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 Exponents-negative-and-fractional/88323: Hello, I'm having a bit of a difficult time figuring out if I have done this problem correctly, and would greatly appreciate if someone could tell me if I've solved it correctly or if I am way off track, and show me what I need to do. Here is the original problem that I have to solve: 9/(x-5) - 1 = 8/(x+5). Here's the solution that I've come to: First, I moved 8/x+5 to the left, so that the equation read like this: 9/x-5 -1 -8/x+5 = 0. Then, I moved -1 to the right of the equation, so that it read like this: 9/x-5 - 8/x+5 -1 =0, which I think is the solution to the problem, right? Is there further solving or simplifying involved that I'm overlooking or is my solution correct? Thank you very, very much in advance for your help! 1 solutions Answer 64150 by Earlsdon(6287)   on 2007-07-13 13:35:59 (Show Source): You can put this solution on YOUR website!Ok, your first move was good! So you have: Now add 1 (move the -1 to the right side) to both sides. Now add the two fractions on the left side. The LCD is so you now have: Simplify the numerator. Continue to simplify. Now multiply both sides by to get: Expand the right side. Now subtract from both sides. or This can be factored: Apply the zero products principle to get: or These are the solutions! Let's check the solutions by substituting the solutions, one-by-one into the original equation: Substitute x = -10. Reduce the fraction on the left side. It checks! Try the other solution yourself and see how you do.
 Quadratic_Equations/88166: Can someone show me how to do this problem with step by step instructions. Thank you The height h in feet of an object after t seconds is given by the function h=16t^2+90t+8. How long will it take the object to hit the ground? Round your answer to the nearest thousandth.1 solutions Answer 64014 by Earlsdon(6287)   on 2007-07-12 11:36:08 (Show Source): You can put this solution on YOUR website!The height of an object propelled upwards with an initial velocity of from an initial height of is given by: Notice that the coefficient of the first term is negative, due to the downward effect of gravity.. In your equation (corrected): The initial upward velocity is and the initial height is To find out how long before the object hits the ground set your equation = 0 and solve for the time, t. Because the equation is a quadratic, you will, of course, get two answers for t. One will be for when the object would have started from the ground (h=0), but because the initial height is 90 feet and not zero feet, this answer will be negative. The other answer will be the one you want because it will show the time that the object reaches the ground after rising then falling. You can use the quadratic formula to solve for t. and in this problem, a = -16, b = 90, and c = 8. Making the appropriate substitutions, we get: Simplifying this: Evaluating this: or Discard the negative solution. Answer is: t = 5.713 seconds.
 Polynomials-and-rational-expressions/87996: I am so lost. What am I overlooking? The problem is : (1-3y / y) / ((9/y^2)-1)1 solutions Answer 63880 by Earlsdon(6287)   on 2007-07-11 14:45:27 (Show Source): You can put this solution on YOUR website!Simplify: First, simplify the denominator. Invert the denomiator and multiply. Cancel a y in the top and bottom.
 Miscellaneous_Word_Problems/87997: The volume of a right circular cone of radius r and height r is given by V= pi/3 x r^3. How fast is the volume changing with respect to the changes in r when the radius is equal to 2 feet? 1 solutions Answer 63878 by Earlsdon(6287)   on 2007-07-11 14:27:03 (Show Source): You can put this solution on YOUR website!The volume of the right circular cone of radius r and height r is given by: The change in volume with respect to r is: and when r = 2, then:
 Graphs/87898: f(x) = -x -2 I'm not sure where to start1 solutions Answer 63761 by Earlsdon(6287)   on 2007-07-10 17:24:58 (Show Source): You can put this solution on YOUR website!Well, to answer the question..."Where do I start" you first need to ask..."Where do I want to go?" What do you want to do with this function?
 Graphs/87899: find the slope and y intercept y= -4x - 91 solutions Answer 63760 by Earlsdon(6287)   on 2007-07-10 17:22:21 (Show Source): You can put this solution on YOUR website!Find the slope and y-intercept: You equation is already in the "slope-intercept" form: so you can read the slope, m, and the y-intercept, b, directly from the equation. The slope, m = -4 The y-intercept, b = -9 If you were to graph this linear equation, you would see the y-intercept.
