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 Quadratic_Equations/25938: Please help me find the vertex and intercepts for this quadratic function, and sketch its graph. y = -3x^2 + 6x1 solutions Answer 13951 by Earlsdon(6287)   on 2006-01-30 11:40:11 (Show Source): You can put this solution on YOUR website!Find the vertex and the x-intercepts of: The quadratic equation is in standard form: where: a = -3, b = 6, and c = 0 The x-coordinate of the vertex is given by: The y-coordinate of the vertex is found by substituting the x = 1 into the original equation and solving for y. The vertex is at (1, 3) The x-intercepts are found by setting y = 0 in the original equation and solving for the x-values. Factor an x Apply the zero products principle. and/or One of the x-intercepts is x = 0 The other one is found from: Subtract 6 from both sides. Divide both sides by -3. The x-intercepts are: x = 0 and x = 2 Here's the graph of the parabola:
 Miscellaneous_Word_Problems/25940: pls.help me with this. a bank teller counts a certain amount of money in 20 mins, but if she is helped by another teller, they count the money in 15 mins. how long would it take the second teller to count the money alone?1 solutions Answer 13945 by Earlsdon(6287)   on 2006-01-30 11:22:18 (Show Source): You can put this solution on YOUR website!Here's one approach: Let the tellers be Teller A and Teller B. If A can do the job in 20 minutes, then he/she can do 1/20 of the job in 1 minute. If A and B together can do the job in 15 minutes, then they can do 1/15 of the job in 1 minute. So, if we subtract A's part of the job for 1 minute from the part of the job for 1 minute for A + B, then we will have the part of the job done by B in 1 minute. A + B = 1/15 B = 1/15-A But A = 1/20, so: B = 1/15 - 1/20 B = 4/60 - 3/60 B = 1/60 which means that Teller B can do 1/60 of the job in 1 minute, therefore, B can do the entire job in 60 minutes. Answer: It would take Teller B 60 minutes to count the money.
 Sequences-and-series/25943: What is the geometric notation for a parallel lie?1 solutions Answer 13943 by Earlsdon(6287)   on 2006-01-30 11:07:37 (Show Source): You can put this solution on YOUR website!The geometric notation for parallel lines is: || For example, if line A and B are parallel, you would indicate this: A||B
 real-numbers/25945: i've got maths homework from my teacher i want to know:why do you need to have a take away sign in front of the equation whilst subtracting terms e.g -y-4y what does the first take away sign mean?1 solutions Answer 13942 by Earlsdon(6287)   on 2006-01-30 11:05:02 (Show Source): You can put this solution on YOUR website!The negative (take-away) sign in front of the variable (unknown), y, indicates that you must negate (make negative) the value that you put in place of y. For example: If the value assigned to y is -5 (negative 5), then your expression (-y-4y) becomes: -(-5)-4(-5) = 5 + 20 = 25 If the value assigned to y is 6 (positive 6), then your expression becomes: -(6)-4(6) = -6-24 = -30 Good luck on your maths homework.
 Complex_Numbers/25761: Can you please help me with this, we are doing differential Calculus. Find the equation of the tangetn for each given x-value. y=x^2+8x+12, where x = -4. At the back of the book, it says the answer is y=-4 I have no idea how to get that. thank you.1 solutions Answer 13875 by Earlsdon(6287)   on 2006-01-29 11:27:51 (Show Source): You can put this solution on YOUR website!As you probably know, the slope of the tangent at the given point (x = -4) is given by the value of the 1st derivative of the function at that point (x = -4). Substitute x = -4 and solve. So, the slope of the tangent is 0 which means that it's a horizontal line. To find the point (x, y) of tangency, you'll substitute x = -4 into the original equation. The point of tangency is (-4, -4) and the equation of the line passing through that point with a slope of m = 0 is: Using the point-slope form: Simplify. This is the equation of the tangent at x = -4 Here's what it looks like in a graph:
 Graphs/25784: I just want to see if I have the below problem done correctly: Find the equation of the line with slope m=-7/5 and x-intercept 5 I used the equation y=mx+b y=(-7/5)x+b y=-1.4(5)+0 y=-7 Thank you1 solutions Answer 13870 by Earlsdon(6287)   on 2006-01-29 10:46:27 (Show Source): You can put this solution on YOUR website!Well, you are on the right track! Your answer should be in the form of y = mx + b as you have correctly stated but given the slope (m=-7/5) and x-intercept of 5 allows you to calculate the y-intercept, b, which what you need for your equation. A key point here is recognising that having an x-intercept of 5 means that x = 5 when y = 0. So, starting with y = mx + b and substituting y = 0, x = 5, and m = -7/5, you can solve for b. Simplify and solve for b. Add 7 to both sides of the equation. Now you can write your equation.
 Mixture_Word_Problems/25767: After getting a 15% discount on the price of a new Chrysler Sebring convertible, Hellen paid \$ 27,000. What was the original price of the convertible?1 solutions Answer 13864 by Earlsdon(6287)   on 2006-01-28 21:51:22 (Show Source): You can put this solution on YOUR website!Original price - discount = \$27,000.00 Let x = original price. Change 15% to decimal (0.15) Simplify and solve for x. Divide both sides by 0.85 Original price is \$31,764.70
 Linear-equations/25769: 2(a+4)=3a-1 or help me with Solving Multi-Step Equasions, please 1 solutions Answer 13863 by Earlsdon(6287)   on 2006-01-28 21:39:07 (Show Source): You can put this solution on YOUR website!Solve: Apply the distributive property to the left side. Subtract 2a from both sides of the equation. Add 1 to both sides. Answer: a = 9
 percentage/25755: Bob bought a goat. He expected to sell it at a price that would give him a 10% profit on his purchase. However, he had to sell it for \$50 less than he expected, which was a loss of 15% on what it cost him. What did Bob pay for the goat? 1 solutions Answer 13858 by Earlsdon(6287)   on 2006-01-28 18:59:48 (Show Source): You can put this solution on YOUR website!Let C = the cost of the goat. Expected sale price = C + 10% of C Actual sale price = (C + 10% of C) - \$ 50 Cost less 15% = C - 15% 0f C C + 0.1C - \$50 = C - 0.15C Simplify and solve for C 1.1C - \$50 = 0.85C Add \$50 to both sides. 1.1C = 0.85C + \$50 Subtract 0.85C from both sides. 0.25C = \$50 Divide both sides by 0.25 C = \$200 Bob payed \$200 for the goat.
 Polynomials-and-rational-expressions/25625: Factor: 6f^2+5f+1 thanks1 solutions Answer 13840 by Earlsdon(6287)   on 2006-01-28 00:19:52 (Show Source): You can put this solution on YOUR website!Factor: =
 Radicals/25631: Simplify: 2 sqrt 12 + sqrt 31 solutions Answer 13839 by Earlsdon(6287)   on 2006-01-28 00:16:39 (Show Source): You can put this solution on YOUR website!Simplify: = = = =
 Divisibility_and_Prime_Numbers/25693: Do you have a list of prime numbers up to 1000?1 solutions Answer 13838 by Earlsdon(6287)   on 2006-01-28 00:11:58 (Show Source): You can put this solution on YOUR website!Yes, but you're talking about over 160 prime numbers. That's too many to list here but look in the CRC Standard Mathematical Tables. Or you could try Google.com and see what they can provide.
 Rational-functions/25638: Please help me understand how to solve this rational expression.(thank you) x^3-y^3/x^2+xy+y^2 I think the denomiator factors out to: (x+y)(x+y) but I am not sure what to do with the numerator! Is it, xy(x^2-y^2) and if it is, where do I go from there???? Thanks SO much for the help!!1 solutions Answer 13837 by Earlsdon(6287)   on 2006-01-28 00:03:49 (Show Source): You can put this solution on YOUR website!Simplify the expression: (You don't "solve" expressions, you simplify them) The numerator is the difference of two cubes and can be factored. Cancel the like-terms in the top and bottom. This is the answer!
 Exponents/25691: I need help solving this problem solve for X. This is how I tried to solve it, I tried two way but I am unsure 2X^2=288 (2x)(2x)=288 4X=288 X=72 Or I also tried this way 2*X^2=288 2*(X)(X)=288 2X=288 2X/2=288/2 X=144 1 solutions Answer 13808 by Earlsdon(6287)   on 2006-01-27 18:32:22 (Show Source): You can put this solution on YOUR website!Solve for x: Notice that only the x is squared, not the 2. Divide both sides of the eqaution by 2. Now take the square-root of both sides. and + or - x = + or - 12
 Miscellaneous_Word_Problems/25703: Can you please tell me if 75.19 minutes is correct answer for the below problem? If not, how should I set it up? The time t required to empty a tank varies inversely as the rate r of the pumping. If a pump can empty a tank in 45 minutes at a rate of 600 kL/min, how long will it take a pump to empty the same tank if its rate is 1000 kL/min? 1 solutions Answer 13805 by Earlsdon(6287)   on 2006-01-27 18:15:37 (Show Source): You can put this solution on YOUR website!First, it's always a good idea to see if your answer is "reasonble" If it takes 45 minutes to empty the tank pumping at 600 KL/min, then it would seem reasonable to expect it to take less time time to empty the tank if the pumping rate is higher, wouldn't it? Your answer is a lot higher than you should expect. Here's how you should do this problem. Write the proportionality equation: Now substitute the given values of t (45 min) and r (600 KL/min) and solve for k, the proprtionality constant. Multiply both sides by 600. Now you can solve the problem for r = 1000 KL/min. minutes.
 Inequalities/25666: This question seems too hard to set up. Could someone help me out? -Find all sets of three consecutive positive even integers whose sum is less than 40.1 solutions Answer 13770 by Earlsdon(6287)   on 2006-01-26 20:58:30 (Show Source): You can put this solution on YOUR website!You can start with x as the first positive even integer, the next positive even integer would be x+2 and the next one would be x+4. Now you could set up the inequality: Solve for x. Subtract 6 from both sides. Divide both sides by 3. But you want even integers, so use x = 10 10+12+14 = 36 < 40 8+10+12 = 30 < 40 6+8+10 =24 < 40 4+6+8 = 18 < 40 2+4+6 = 12 < 40 0+2+4 = 6 < 40
 Angles/25343: what is a regular or not regular polygon?1 solutions Answer 13663 by Earlsdon(6287)   on 2006-01-25 12:16:51 (Show Source): You can put this solution on YOUR website!A regular polygon is one in which all of the sides are of equal length and all of the angles are equal.
 Proportions/25344: Please show me how to do this! Thank you! If a 30 oz can of lemonade drink mix makes 8 quarts, how much mix is needed to make 10 quarts of drink? i know how to set it up but i don't know how to round the anwser to the nearest hundreth when neccessary 1 solutions Answer 13662 by Earlsdon(6287)   on 2006-01-25 12:15:09 (Show Source): You can put this solution on YOUR website!You can use proportions to solve this problem. Multiply both sides by 10. No rounding is necessary. You'll need 37.5 oz of mix to make 10 quarts of drink.
 Angles/25347: What is a closed plane figure formed by three or more line segments?1 solutions Answer 13658 by Earlsdon(6287)   on 2006-01-25 12:00:44 (Show Source): You can put this solution on YOUR website!This would be called a polygon.
 Linear-equations/25383: Jerry and Lucy have \$29,000 invested in stocks paying 5%. How much additional money should they invest in certificates of deposit paying 2% so that the total return on the two investments is 3%? I have tried so many solutions and can't figure it out1 solutions Answer 13657 by Earlsdon(6287)   on 2006-01-25 11:57:01 (Show Source): You can put this solution on YOUR website!Let x = the additional amount to be invested at 2%. The problem is: 5% of \$29,000 + 2% of \$x = 3% of (\$29,000 + \$x) Let's put this into an equation so you can solve for x. First, convert the percentages to their equivalent decimals. (2% = 0.02, 3% = 0.03, 5% = 0.05) Simplify and solve for x. Subtract 870 from both sides. Subtract 0.02x from both sides. Finally, divide both sides by 0.01 The additional amount required is \$58,000 Check: = \$2,610 = \$2,610
 Linear_Equations_And_Systems_Word_Problems/25423: In a certain mill the cost C is thousands of dollars of producing x tons of steel is given by C = 0.3x + 3.5. The revenue R in thousands of dollars from selling x tons if given by R = 0.5x. Find the point at which R=C (the break-even point).1 solutions Answer 13654 by Earlsdon(6287)   on 2006-01-25 11:39:53 (Show Source): You can put this solution on YOUR website!To find the break-even point, set R = C and solve for x. Simplify and solve for x. Subtract 0.3x from both sides. Divide both sides by 0.2 Break-even point is 17.5 tons.
 Square-cubic-other-roots/25424: simplify: (xy)^(1/4) (x^2y)^(1/2)1 solutions Answer 13653 by Earlsdon(6287)   on 2006-01-25 11:33:59 (Show Source): You can put this solution on YOUR website!Simplify: = =
 Functions/25425: Can you please show me the surface area of a box as a function of length, width, and height.1 solutions Answer 13652 by Earlsdon(6287)   on 2006-01-25 11:26:15 (Show Source): You can put this solution on YOUR website!Yuo don't say whether the box is open (no top) or closed. Let's assume that it is a closed box so we include the area of the top in the total surface area (SA). The total surface area comprises the sum of the areas of the base & top, the back & front, and the two sides. SA = 2(LW + WH + LH) Where: L = Length, W = Width, and H = Height.
 Volume/25284: I am stumped. I have the following equation and can only get so far because this is the first time I am working with pie. I will show you what I have and would greatly appreciate it if you can show me step by step how i am supposed to do it so that I can refer to it and finish the rest of my assignment i would be ever so grateful. The volume of a cylinder (think about the volume of a can) is given by V=pie r²h where r is the radius of the cylinder and h is the height of the cylinder. Suppose the volume of the can is 100 cubic centimeters. Write h as a function of r. this is what I got: 100=pie r²h 100=3.14r²h I am lost after that.1 solutions Answer 13542 by Earlsdon(6287)   on 2006-01-24 11:03:01 (Show Source): You can put this solution on YOUR website! but . Solve for h. Divide both sides of the equation by
 Rational-functions/25258: Hello, I just tried to locate "x" and couldn't get it. The problem is -2[4-3(x+5)]=4(2-x). I cannot get "x" no matter how hard I try. Thank you if you can help me.1 solutions Answer 13528 by Earlsdon(6287)   on 2006-01-23 22:37:15 (Show Source): You can put this solution on YOUR website!Solve: First, apply the "distributive property" to both sides to simplify. Do the "distributive property" once more on the left side. Simplify the left side. Add 4x to both sides of the equation. Subtract 22 from both sides. Finally, divide both sides by 10.
 Coordinate-system/25267: Write the equation of a line parallel to y=-3/4x-2, which has a y-intercept of 5.1 solutions Answer 13527 by Earlsdon(6287)   on 2006-01-23 22:25:01 (Show Source): You can put this solution on YOUR website!Recall that parallel lines have equal slopes. The slope of the given line is: so this will be the slope of your new line. You have also been given the y-intercept of the new line, so b = 5 Now you can write the equation of the new line in the form:
 Equations/25262: I am a parent trying to help a 7th grader: how can I explain: r-7 = 13 Thanks DAwn1 solutions Answer 13526 by Earlsdon(6287)   on 2006-01-23 22:16:43 (Show Source): You can put this solution on YOUR website!Try this: The object is to get the variable r by itself. In your equation however, r has a 7 subtracted from it, so you need to "undo" this subtraction of 7 by adding (that's the opposite of subtracting) 7. But don't forget that whatever you do to one side of the equation, you must do exactly the same to the other side. So you must add 7 to the other side as well. Add 7 to both sides of the equation. Simplify this. This is the answer!
 Rational-functions/25172: I have no idea what i am doing wrong, could you please help me. The directions say: Solve each equation: the problem: x/6 + 4x/3 = x/18 I have the problem done but i didnt do it right cause the answer dosent check: the LCD is 15 then it comes to 3x + 24x= x, my final answer comes to 27 but it cant be right, help!1 solutions Answer 13505 by Earlsdon(6287)   on 2006-01-23 11:28:10 (Show Source): You can put this solution on YOUR website!Solve: Multiply through by the common denominator of 18. Collect like-terms. Subtract x from both sides. Divide both sides by 26.
 logarithm/25133: 10xsuared-2x-4=0 How do i work that out1 solutions Answer 13477 by Earlsdon(6287)   on 2006-01-22 20:48:27 (Show Source): You can put this solution on YOUR website!Solve: Factor a 2. Use the quadratic formula: Solution:
 Quadratic_Equations/25096: please explaen me how to solve this equations 7n+2=4n+17 -2k+19=3k-11 solutions Answer 13467 by Earlsdon(6287)   on 2006-01-22 14:58:04 (Show Source): You can put this solution on YOUR website!The goal is to get the variable, n in this case, by itself onto one side of the equation using the standard rules of algebra. Solve: Notice that the variable n appears on both sides of the equation. You need to get the variable onto one side or the other. You can do this by subtracting 4n from both sides of the equation. (Remember, whatever you do to one side you must do exactly the same to the other side) Simplify. Now you need to isolate the term with the variable (3n) so you will subtract the 2 from both sides ot the equation. Simplify. We're almost there. You have 3n isolated but you really want just n, not 3n, so you must divide the 3n by 3 to get n by itself. And, of course you must divide the other side of the equation by 3 also. Simplify. There, we're done!
 Evaluation_Word_Problems/25094: I have a word problem I do not understand could someone PLEASE help? A toy airplane is 10 inches long. If the actual plane is 75ft. long, find the scale of the model.1 solutions Answer 13466 by Earlsdon(6287)   on 2006-01-22 14:46:48 (Show Source): You can put this solution on YOUR website!The scale would be found by dividing the given dimension of the model plane by the known dimension of the real plane. Be sure that the units are all the same. All in inches or all in feet. Let's use inches, so convert 75 feet to inches. (75 ft.)(12 in./ft) = 900 inches. The scale is: This is often written as: 1:90 The scale of the model is: 1:90