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# Recent problems solved by 'Earlsdon'

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 Linear-equations/76628: for each pair of equations, determine if the lines are parallel, perpendicular, or neither. y-3x=10 and 3y+x = -5 I have no idea how to start. Thank you.1 solutions Answer 54958 by Earlsdon(6287)   on 2007-04-01 20:07:06 (Show Source): You can put this solution on YOUR website!Determine whether the lines are parallel, perpendicular, or neither. 1) and 2) First, put your equations into the slope-intercept form: y = mx + b 1) and 2) Notice that the slope (m) in equation 1) is 3 and the slope (m) in equation 2 is -1/3 Recall that perpendicular lines have slopes that are the negative reciprocal of each other. So, equation 1) has a slope of 3 while equation 2) has a slope of -1/3 which is the negative reciprocal of 3. The lines are, therefore, perpendicular.
 Quadratic_Equations/76574: I don't know exactly how to go about solving this one problem. Here's is the question I have to answer. Amanda has 400 feet of lumber to frame a rectangular patio (the perimeter of a rectangle is 2 times length plus 2 times width). She wants to maximize the area of her patio ( area of a rectangle is length times width). What should the dimensions of the patio be, and show how maximum area of the patio is calculated from the algebraic equation. Use the vertex form to find the maximum area. I can only get so far and don't know how to go about solving it.1 solutions Answer 54916 by Earlsdon(6287)   on 2007-04-01 12:57:23 (Show Source): You can put this solution on YOUR website!First, you know that the perimeter is given as P = 400 ft. and you have the formula for the perimeter of a rectangle: P = 2L + 2W, so you can write: Solve this for L Divide both sides by 2. You also know that the area of a rectangle is given by: Now substitute the L=200-W from above into this equation and solve for W. Simplify this. You can rewrite this as: Ok, now you have a quadratic equation which, when graphed, will show a parabola that opens downward (because of the negative coefficient). This means that the vertex of this parabola will be a maximum and it represents the maximum value of A, the area. This is exactly what you are looking for, right? So, let's find the value of W that will give us the maximum value of A. Using the relationship: where: W is the width, as it was defined above. The a is the coefficient of the term, that's (-1), and the b is the coefficient of the term, and that's 200, so: Now, when W = 100, then L = 200-100 = 100 So, to obtain the maximum area from the given perimeter of 400 ft, the width must be 100 ft and the length must be 100 ft. In othe words, the patio will be a 100 by 100 ft square. When you graph the quadratic equation, you will see the following parabola: This shows you the relationship between the width, W, (the horizontal axis) and the area, A, (the vertical axis).
 Equations/76556: I tried this and came up with 5 but I'm not real sure I have the right answer if it is wrong could you pleae show me how to work this out? Solve the equation ln(x+5)-ln(3)=ln(x-3)1 solutions Answer 54911 by Earlsdon(6287)   on 2007-04-01 10:40:44 (Show Source): You can put this solution on YOUR website!Solve for x: Apply the quotient rule for logarithms to the left side: Now, if then A = B, so... Multiply both sides by 3. Subtract x from both sides. Add 9 to both sides. Divide both sides by 2. Check: Substitute x = 7 into the original equation. Using your calculator to find the natural logs: = 1.3863 and...
 Polynomials-and-rational-expressions/76544: please help me i need your help .Thanks in advance .It has do be factor completely . 1) x^2+17x+16 2) 3x^2-75y^21 solutions Answer 54897 by Earlsdon(6287)   on 2007-03-31 20:56:13 (Show Source): You can put this solution on YOUR website!Factor completely: 1) 2) First, factor a 3. Now, can you see that the parentheses contain the difference of two squares?:. The difference of two squares can be factored thus: Applying this to your problem, you will get: ...and there it is!