 Quadratic_Equations/87894: Could someone help me please? The problem is: A ball is thrown upward from the roof of a building 100m tall with an initial velocity of 20m/s. When will the ball reach a height of 80m?1 solutions Answer 63759 by Earlsdon(6287)   on 2007-07-10 17:05:38 (Show Source): You can put this solution on YOUR website!Well, you can start with the function that gives the height, as a function of time, h(t) of an object propelled upward with an initial upward velocity of m/s from an initial height of m. In this problem: m. m/s. You would like to know at what time, t, will h = 80 meters. Making the appropriate substitutions into the formula: Subtract 80 from both sides. Solve this quadratic equation using the quadratic formula: In this equation, a = -4.9, b = 20, and c = 20 Simplifying this, you'll get: Evaluating this gets you: or Discard the negative solution. seconds.
 Graphs/87879: This is my first time on this site and the problem looks easy but I am really having the blues. Graph y=3x=4 and y=-1/3x-4 determine whether the two lines are parallel,perpendicular ot neither.The teacher taught it this way but I am still having a hard time with it. 1 solutions Answer 63738 by Earlsdon(6287)   on 2007-07-10 14:28:19 (Show Source): You can put this solution on YOUR website!I assume that there is a typo in the first equation since you have written: y=3x=4 and it most likely should be: (Red line on the graph) The second equation is: (Green line on the graph) Graph these two equations. You can determine the answers from the graph.
 Polynomials-and-rational-expressions/87841: find the length of x its a triangle right side is 51 ft left side is x and bottom is 45 ft1 solutions Answer 63736 by Earlsdon(6287)   on 2007-07-10 13:04:22 (Show Source): You can put this solution on YOUR website!With the limited information you have supplied, x could be any number with the following constraints: Do you see why this is so? Imagine two sticks, one 51 ft. long and the other 45 ft. long. Imagine that these sticks are joined at one end by a hinge that allows you to open and close them like a door. Well, let's say that you can join the two unconnected ends together with another stick whose length is x ft to form a triangle. You can easily see that the length of x depends entirely upon how wide open the two sticks are, doesn't it? So, to find the length of x, you need to provide an angle. Is the triangle a right-triangle? If it is, then you can use the Pythagorean Theorem to figure out the length of x. Let's assume that you forgot to mention that it is a right triangle. We can find the length of x using the Pythagorean Theorem: But to do this, we have to make another assumption about which side is the hypotenuse...is it 51 ft. or is it x ft. (It can't be 45 ft because the hypotenuse of a right triangle is always the longest side). Let's assume that x is the hypotenuse, then: feet. Now let's assume that 51 ft is the length of the hypotenuse, then: feet.
 Radicals/87858: I need to solve the following and I know the answer is 8x^3 but I can't seem to figure it out. Please help. Square root of 2x multiplied by square root of 32x^5.. THANK YOU! 1 solutions Answer 63719 by Earlsdon(6287)   on 2007-07-10 12:24:03 (Show Source): You can put this solution on YOUR website!Simplify: Recall that: Apply this to your problem: Simplify. Rewrite this as: Now you can take the square root of the squared quantities out from under the radical, because: so you get:
 Polynomials-and-rational-expressions/87862: assume x represents a positive number square root of 75x^41 solutions Answer 63716 by Earlsdon(6287)   on 2007-07-10 12:14:43 (Show Source): You can put this solution on YOUR website!What would you like to do with this? Simplify it? Simplify: Factor whatever you can under the radical to get: rewrite this as: Take the squared quantitites out from under the radical: ...and there you have it!
