoons)
 Percentage-and-ratio-word-problems/252261: Sean won 60% of the car races that he entered,What fraction of the races did Sean win? 3/5 2/3 1/60 3/501 solutions Answer 184083 by actuary(112)   on 2009-12-25 17:13:09 (Show Source): You can put this solution on YOUR website!This question tests your ability to understand the equivalence of number represented as percents, decimals and fractions. First, convert 60% to a decimal number. To do this, drop the "%" sign and divide by 100. So 60% = .60 Next, either convert each of the fractions that are the possible answer to decimals, for example 3/50 = .06 or convert .60 to a fraction in lowest terms. .60 = 60/100 = 3/5 So, 60% = .60 = 60/100 = 3/5
 Linear-equations/251046: Find the x-intercepts Y= x^2+4x-1 1 solutions Answer 182872 by actuary(112)   on 2009-12-17 17:10:35 (Show Source): You can put this solution on YOUR website!The x-intercepts of the equation can be found by finding the roots of the equation x^2+4x-1. Use the quadratic formula x =( -b +/- Square Root[b^2-4ac])/(2*a) where a= 1, b=4 and c=-1. Sunstituting these values intp the quadratic formula we have -4 +/- Square Root[16-4*1*(-1) = =4 +/- Square Root[20] You can simplifly Square Root[20]=Square Root[4]*Square Root[[5]=Square[2^2]*Square[5]=2*Square Root[5] The the x-intercepts are (-4+2*Square[5])/2 = -2+Square Root[5] AND -2-Square Root[5]. In both cases, I was able to cancel 2 in the ny=umerator and denominator. Learning how to simplify the Sqyare Root of a number was probably one of the objectuves of this problem along with practice using the quadatic formula. Also, don't forget that a negative number times anegative number is a positive number.
 Geometry_Word_Problems/251109: if a pole is 24 feet tall and has a shadow of 8 ft, how tall is the shadow of a 72 foot pole?1 solutions Answer 182860 by actuary(112)   on 2009-12-17 16:48:27 (Show Source): You can put this solution on YOUR website!This is a problem involving similar triangles. The ratios of corresponding sides are equal. Since the ratio of the lengths of the poles is 72/24 = 3 the ratio of the shadows is also 3 = length of longer shadow divided by 8. Therefore the length of the longer shadow is 8*3=24 feet.
 percentage/250941: I am having a lot of problems with percentages. please help. 12 is 60% of what number.1 solutions Answer 182711 by actuary(112)   on 2009-12-17 05:31:41 (Show Source): You can put this solution on YOUR website!First convert 60% to a decimal number. 60% = .6 The word problem translated into an algebraic equation is 12 = .6*x where is the number you are looking for. THINK ABOUT THIS SO THAT YOU CAN SOLVE FUTURE PROBLEMS. Next divide both sides of the equation by .6 You now have 12/.6 = x but 12/.6 = 20 so x = 20. Check your answer by multiplyimg 20 by .6
 Equations/250938: solve by the substitution method 3m+n=13 m-2n=23 what is the solution of the system1 solutions Answer 182710 by actuary(112)   on 2009-12-17 05:26:03 (Show Source): You can put this solution on YOUR website!Rearrange the first equation so that n=13-3m SUBSTITUTE the rearranged equation into the second equation for n. The second equation then becomes m-2(13-3m)=23 Use the DISTRIBUTIVE property so that this equation becomes m-2*13+2*3m = 23 (REMEMBER - negative times a negative is a negative) We now have m-26+6m = 23 The next step is to combine like terms We now have 7m - 26 = 23 Add 26 to each side of the equation so that 7m = 49. Divide both sides of the equation by 7 so that m = 7 Substitute this value for m into the first equation to solve for n. We now have 3*7+n=13 Therefore n = 13-3*7= 13-21 = -8 So m = 7 and n = -8
 Linear-systems/250469: the line contains the point (-2,3) and is perpedicular to y=2x+7. Find the equation and write answer in slope intercept form.1 solutions Answer 182389 by actuary(112)   on 2009-12-16 07:45:08 (Show Source): You can put this solution on YOUR website!The slope of the desired is -(1/2) since the desired line is perpendicular to the given line So the equation of the desired line in slope intercept form is y = -(1/2)x+b Since the point (-2,3) is on the line, this information can be used to solve the equation for "b" 3=-(1/2)(-2)+b (Multiply -(1/2) times (-2) and then solve for b So b = 1 So the equation is y = -(1/2)x+1
 Average/250503: a student has grades on three examinations of 70,86,and 78. what must the student earn on a fourth examination in order to have an average of at least 80?1 solutions Answer 182387 by actuary(112)   on 2009-12-16 07:24:59 (Show Source): You can put this solution on YOUR website!Since the definition of "average" is ave = sum of all scores divided by the number of scores, we have 80 =(70+86+78+fourth exaximation score)/4 So 320 = 234 + fourth examination score (multiply both sides of the equation by 4 and add the known scores) So 320-234 = fourth examination score (subtract 234 from each side of the equation so fourth examination must be greater than or equal to 86 in order to have an average of at 80.