 Quadratic_Equations/76541: I don't know exactly how to get this form y=a(x-h)^2+k from the function y=x^2-6x+8. I don't know how to get this function into this particular form.1 solutions Answer 54896 by Earlsdon(6287)   on 2007-03-31 20:45:16 (Show Source): You can put this solution on YOUR website!Convert: to: from. Use the process known as "completing the square" You want to make the constant term here equal to the square of half the x-coefficient (that's the -6). So you must add a 1 to the 8 to make the required 9. But to keep the same equation, you must also subtract 1 to compensate for the added 1. Now rearrange this as follows: Factor the parentheses. ...and there you have it! Compare with: Here: a = 1, h = 5, and k = -1
 Miscellaneous_Word_Problems/76455: Science and medicine. Celsius temperature readings can be converted to Fahrenheit readings using the formula F=9/5C + 32. What is the Fahrenheit temperature that corresponds to each of the following Celsius temperatures: -10, 0, 15, 100? Please help me I have try to solve this problem but cannot seem to get it. Thanks, Peggy1 solutions Answer 54827 by Earlsdon(6287)   on 2007-03-30 19:41:40 (Show Source): You can put this solution on YOUR website! Calculate F for C = -10, 0, 15, 100 Just substitute the given numbers for C in the formula and solve for F. C = -10 So, If C = -10 then F = 14. C = 0 So, if C = 0 then F = 32 Now do exactly the same for C = 15 and for C = 100
 Polynomials-and-rational-expressions/76380: CAN SOMEONE CHECK THIS PLEASE? FUNGICIDES ACCOUNT FOR 1/10 OF THE PESTISIDE USED IN THE USA. INSECTICIDES ACCOUNT FOR 1/4 WRITE RATIO TO THE SIMPLEST FORM. 1/10 DEVIDED BY 1/4 = 1/401 solutions Answer 54797 by Earlsdon(6287)   on 2007-03-29 22:53:10 (Show Source): You can put this solution on YOUR website!It appears as though you have multiplied instead of dividing. = =
 logarithm/76391: what is the solution of 1+3logx=logx+logxto the 3rd power1 solutions Answer 54796 by Earlsdon(6287)   on 2007-03-29 22:48:31 (Show Source): You can put this solution on YOUR website!Solve for x: Apply the law of exponents for logarithms to the left-hand side. Subtract from both sides. Rewrite the this in exponential form. Solution: x = 10
 Polynomials-and-rational-expressions/76387: how do i solve this? a+1 over 2 = 1 over a? Please Help fast as you can!1 solutions Answer 54794 by Earlsdon(6287)   on 2007-03-29 22:39:57 (Show Source): You can put this solution on YOUR website!Solve for a: Multiply both sides by a. Multiply both sides by 2. Subtract 2 from both sides. Factor this quadratic equation. Apply the zero product principle. and/or The roots are:
 Distributive-associative-commutative-properties/76361: PLEASE HELP ME!!! question: The area of a circle is given by A = pi(4x^2 + 12x + 9. Find the expression for the radius of the circle. H_E_L_P!!!1 solutions Answer 54792 by Earlsdon(6287)   on 2007-03-29 22:31:54 (Show Source): You can put this solution on YOUR website!The area of a circle is given by: As you probably know,the formula for the area of a circle is: Set these two equal to each other: Divide both sides by Now factor the right-hand side. Take the square root of both sides.
 Polynomials-and-rational-expressions/76171: Factor each expression as a difference of two squares: 1 solutions Answer 54666 by Earlsdon(6287)   on 2007-03-28 19:22:06 (Show Source): You can put this solution on YOUR website!Factor: =
 Expressions-with-variables/76123: Solve each of the following systems by substitution 8x - 4y =16 y = 2x - 4 1 solutions Answer 54653 by Earlsdon(6287)   on 2007-03-28 11:32:01 (Show Source): You can put this solution on YOUR website!Solve by substitution: 1) 8x-4y = 16 2) y = 2x-4 Substitute this for the y in equation 1) and solve for x. 1a) 8x-4(2x-4) = 16 Simplify and solve for x. 1a) 8x-8x+16 = 16 1a) 16 = 16 The two equations represent the same line and any value of x will satisfy the equations.
 Inequalities/76074: 5-3x>561 solutions Answer 54613 by Earlsdon(6287)   on 2007-03-27 21:49:38 (Show Source): You can put this solution on YOUR website!Solve for x: Subtract 5 from both sides. Divide both sides by -3...remember to reverse the inequality sign (> to <).
 Miscellaneous_Word_Problems/75920: If the product of a number and -3 is reduced by 5, the result is 25 less than twice the opposite number. Find the number1 solutions Answer 54506 by Earlsdon(6287)   on 2007-03-26 22:10:07 (Show Source): You can put this solution on YOUR website!Let n be the required number. The opposite of n is -n. From the problem description, you can write: -3n-5 = -2n-25 Simplify and solve for n. Add 3n to both sides. -5 = n-25 Addd 25 to both sides. 20 = n The number is 20
 Expressions-with-variables/75918: I need help with factoring. I can't seem to get it, especially when there is an X first. Please help me. thanks X^3-1251 solutions Answer 54500 by Earlsdon(6287)   on 2007-03-26 22:01:09 (Show Source): You can put this solution on YOUR website!Factor: Do you see this as the difference of two cubes? The difference of two cubes can be factored thus: Applying this to your problem, where A = x and b = 5, we get:
 Expressions-with-variables/75919: Please help me factor. thanks 1000x^3+11 solutions Answer 54496 by Earlsdon(6287)   on 2007-03-26 21:52:50 (Show Source): You can put this solution on YOUR website!Factor: Do you recognise this as the sum of two cubes? You can factor the sum of two cubes as follows: Applying this to your problem, where A = 10x and B = 1, you get: Simplify.
 Linear-systems/75922: I have a problem with changing this->->y=4x-11 to standard form. There are others, but If I can figure out how to do this, I'll be able to finish my homework. Here's another one that could also help->-> y=-x/3+2/3 Stupid standard form... (this is from a worksheet I got)1 solutions Answer 54494 by Earlsdon(6287)   on 2007-03-26 21:44:14 (Show Source): You can put this solution on YOUR website!The standard form is: ax + by = c y = 4x-11 Add 11 to both sides. y+11 = 4x Now subtract y from both sides. 11 = 4x+y Rewrite as: 4x+y = 11 This is now in standard form. Multiply everything by 3 to clear the fractions. Now add x to both sides. This is now in standard form.
 Graphs/75709: This question is from textbook Can you help me solve this? my answer is not matching the textbook answer. 1/2(2x+3)>10 x>8.5 is my answer and the text book answer is x>17/2. Thank you.1 solutions Answer 54388 by Earlsdon(6287)   on 2007-03-25 14:37:12 (Show Source): You can put this solution on YOUR website!You have the correct answer...and so does your book! Multiply both sides by 2. Subtract 3 from both sides. Finally, divide both sides by 2. or
 Graphs/75697: This question is from textbook Beginning Algebra For each equation in exercises 25 to 28, identify the axis to symmetry, create a suitable table of values, and sketch the graph (including the axis of symmetry). y=-x^2+6x-2 I am needing some assistance with this problem. I am not quiet sure how to find ths symmetry and need further help. Thanks.1 solutions Answer 54379 by Earlsdon(6287)   on 2007-03-25 11:11:33 (Show Source): You can put this solution on YOUR website!Find the axis of symmetry: The axis of symmetry is the line that divides the curve represented by this equation, into two mirror-halves. Since your equation is already in the standard form of: you can find the axis of symmetry which is given by: In this case, a = -1 and b = 6 The axis of symmetry is the line represented by the equation x = 3. If you graph this, it would be a vertical line passing through the point (3, 0) For creating the table of points, you select a value for the independent variable (that's x), substitute this into your equation and solve for the corresponding value of y. This will give you the (x, y) of one point. Do this several times to get several points for your table. Then you plot these points on a piece of coordinate graph paper on which you have previously drawn the x-axis and the y-axis. Here's an example of how you would generate one of these ponts: Pick a value for x: x = 0 and substitute this into your equation and solve for y. Set x = 0 For x = 0, y = -2 So, for one of the points, you have (0, -2) Do this for a few more points then plot them on graph paper and sketch the graph. The graph should look like this:
 Graphs/75698: This question is from textbook Beginning Algebra For each equation in exercises 29-34, find the x- intercepts. y= x^2 +x -6 I am not sure what I am doing wrong but I cannot seem to get this one. Please help. Thanks.1 solutions Answer 54373 by Earlsdon(6287)   on 2007-03-25 10:41:15 (Show Source): You can put this solution on YOUR website!Find the x-intercepts: Since the x-intercepts occur at y = 0, set the equation to zero and solve for the x's. This can be factored. , so x = 2 and x = -3
 Polynomials-and-rational-expressions/75700: please help!! 3w^2-9w-1 and 8w^2-9w-4 1 solutions Answer 54372 by Earlsdon(6287)   on 2007-03-25 10:36:23 (Show Source): You can put this solution on YOUR website!What kind of help would you like? What do you have to do with these two trinomial expressions? Please clarify and re-post.