 Exponential-and-logarithmic-functions/87836: This question is from textbook hello, i am having trouble with this problem is says to simplify the expression and that your answer must be in fraction form. Also all exponents must be positive. simplify: 3^-7 x^3 y^6/3^8 x^6 y^6 this is what i figured out so far:3^-7 x^3 y^6/3^* x^6 Y^6 3^7 x^3 x^6/ 3^81 solutions Answer 63712 by Earlsdon(6287)   on 2007-07-10 11:25:31 (Show Source): You can put this solution on YOUR website!Simplify: The can be put in the denominator as and you can cancel the 's to leave you with: Finally, add the exponents on the 3's and subtract the exponents on the x's so that you end up with: ...and if you have to evaluate: your answer would be:
 Linear-equations/87837: I have been trying for days now to solve this problem. It is really tricky because I got the top but not the bottom or I got the bottom nuber but not the to. I need help!!! The problem goes like this: Determine k so that the line through(k+2,k) and (3,2) has slope of 3. Can you explain to me how to do it?1 solutions Answer 63711 by Earlsdon(6287)   on 2007-07-10 11:10:45 (Show Source): You can put this solution on YOUR website!You can start with the formula for finding the slope, m, of a line that passes through two points, (x1, y1) and (x2, y2): You are given the slope, m = 3. And the two points are: (x1, y1) = (k+2, k) and (x2, y2) = (3, 2) Now if you substitute the given values into the formula, you can solve for k. Simplify this. Notice the change of sign on the 2 in the denominator. Now multiply both sides by (1-k). Apply the distributive property on the left side. Add 3k to both sides. Subtract 2 from both sides. Finally, divide both sides by 2. Answer is: Let's check the answer by substituting into the slope formula. Simplifying this, we get: ...and this is the expected slope!
 Miscellaneous_Word_Problems/87623: Please i need help on this question: If one angle of a triangle is tree times a second angle and the third angle is 20 degrees more than the second angle, the SECOND ANGLE is.....1 solutions Answer 63526 by Earlsdon(6287)   on 2007-07-08 23:23:00 (Show Source): You can put this solution on YOUR website!Let the angles be A, B, and C. From the problem description, you can write: A = 3B "One angle is 3 times a second." C = B+20 "The third angle is 20 degrees more than the second angle." So, we are looking for the measure of angle B, the second angle. You already are aware that, in any triangle, the sum of the angles is 180 degrees, so you can write: A + B + C = 180 Now substitute for A and C their equivalent values from above: (3B) + B + (B+20) = 180 Simplify and solve for B. 5B + 20 = 180 Subtract 20 from both sides. 5B = 160 Divide both sides by 5. B = 32 degrees. Check: A+B+C = 180 3(32)+32+(32+20) = 180 96+32+52 = 180 180 = 180 Check!
 Rational-functions/87625: Given the functions f(x)=sqrt-3x+15 and g(x)=5/x, determine g * f(x) and find its domain. *please note that the question has a small o where I have placed an * symbol. I am not sure what that means. Please someone help me.1 solutions Answer 63525 by Earlsdon(6287)   on 2007-07-08 23:11:27 (Show Source): You can put this solution on YOUR website!Given: and , determine What you are being asked to determine is "the composite of g and f" This can also shown be as These are both read as "g of f of x" and it is really a function of a function. Here's how it works: You are given that: so when you are asked for g(f(x)) you are being asked for: so in the function you would substitute to get: You are also being asked to find the domain which is the set of all possible values of the independent variable, in this case, that's x. You have to look at the denominator of the composite to see that, if x were equal to 5, the the denominator would becom zero, and this is not permissable because division by zero is undefined.. So x = 5 is an excluded value of the domain. Also you should notice that if x > 5, the denominator would become a complex number so it looks like the domain, x, can be any real number that is less than 5, or x < 5.