 Linear-equations/250073: Is the ordered pair (0,5) a solution of the system of linear equations: x + y = 5 -5x + 2y = 10 1 solutions Answer 182053 by actuary(112)   on 2009-12-15 06:18:47 (Show Source): You can put this solution on YOUR website!This question is asking you to substitute 0 for X and 5 for y in both equations. If the right hand value is equal to the left hand value after making the substitution, the answer is "yes". Otherwise, the answer is "no". Substitute 0 for x and 5 for y in the first equation and then the second equation. Since 0 + 5 = 5 and -5*0 + 2*5 = 10 the answer is "yes".
 Linear-equations/250068: Use the substitution method to solve the linear system given. Express the answer as an ordered pair of the form (x,y) y = x + 2 3x + 2y = 9 1 solutions Answer 182043 by actuary(112)   on 2009-12-15 04:39:25 (Show Source): You can put this solution on YOUR website!Substitute the "value" for y from the first equation into the second equation. The second equation then becomes 3x+2(x+2)=9 ASp;ve the after using the DISTRIBUTIVE PROPERTY, the second equation becomes 3x+2x+4=9 Solve 3x+2x+4=9 for x Subtract 4 from each side of the equation The equation is now 3x+2x=5 Combine like terms so 5x=5 Divide each side of the equation by 5 so x = 1 To solve the system of equations for the other variable "y", replace "x" with 1 in he first equation, so y = 1 + 2 = 3. So, x = 1 and y = 3.
 Linear-equations/250023: How do you graph the line y=-x+6?1 solutions Answer 182034 by actuary(112)   on 2009-12-14 22:50:37 (Show Source): You can put this solution on YOUR website!Determine 2 points with each point consisting of a x-value and a y-value. When x = 0, y = -0+6=6 When x = 1, y = -1+6=5 Plot the two points and draw a line running through the two points.
 Rectangles/249967: A rectangular floor measures 3.5 meters by 4.5 meters. What is the are of the floor in square inches?1 solutions Answer 182031 by actuary(112)   on 2009-12-14 22:41:54 (Show Source): You can put this solution on YOUR website!The formula for the area of a rectangle is A=l*w. So, the area is 3.5*4.5 = 15.75 meters. You are asked to express your answer in inches. Presumably, your teacher or your textbook contains a factor that converts meters to inches. THe conversion factor to two decimal places is 1 meter = 39.37 inches. Check to see if you were given a different conversion factor. 15.75 meters * 39.37 inches per meter = 620.078 inches.
 Distributive-associative-commutative-properties/249975: Solve. 0.9x + 3 < 1.7x -4.1 solutions Answer 182027 by actuary(112)   on 2009-12-14 22:30:28 (Show Source): You can put this solution on YOUR website!Inequality are solved in a manner just like equalities. You use arithmetic operations (addition, subtraction, multiplication and division) to get the unknown (in this "x")on one side of the inequality and the terms without an unknown on the other side of the inequality. So, 0.9x+3 < 1.7x-4 Subtract 0.9x from each side of the inequality. The inequality then reads 3 < 0.8x-4 Add 4 to each side of the inequality. The inequality then reads 7 < .8x Divide each side of the inequality by .8 The inequality then reads 7/.8 < x. Then 70/8 < x
 Travel_Word_Problems/249162: if a vehicle traveled 3,000 ft in 25 second. How fast would that vehicle be traveling. please show how you arrived at answer. 1 solutions Answer 181529 by actuary(112)   on 2009-12-13 08:03:20 (Show Source): You can put this solution on YOUR website!3000 feet/25 seconds = 120 feet per second
 percentage/249128: If the population of a town grew from 40 thousand to 50 thousand in ten years, by what percent did the population grow?1 solutions Answer 181528 by actuary(112)   on 2009-12-13 07:56:47 (Show Source): You can put this solution on YOUR website!The growth in population is 50,000-40,000=10,000. Express the growth in popupation compared to the starting population, i.e. 10,000/40,000. Reduce this fraction to lowest terms. 10,000/40,000=1/4. Convert 1/4 to a decimal by dividing 1 by 4. 1/4 = .25. Convert .25 to percent by multipying by 100 and putting a percent sign after the number. So 1/4 = .25 = 25%
 Equations/249127: 2^3-10[4-(-2+18)3]1 solutions Answer 181527 by actuary(112)   on 2009-12-13 07:50:53 (Show Source): You can put this solution on YOUR website!The calculation is performed by following the "order of precedence of operations". First, do the calculaion inisde of the inner parenthesis, so -2+18=16. so the expression is now 2^3-10*(4-16*3) Next, multiply 16 times 3 remembering that a negative sign is in fron of the 16. The expression is now 2^3-10 Now do the calculation inside of the parenthesis, remembering the sign of the answer. The expression is now 2^3-10*(-44) Now multiply -10 times -44 (A negative number times a negative number is a positive number. So the expression is now 2^3+440 But 2^3=8 So we now have 8+440 and 8+440 = 448
 test/249096: solve for p: 8p + 3w = w -15 -2p1 solutions Answer 181520 by actuary(112)   on 2009-12-13 06:52:53 (Show Source): You can put this solution on YOUR website!The first step is get all the terms of the expression with a "p" on one side of the expression and the other terms on the other side. So, 8p+3w = w -15-2p can be rewitten as 8p+2p=w-3w-15. Then combine "like" terms. The equation then becomes, 10p= -2w-15. Since you are being asked to solve for "p", divide both sides of the equation by 10, Then p = (-2w-15)/10
 Triangles/249153: A triangle has a side of length 6 cm, a side of length 8 cm and a right angle. What is the shortest possible length of the remaining side of the triangle? Express your answer as a decimal to the nearest hundredth1 solutions Answer 181518 by actuary(112)   on 2009-12-13 06:34:36 (Show Source): You can put this solution on YOUR website!Since the triangle is a right triangle, the hypoteneuse of the right triangle will be the longest side of the triangle. You are looking for the shortest side of the triangle. The Pythagorean Theorem says that c^2 = a^2 + b^2, where c is the length of the hypoteneuse. In this case, c=8 and you are looking for b. In this problem, it doesn't matter whether you call the shortest side "a" or "b", all you know for sure is that the shortest side isn't "c". Therefore, 8^2=6^2+b^2 or 64=36+b^2. So, b^2=64-36=28. Therefore b = Square Root of 28. rounded to the nearest hundreth is 5.29.
 Coordinate-system/249117: Find the graph of the equation by plotting points y=-3x1 solutions Answer 181517 by actuary(112)   on 2009-12-13 06:19:57 (Show Source): You can put this solution on YOUR website!First, find two pairs of points that satisfy the given equation. point 1 -- When x = 0, y = -3*0=0. So (0,0) is one point on the graph of the equation. point 2 -- When x = 1, y = -3*1=-1, So (1,-3) is another point on the graph of the equation. You can plot more points but two points determine the graph of a line.
 Rectangles/249152: the length of a rectangle is 2 feet more than the width. the perimeter of the rectangle is 20 feet. find the length1 solutions Answer 181516 by actuary(112)   on 2009-12-13 06:00:00 (Show Source): You can put this solution on YOUR website!Let l = the length of the rectangle. Let w = the width of the rectangle. l = 2 + w. The perimeter of rectangle is 2*length + 2*width and in this problem the perimeter is 20. Putting this information into an algebraic equation, you have 2*l+2*w = 20. Now you know that l = 2 + w so you can substitue this expression for "l" into the equation for the perimeter. This gives you, 2*(2+w)+2*w=20. Use the Distributive Property to simplify the equation so you now have 4+2*w+2*w=20. Combining like terms, you have 4+4*w=20. Since 4 is a factor of each term in the equation, you can divide each term of the equation by 4 and you now have 1 + w = 5. Subtract 1 from each side of the equation and you have w=4. Since l = 2+w, l=6. Therefore the width of the rectangle is 4 feet and the length is 6 feet. Have fun studying math. Larry
 Angles/249136: Decided weather or not the points are vertices of a right triangle: (-3,8) (3,10) (7,-2)1 solutions Answer 181515 by actuary(112)   on 2009-12-13 05:42:05 (Show Source): You can put this solution on YOUR website!Using the distance formula, fund the length of each of the 3 ides of the triangle, Length of side 1 --- Square Root of [(3-(-3))^2+(10-8)^2]=Square Root of [6^2+2^2]=Square Root of 40. Length of Side 2 --- Square Root of [7-3)^2+(-2-10)^2]=Square Root of [4^2+(-12)^2]=Square Root of [16+144] =Square Root of 160. Length of Side 3 --- Square Root of [-3-7)^2+(8-(-2))^2]=Square Root of [(-10)^2+(8+2)^2]=Square Root of [100+100] =Square Root of 200. Since the length of side 3 is the largest it must be the hypoteneuse of the right triangle if the triangle is to be a right triangle. For the triangle to be a right triangle, the Pythagorean Theorem has to be met so that 200^2 must be equal 160^2 + 40^2. In other words, 200^2=40^2+160^2. But this isn't true, so the triangle is NOT a right triangle. The problem is an attempt to get you to show that something isn't true by using facts that must be true if the original statement was true. Have fun studying math.
 Numbers_Word_Problems/249141: five less than a number is 15. Find the number.1 solutions Answer 181513 by actuary(112)   on 2009-12-13 05:19:06 (Show Source): You can put this solution on YOUR website!Let n = the number you are interested in finding. The description of the problem says "5 less than the number is 15". The key is to find the important words such as "is less than" and "is". "Is less than" means "subtraction" and "is" mean "= (equals)" Rewriting the words as an algebraic equation you have n-5=15. Using the "Rules of algebra", add 5 to each side of the equation, s0 n-5+5=15+5. So n=20. Good luck studying math. Larry
 Numbers_Word_Problems/249047: 1) Two consecutive integers are added. The square of their sum is 361. What are the integers ? 2) The product of two consecutive even numbers is 288. What are the numbers ?1 solutions Answer 181458 by actuary(112)   on 2009-12-12 19:15:59 (Show Source): You can put this solution on YOUR website!PROBLEM 1 Let n = the first integer, so n+1 is the next integer. Now translate the word problem into an algebraic expresion. So, (n+(n+1))^2=361. Take the square root of both sides of the equation, so, n+(n+1)=19 and n+(n+1)=-19. Case 1 yields the following linear equation 2n+1=19. Solving this linear equation results in the value n = (19-1)/2=9. The pair is 9 and 10 Case 2 yields the folowing linear equation n+(n+1)=-19. Solving this linear equation results in the value for n = (-19-1)/2=-10. The pair is then -10 and -9. Problem 2 Let n = the first even integer. So n = 2k for some k. The next even integer is then n+2 = 2k+2. Therefore, the words of the problem can be translated into the following algebraic equation 2k*(2k+2)=288. Expanding this equation we have 4k^2+4k-288=0. Dividing both sides by 4 produces k^2+k-72=0. This equation can be solved for k by factoring. k^2+k-72=(k+9)(k-8)=0. Therefore, k=-9 and k=8. So, the first pair of integers is n=2*k = -18 and the second integer is -16. The second pair of integers is 2*8=16 and 18. It is important to recognize the pairs of solutions for each question. Good luck with your study of math. Larry
 Polynomials-and-rational-expressions/249046: 4x^3 - 25x / x^2 - 14x +48 how do you factor this?1 solutions Answer 181439 by actuary(112)   on 2009-12-12 17:49:56 (Show Source): You can put this solution on YOUR website!I'm assuming that the question is: Factor (4x^3-25x)/(x^2-14x+48) 4x^3-25x= x*(4x^2-25)=x*(2x+5)*(2x-5) and x^2-14x+48=(x-8)(x-6) Therefore, (4x^3-25x)/(x^2-14x+48)=x*((2x+5)*(2x-5))/((x-8)(x-6)) Good luck with your math studies.
 Miscellaneous_Word_Problems/249038: If the side of a square are lengthened by 8 cm, the area becomes 289 cm^2. Find the length of a side of the original square.1 solutions Answer 181435 by actuary(112)   on 2009-12-12 17:38:44 (Show Source): You can put this solution on YOUR website!Let x = length of the original square So (x+8)^2=289 Take the square root of each side of the equation. So x+8 = 17 and -17 Solve each linear equation x+8=17, so x=9 and x+8=-17, so x = -25. Since I believe that the question is dealing with a real, physical square, the second answer (x=-25) is dropped and the answer is x=9 cm. Good luck with your math studies.
 Miscellaneous_Word_Problems/249036: Write a quadratic equation in the variable x having the given numbers as solutions. Type the equation in standered form, ax^2+bx+c=0 solution: 8, only solution1 solutions Answer 181428 by actuary(112)   on 2009-12-12 17:20:12 (Show Source): You can put this solution on YOUR website! This problem is basically the inverse of being asked to factor a quadratic equation. The solution (roots) of the equation are 8 and 8. Ues, 8 is a repeating root since the goal is to produce an equation in standard form of degree 2. An equation of degree 2 has 2 solutions therefore 8 is a repeating solution. If "a" is a solution (root) of an equation then "(x-a)" is a factor. So, in this case, the equation that you are being asked to produce has factors "(x-8)" and "(x-8)". Multiply the the factors using the "FOIL" method. Therefore, the equation that you are being asked to produce is (x-8)(x-8)= x^2-16x+64=0.
 Quadratic_Equations/199114: how many solutions exist for a quadratic equation?1 solutions Answer 149589 by actuary(112)   on 2009-06-05 21:40:45 (Show Source): You can put this solution on YOUR website!A quadratic equation may have 0,1,or 2 REAL solutions. REAL solutions refers to real numbers as compared to COMPLEX numbers. To determine the number of REAL solutions, you need to calculate the amount under the radical arising from the application of the quadratic formula, i,e b^2-4ac. b^2-4ac is called the determinant. If the determinant = 0, the quadratic equation has one REAL solution. If the determinant > 0, the quadratic equation has 2 REAL solutions. If the determinant < 0, there are 0 REAL solutions. Larry
 absolute-value/198918: The absolute value of -6 minus the absolute value of -2 is 1)-8 2)-4 3)8 4)41 solutions Answer 149395 by actuary(112)   on 2009-06-03 22:58:25 (Show Source): You can put this solution on YOUR website!The absolute value of -6 is 6. The absolute value of -2 is 2. So the absolute value of -6 minus the absolute value of -2 is 6 - 2 = 4. Larry
 Graphs/198919: Find the slope of the y-intercept? f(x)= -8x-10. The slope is _ ? The y-intercept is (0, ). Thank you.1 solutions Answer 149393 by actuary(112)   on 2009-06-03 22:54:23 (Show Source): You can put this solution on YOUR website!The function is in slope intercept form. So the slope is the coefficient of the x term. So the slope is -8. To find the y-intercept, substitute 0 for x in the function. So when x = 0, y = -8*0-10 = -10. The y-intercept is (0,-10). Larry