 Polynomials-and-rational-expressions/75701: remove parentheses and simplify? 8y-(2y-5x)1 solutions Answer 54370 by Earlsdon(6287)   on 2007-03-25 10:32:18 (Show Source): You can put this solution on YOUR website!Simplify: Remove the parentheses and change all of the signs inside the parentheses. This usually be written:
 Polynomials-and-rational-expressions/75699: can some help me simplify this? x^2+2x-801 solutions Answer 54369 by Earlsdon(6287)   on 2007-03-25 10:23:32 (Show Source): You can put this solution on YOUR website!Simplify: This trinomial can be factored. The factors will take the form: (x+m)(x+n) where m and n must meet the follwing restrictions: m*n = -80 and m+n = 2 How do we know this? Well, when you multiply the two factors, you should get back the original trinomial, right? Right!...so, usinf FOIL: = and if you compare this with the original trinomial, you can see that: m+n = 2 and m*n = -80 Since the sum of m and n is quite small (2), this would indicate that the absolute values of m and n are are very close to each other. A wise choice would be: m = 10 and n = -8 or m = -10 and n = 8 because both of their products are -80. Select the pair whose sum is 2, that has to be m = 10 and n = -8. So, now you can write:
 Polynomials-and-rational-expressions/75660: Hi I need help solving this one. I am really stuck!!! I am not sure if I enterend the exponents properly? But the problem reads: (2m to the 3rd x to the 2nd)to the neg. 1 (3m to the 4th x) to the neg 3 divided by (m to the 2nd x to the 3rd) to the neg 3 (m to the 2nd x) to the neg 5th Thank you in advance for any help that you can offer me.1 solutions Answer 54351 by Earlsdon(6287)   on 2007-03-24 20:21:08 (Show Source): You can put this solution on YOUR website!By "solve" I expect you "simplify" Simplify: Now multiply the exponents inside the parenthese by the ones outside the parentheses. Combine like-factors: Remember that you can change the sign of the exponents by moving the factor down or up as the case maybe. To simplify this expression, you want all the exponents to be positive.
 Polynomials-and-rational-expressions/75659: (r+4)4 Hi, I need help solving this one. I couldn't submit the format properly, not sure how to type exponents? But it is r+4 to the 4th not times 4. Thank you in advance.1 solutions Answer 54347 by Earlsdon(6287)   on 2007-03-24 19:18:17 (Show Source): You can put this solution on YOUR website!First, you can indicate an exponent by using the caret (^) following the variable or number, thus: (r^4)^4 It will look even better if you use three opening curly brackets before the expression or equation and three closing curly brackets after the expression or equation: Is this what you intended? If so, then using the laws of exponenets, you would multiply the two exponents to get:
 Linear-equations/75639: This question is from textbook Functions and Change The Americans with Disability Act requires, amoung other things, that wheelchair service ramps have a slope not exceeding 1/12. Problem A- Suppose the front steps of a building are 2 feet high. You want to make a ramp conforming to the ADA standards that reaches from the ground to the top of the steps. How far away from the building is the base of the ramp? Problem B- Another way to give specifications on a ramp is to give allowable inches of rise per foot of run. In these terms, how many inches of rise does the ADA requirement allow in 1 foot of run? 1 solutions Answer 54327 by Earlsdon(6287)   on 2007-03-24 10:57:40 (Show Source): You can put this solution on YOUR website!Problem A: If the mandated slope is not to exceed (rise over run) and the steps (rise) are 2 feet high, you can write the proportion: Simplify and solve for x ft. feet. The base of the ramp has to be 24 feet from the building. Since the allowable slope is and the run is 1 foot or 12 inches, then the allowable rise would be 1 inch.
 Polynomials-and-rational-expressions/75490: This is a practice question for me so I know the answer but how do I work this? Let f(x) = 5x-2. Find: (a) f(4) – f(3) Answer is: 5 (b) f(9) – f(8) Answer is: 5 (c) f(12) – f(11) Answer is: 5 (d) How do the results of (a) through (c) compare to the slope of the line that is the graph of f? Answer is: same 1 solutions Answer 54294 by Earlsdon(6287)   on 2007-03-23 17:54:18 (Show Source): You can put this solution on YOUR website!The way you solve these problems is just replace the x in the function with the number given. a) If f(x) = 5x-2, find: f(4)-f(3) First, to find out what f(4) is, you replace x with 4 in the function f(x) = 5x-2, so: f(4) = 5(4)-2 f(4) = 20-2 f(4) = 18 Similarly for f(3) f(3) = 5(3)-2 f(3) = 15-2 f(3) = 13 Now, f(4)-f(3) = 18-13 = 5 b) For f(9)-f(8) f(9) = 5(9)-2 f(9) = 45-2 f(9) = 43 Similiarly for f(8) f(8) = 5(8)-2 f(8) = 40-2 f(8) = 38 Now, f(9)-f(8) = 43-38 = 5 You should get the picture by now. d) The given function can be written as an equation in the slope-intercept form: y = mx+b where m is the slope and b is the y-intercept. Your function can be similarly written: y = 5x-2 where the slope m = 5 and the y-intercept, b = -2 So you can see that the slope of the given function is the same as the the differences given by: f(x)-f(x-1)
 Equations/75618: Hello out there,I have some questions towards some difficult equations,can someone help me please,the first question is,A solution of the equation 4x=10-cy is (5,-2).What is the value of c?The next one is,Find g(9) given that g(x)=2x+3.The next is,Find h(4) given that h(x)=x/2minus7.And the last one is,Assume that y varies directly as x.Find y when x =54 if y= 1/4 when x=3/2.Thanks for whoever can help.1 solutions Answer 54285 by Earlsdon(6287)   on 2007-03-23 16:40:36 (Show Source): You can put this solution on YOUR website!1) The solution to is (5, -2). What is the value of c? Since you have been given the solution of (5, -2) you can substitute x = 5 and y = -2 into the given equation and solve for c. Simplify. Subtract 10 from both sides of the equation. Finally, divide both sides by 2. 2) If g(x) = 2x+3 find g(9) Substitute 9 for x in the function. g(9) = 2(9)+3 g(9) = 18+3 g(9) = 21 3)If , find h(4) Substitute 4 for x in the function. If y varies directly as x, you can write: y = kx where k is the constant of proportionality. To find the value of k, susbstitute the given x = 3/2 and y = 1/4 Multiply both sides by Now you have: Substitute x = 54.
 decimal-numbers/75593: Her parents have given Silly Sally a choice of payment method for her allowance: She can receive \$25.00 dollars at the end of two weeks or she can get \$.01 today and double that, \$.02 tomorrow and double that for each day doubling the amount from the day before every day for two weeks. Decide which type of payment Sally should pick by calculating the amount she receives for each.1 solutions Answer 54255 by Earlsdon(6287)   on 2007-03-23 11:34:53 (Show Source): You can put this solution on YOUR website!Well, Silly Sally ought to ask her math teacher for help on this before she decides. If she accepts the \$25.00-offer, she will, of course, have \$25.00 at the end of the two-week period. If, however, after consulting with her math teacher, she decides to accept the second offer, she would soon see that this is the better offer because, after 14 days, she would get a total of pennies. This equals \$163.83:
 Graphs/75364: Explain what it means to solve a system of linear equations?1 solutions Answer 54138 by Earlsdon(6287)   on 2007-03-22 11:36:02 (Show Source): You can put this solution on YOUR website!A linear equation represents a straight line on a graph. A system of linear equations would be more than one line. Let's say the system of linear equations represents two straight lins on a graph. To solve such a system of linear equatins means to find the point (x, y) at which these two lines intersect. If the two lines do indeed intersect, then you can find the point of intersection algebraically or by graphing the two lines and inspecting the graph to find the point of intersection. This is called a "consistent system". If the two lines do not intersect, then there are two posibilities: 1) They are parallel, in which case, there is no point of intersection and thus, no solution to this system of equations. This is called an "inconsistent system". 2) The two lines are collinear (one lies on top of the other), in which case, there is an infinite number of solutions because any point that lies on one of the lines will also lie on the other line. This is a "consistent system" and the equations are "dependent equations">
 Inverses/75438: Please help me solve this equation. It has been awhile. 3/4 + 7/y = 91 solutions Answer 54137 by Earlsdon(6287)   on 2007-03-22 11:11:08 (Show Source): You can put this solution on YOUR website!Solve for y: Add the fractions on the left side. The common denominator is 4y Multiply both sides by 4y Subtract 3y from both sides. Finally, divide both sides by 33. or y = 0.8484...