 Quadratic_Equations/87565: Write the equation of a line in slope intercept form given the following points (-3 7) and (4 -7) Kind of confused here. Can you help?1 solutions Answer 63492 by Earlsdon(6287)   on 2007-07-08 18:46:35 (Show Source): You can put this solution on YOUR website!Write the equation in slope-intercept form: for the line containing the two points (-3, 7) and (4, -7). You can find the slope, m, by: where: (, ) = (-3, 7) and (, ) = (4, -7) So now you have: Next, you need to find the value of the y-intercept, b. To do this, you will substitute the x- and y-coordinate values from either one of the two given points into this equation and solve for b. Let's choose the second point (4, -7) so we'll substitute x = 4 and y = -7 and solve for b. Simplify. Add 8 to both sides. Now you can write the final equation in the point-slope form. ...and there it is! And here's what the graph of this line would look like:
 Equations/87563: This question is from textbook Beginning Algebra Tutor Please Help...This question is from a textbook and I keep getting different answers. Solve for x and check your result: 6x-1 over 5 minus 2x over 3 = 3 6x-1/5 - 2x/3 = 3 Sorry I am not sure how to do the fractions I will try and type it below 6x-1 - 2x ----------------- = 3 5 3 I have come up with 1.5, 2.1, & 6 I am thinking 6 may be close but I can not get any numbers so far to come out properly when I check. Any insight into this problem would be greatly appreciated. Thank you. 1 solutions Answer 63488 by Earlsdon(6287)   on 2007-07-08 18:15:40 (Show Source): You can put this solution on YOUR website!Solve for x: First,multiply through by the LCD of 15. Simplify. Combine like-terms. Add 3 to both sides. Divide both sides by 8. Check: Substitute x = 6 Simplify. Check!
 Polynomials-and-rational-expressions/87554: He there im stuck on a problem I cant figure out. Simplify by removing a factor equal to 1 8y^5 z^3 / 4y^9 z^41 solutions Answer 63471 by Earlsdon(6287)   on 2007-07-08 14:42:09 (Show Source): You can put this solution on YOUR website!Simplify: Factor from numerator and denominator. The answer is:
 Quadratic_Equations/87519: Solve using the square root method or quadratic formula. 20x^2 - 31x-9 =0 I cant figure this one out because the numbers are so big, can you help me please? 1 solutions Answer 63463 by Earlsdon(6287)   on 2007-07-08 10:40:44 (Show Source): You can put this solution on YOUR website!Solve for x: Use the quadratic formula: Here, a = 20, b = -31, and c = -9 ...and + or -, so... or or or
 real-numbers/87499: S is 1/4 if the age of father. in 12 years he will be 2/5 of the age of father so what is their ages now? please show me the equations to solve.1 solutions Answer 63420 by Earlsdon(6287)   on 2007-07-07 12:01:27 (Show Source): You can put this solution on YOUR website!Let S = age of S and F = age of father. 1) "S is 1/4 of the age of father". 2) "In 12 years (S+12) he will be 2/5 of the age of father (F+12)". Substitute the S from eqation 1) into equation 2) and solve for F. Simplify. Multiply through by the LCD of 20 to clear the fractions. Subtract 5F from both sides. Subtract 96 from both sides. Finally, divide both sides by 3. So, Father's present age is 48 years. So, S's present age is 12 years.
 Signed-numbers/87459: How do I solve 4-2(x-4)>5x-(2x+3)?1 solutions Answer 63383 by Earlsdon(6287)   on 2007-07-06 20:36:42 (Show Source): You can put this solution on YOUR website!Solve: Apply the distributive property. Combine like-terms. Add 2x to both sides. Add 3 to both sides. Finally, divide both sides by 5. or
 Coordinate-system/87431: What does the graph of the Linn x+y= 1 look like?1 solutions Answer 63354 by Earlsdon(6287)   on 2007-07-06 17:10:37 (Show Source): You can put this solution on YOUR website!It looks like this!
 real-numbers/87415: Can someone help me show the number is rational by writing it as a quotient of two integers: 22 1 solutions Answer 63348 by Earlsdon(6287)   on 2007-07-06 14:58:55 (Show Source): You can put this solution on YOUR website!22 = 22/1
 real-numbers/87417: Can someone help me show the number is rational by writing it as a quotient of two integers: -1 1/31 solutions Answer 63347 by Earlsdon(6287)   on 2007-07-06 14:58:21 (Show Source): You can put this solution on YOUR website!-1 1/3 = -4/3
 Polynomials-and-rational-expressions/87289: 5x divided by 8y subtracted from 3x divided by 5y 1 solutions Answer 63235 by Earlsdon(6287)   on 2007-07-05 11:38:10 (Show Source): You can put this solution on YOUR website! The LCD is 40y. Simplify.
 Expressions-with-variables/87242: Translate this sentence into mathematical symbols: five more than ten times a number equals its square root.1 solutions Answer 63184 by Earlsdon(6287)   on 2007-07-04 10:47:38 (Show Source): You can put this solution on YOUR website!Let n = the number.
 Miscellaneous_Word_Problems/87236: Please solve the problem, if possible step by step A rock falls from a tower that is 73.5 m high. As it is falling, its height is given by the formula h = 735 - 4.9t^2, with t in seconds. How many seconds will it take for the rock to hit the ground (h = 0)? Question 10 answers 8.3 sec 3.9 sec 1102.5 sec 8.6 sec1 solutions Answer 63183 by Earlsdon(6287)   on 2007-07-04 10:11:47 (Show Source): You can put this solution on YOUR website!Given where 73.5 meters is the initial height of the rock, how long before it hits the ground? Set h(t) = 0 and solve for t. Add to both sides. Divide both sides by 4.9 Now take the square root of both sides. seconds. The best choice of answers is: 3.9 seconds.
 Numeric_Fractions/87211: Hey everyone this is a complex fraction. x/4 - 4/x ________ 1 - 4/x My solution is: x+4/4 Thanks for your help. 1 solutions Answer 63156 by Earlsdon(6287)   on 2007-07-03 21:25:52 (Show Source): You can put this solution on YOUR website!Good work! Your answer is correct! Simplifying the numerator and the denominator: Factor the top numerator and simplify.
 Inequalities/87199: how can I graph this equation where I am using the distance formula d=vt 50mi=x(1/2) I supposed to graph my answer to depict the variables in my situation. This is my situation: We were traveling to the valley over the weekend, after traveling 50 miles at a constant speed for 1/2 hour we were pulled over by a state trooper and wrote us a ticket for speeding. How fast were we traveling? My answer is (2/1)(50/1)=x(1/2)(2/1) x= 100 mph and with this answer I need help to make a graph were I can proof my situation!1 solutions Answer 63155 by Earlsdon(6287)   on 2007-07-03 21:15:37 (Show Source): You can put this solution on YOUR website!Well, at that speed, you desewrved the ticket! Your answer for the speed is correct, but let's get to the graph. First, you need to identify the dependent and independent variables. Since the distance is dependent upon the speed (x) at which you are trveling (for a constant time), speed is the dependent variable. Let's call this D (for Distance) So the independent variable would then be speed or x. And the time is a constant 1/2 hour. So you could write: If you were to graph this, you'd get: Where the horizontal axis is speed and the vertical axis is distance.
 Polynomials-and-rational-expressions/87208: solve as quaditic equations 4x^2=13x+121 solutions Answer 63153 by Earlsdon(6287)   on 2007-07-03 20:49:37 (Show Source): You can put this solution on YOUR website!First, write the equation in standard form: Solve by factoring. Apply the zero products principle. or Therefore: Or
 Linear_Equations_And_Systems_Word_Problems/87146: the denominator of a fraction exceeds the numerator by 1. If 4 is added to the numerator and 3 is subtracted from the denominator, the result is 7. Find the original fraction. I'm getting x+4/(x+1)-3. Is this even right and if it is what do I do now?1 solutions Answer 63095 by Earlsdon(6287)   on 2007-07-03 11:36:54 (Show Source): You can put this solution on YOUR website!What you have done is correct so now you need to follow the diections in the problem which say -"...the result is 7" So... Simplify. Multiply both sides by (x-2) Subtract x from both sides. Add 14 to both sides. Finally, divide both sides by 6. The original fraction is: