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Quadratic_Equations/147835: What does it mean when it says "find the quadratic equation where f(1)=2 and the maximum value of f is f(3)=-5"? 1 solutions Answer 108212 by Fombitz(13828)   on 2008-07-10 16:38:09 (Show Source): You can put this solution on YOUR website! A quadratic function has a general form of A quadratic function has a maximum value where its derivative equals 0. The derivative of f(x) is, So now add your values that you know, 1. and for the maximum value, 2. Generally, you need three points to solve for a quadratic equation. We can solve for the other two variables in terms of one variable. From eq. 2, 2. Then from eq.1, 1. So the general form of the solution is, There are some limits on a also. Since the value at x=3 is a maximum, then a<0. Here are three graphs for a=-.5,-1,-2 just to give a sense of the family of solutions.

Triangles/147838: I got an answer for this, but I'm not sure if i'm right. thanks!!!! Standing on a cliff 380 meters above the sea, Sue sees an approaching ship and measures its angle of depression, obtaining 9 degrees. How far from the shore is the ship? Now Sue sights a second ship beyond the first. The angle of depression of the second ship is 5 degrees. How far apart are the 2 ships? My answer was about 2399.226 meters away, and 1944.194 meters apart. 1 solutions Answer 108210 by Fombitz(13828)   on 2008-07-10 16:10:01 (Show Source): You can put this solution on YOUR website! Yes, you are correct.

Coordinate-system/147837: I don't understand this: find the value of k if the line joining (4,k) and (3,1) is parallel to the line y=-1/2x-9/2 1 solutions Answer 108209 by Fombitz(13828)   on 2008-07-10 16:06:38 (Show Source): You can put this solution on YOUR website! If lines are parallel, it means their slopes are equal. The line has a slope of (-1/2). The formula for the slope given two points is, For parallel lines, set the slope equal to (-1/2) and solve for k. Here is a graph of the line, the two points and the new line.

Linear-equations/147809: solve the system of equations by graphing.then classify the system as consistent or inconsistant, dependant or independant; 7x-8y=-16 8y-7x=16 1 solutions Answer 108194 by Fombitz(13828)   on 2008-07-10 11:13:14 (Show Source): You can put this solution on YOUR website! 1. 2. Rearrange eq. 2, and multiply by (-1), 2. 2. Eq. 1 and Eq. 2 are the same equation, consistent and dependent.

Quadratic-relations-and-conic-sections/147722: Please solve, show work and include all relevant points (i.e vertices, intercepts, foci,directrix,asymptotes, ect..) x^2-4y^2+2x=32y=67 1 solutions Answer 108193 by Fombitz(13828)   on 2008-07-10 11:09:09 (Show Source): You can put this solution on YOUR website! Complete the square in both x and y. This is an equation for a hyperbola which has a general form of Center of the hyperbola is (h,k) or in this case (-1,-4) Distance between the foci is 2c where The eccentricity,e, is then The foci of the hyperbola are located at (,)=(,) The vertices of the hyperbola are located at (,)=(,)=(-3,-4) and (1,-4) The equation of the asymptote lines is given by The directrix of a hyperbola is given by

Linear-equations/147804: find the indicated outputs for f(x)= 4x to the second power-5x f(0)=? f(-1)=? f(2)=? 1 solutions Answer 108192 by Fombitz(13828)   on 2008-07-10 10:08:34 (Show Source): You can put this solution on YOUR website! Wherever there is an x, replace it with the actual value, . . . . . . Here's a graph of the function, and the 3 points.

Linear-equations/147805: graph the equation using the slope and y intercept; y=7/5x+2 1 solutions Answer 108191 by Fombitz(13828)   on 2008-07-10 10:00:58 (Show Source): You can put this solution on YOUR website! The y intercept occurs when x=0. At x=0, then Plot (0,2) on the graph Now starting at (0,2) use the slope to find another point. Slope is rise (change in y) over run (change in x). Starting at (0,2) with a slope of (7/5) would give you, y:Starting y + Change in y=2+7=9 x:Starting x + Change in x=0+5=5 Plot (5,9) on the graph. Then draw the line joining the two points. To complete the graph, extend the line in both directions, from the points.

Linear-equations/147753: This question is from textbook use the echelon method to solve. x + y/3 = -6 x/5 + y/4 = -7/4 1 solutions Answer 108189 by Fombitz(13828)   on 2008-07-10 09:30:08 (Show Source): You can put this solution on YOUR website! 1. 2. or in matrix form, Multiply eq. 1 by (-1/5) and add to eq. 2, to remove x. 2'. 2'. Now your two equations, in echelon form, are 1. 2'. or in matrix form, You can solve for y from 2'. 2'. From 1, 1.

Exponential-and-logarithmic-functions/147790: g(x)=e^x+3 Description of transformation: Equation(s) from Horizontal Asymptote(s): y-intercept in (x,y) form: I am not sure what this is asking me to do? Help 1 solutions Answer 108188 by Fombitz(13828)   on 2008-07-10 08:51:42 (Show Source): You can put this solution on YOUR website! Here's a graph of your equation. Let me see if I can decipher what you need. . . . Horizontal asymptote. From the equation, as x becomes large (negative), the exponent term quickly goes to 0, as x approaches As x goes to negative infinity, the horizontal asymptote is y=3. It's shown here as the blue line. . . . The y intercept in (x,y) form is the point that the graph crosses the y axis. In that case and In (x,y) format that would be (0,4). The y-intercept is shown as the green circle.

Finance/147801: S-C = P P/S = M Can you solve for P ? 1 solutions Answer 108187 by Fombitz(13828)   on 2008-07-10 08:49:11 (Show Source): You can put this solution on YOUR website! 1. 2. You weren't specific in terms of which variables. 2. in terms of S and M. If you need in terms of C and M, then start with eq. 2, 2. Now substitute into eq. 1, 1.

Equations/147735: find the functions f and g so that h(x)=(f*g)(x) h(x)=sqrt(59x^2+78) 1 solutions Answer 108186 by Fombitz(13828)   on 2008-07-10 08:42:53 (Show Source): You can put this solution on YOUR website! One solution is, then

Linear-systems/147794: The solution to the system of equations: x + 3y = 12 4x - y = -17 1 solutions Answer 108185 by Fombitz(13828)   on 2008-07-10 08:37:28 (Show Source): You can put this solution on YOUR website! 1. 2. You didn't specify a method. We'll use substitution. Solve eq.1 for x in terms of y. 1. Now substitute this into eq. 2 and solve for y. 2. From eq. 1, The solution is x=-3 and y=5, also shown graphically.

Polynomials-and-rational-expressions/147796: f(x) = (x + 2)(2x - 3). f(-2) = 1 solutions Answer 108184 by Fombitz(13828)   on 2008-07-10 08:32:44 (Show Source): You can put this solution on YOUR website! Wherever there is an x, substitute -2.

Equations/147720: 2/x-3=5/x-2 1 solutions Answer 108109 by Fombitz(13828)   on 2008-07-09 16:38:37 (Show Source): You can put this solution on YOUR website!

Geometry_proofs/147598: The parallel sides of trapezoid ABCD are AD and BC. Given that sides AB, BC, and CD are each half as long as side AD, find the size of angle D. 1 solutions Answer 108108 by Fombitz(13828)   on 2008-07-09 16:33:40 (Show Source): You can put this solution on YOUR website! Length of AB = x Length of BC = x Length of CD = x Length of AD = 2x Draw two perpendicular lines from BC to AD at points B and C. These create new line BG and CH, and break up AD into AG, GH, and HD. The triangles ABG and CDH are right triangles and from the diagram BC=GH=x. Now you have a right triangle with hypotenuse of x and an adjacent leg of x/2. From trigonometry, Since ABG and CDH are identical, angle A and angle D are the same.

Age_Word_Problems/147671: A man and his brother have a combined age of 164 years. 46 years ago, the man was 7 times as old as his brother. How old is the man? How old is the brother? 1 solutions Answer 108041 by Fombitz(13828)   on 2008-07-09 11:13:20 (Show Source): You can put this solution on YOUR website! Man's age is M. Brother's age is B. 1. 46 years ago the man's age was M-46. 46 years ago his brother age was B-46. 2. We can use eq. 1 to solve for M in terms of B. Then substitute this into eq. 2. 1. Now substitute. 2. Then from eq. 1, The man is 109 years old and his brother is 55.

Numbers_Word_Problems/147664: hello again i have a problem i need help with. the sum of two numbers is 89 adding four times the first number to the second number gives 155 which one of the equations expresses this problem algebraically? A. (X-89)+4X=155 B. 89+4x=155 C.4x+(89-x)=155 D.4(89+x)+x=155 i picked B thank you for all of your help 1 solutions Answer 108034 by Fombitz(13828)   on 2008-07-09 10:24:25 (Show Source): You can put this solution on YOUR website! It would be more helpful if you wrote down the steps that got you to your answer. Anyways, let's go through it step by step. First name your unknown numbers. We'll use x and y. "The sum of two numbers is 89." 1. adding four times the first number to the second number gives 155 2. Now you have two equations. You can use eq. 1 to substitute for y in eq. 2, 1. Now substitute into eq. 2, 2. This line looks like C.

Functions/147653: Find the domain of f(x)=3x^2-6= 1 solutions Answer 108032 by Fombitz(13828)   on 2008-07-09 10:02:43 (Show Source): You can put this solution on YOUR website! The domain of a function is the values of x so that the function makes sense. THere is no x where the function doesn't make sense so the domain is, (,)

absolute-value/147656: A Go-ped traveled 9 miles in 24 minutes. How long would it take to go 27 miles? Thanks 1 solutions Answer 108031 by Fombitz(13828)   on 2008-07-09 09:53:53 (Show Source): You can put this solution on YOUR website! Set up a ratio. 9 miles is to 24 minutes as 27 miles is to X minutes. Mathematically it would look like this, It would take 72 minutes to go 24 miles.

absolute-value/147657: If y varies directly as x, and y = 16 when x = 20. Find y when x = 5. 1 solutions Answer 108028 by Fombitz(13828)   on 2008-07-09 09:51:31 (Show Source): You can put this solution on YOUR website! If y varies directly as x, then it fits a formula, From your examples, When x=5, then

Graphs/147659: Hope someone can help me with this. a. An financial advisor invested a total of $6,000, part at 4% annual simple interest and part at 6.5% annual simple interest. The amount of interest earned for 1 year was $335.00. How much was invested at each rate? Show work. b. Consider the equation 3x2 – 4x + 7 = 0. 1.Find the discriminant, b2 – 4ac, and then determine whether one real-number solution, two different real-number solutions, or two different imaginary-number solutions exist. 2. Use the quadratic formula to find the exact solutions of the equation. Show work. 1 solutions Answer 108027 by Fombitz(13828)   on 2008-07-09 09:47:24 (Show Source): You can put this solution on YOUR website! a.)Let's call the amount invested at 4%, A, and call the amount invested at 6.5%, B. What do we know? The total invested was $6000. 1. After one year the total interest was $335. 2. Let's multiply both sides of eq. 2 by 100 to get rid of denominators. 2. Now we can use eq. 1 to get A in terms of B and substitute into eq. 2, 1. Now substitute into eq. 2, 2. From eq. 1, . . . b1)3x2 – 4x + 7 = 0 The quadratic formula deals with an equation of the form, in your case, The discriminant is, Since the discriminant is negative, there are two imaginary, or complex roots, that solve the equation. . . . b2) The full quadratic formula is The exact solution is, The approximation is,

Linear_Algebra/147403: 1 solutions Answer 107840 by Fombitz(13828)   on 2008-07-07 15:05:45 (Show Source): You can put this solution on YOUR website! Please repost.

Linear_Algebra/147406: 1 solutions Answer 107838 by Fombitz(13828)   on 2008-07-07 15:05:20 (Show Source): You can put this solution on YOUR website! Please repost.

Rational-functions/147096: The question is to find the vertical and horizontal asymptote(s) of f(x)= (x^3+8)/(x^2+4) 1 solutions Answer 107438 by Fombitz(13828)   on 2008-07-02 16:17:13 (Show Source): You can put this solution on YOUR website! There are no vertical asymptotes, the denominator does not go to zero. There are no horizontal asymptotes, as x goes to infinity, the function looks like y=x, as you can see from the graph below. The second graph shows the behavior of the graph near zero.

Geometry_Word_Problems/147101: Please help me solve this word problem step-by-step. (((The Perimeter of the rectangular is 320ft if the length is 5ft longer than twice the width. Find its length and width.))) 1 solutions Answer 107437 by Fombitz(13828)   on 2008-07-02 16:14:15 (Show Source): You can put this solution on YOUR website! THe perimeter of a rectangle using length and width is given by, For your case, the length is 5 ft longer than twice the width. 1. You also know that 2. Solve eq. 1 for 2W and substitute into eq. 2, 1. Substitute into eq. 2 and solve for L. From eq. 1, Check your answers. True. True (off because of roundoff error). Your answers led to true statement. They are good answers.

Graphs/147097: The question is to find the vertical and horizontal asymptote(s) f(x)=(x^3+3x^2)/(x^2-4) 1 solutions Answer 107435 by Fombitz(13828)   on 2008-07-02 16:06:08 (Show Source): You can put this solution on YOUR website! Vertical asymptotes occur whenever the denominator goes to zero. In this case, when and There are no horizontal asymptotes for this function. As x goes to positive and negative infinity, the graph begins to look like y=x.

Geometry_Word_Problems/147098: Please help me to solve this word problem in step-by-step process.(((Ron found that his car used 7 gallons of gas to travel 200 miles. He plans to drive 1300 miles from his home to Denver, Colorado. How many gallons of gas will he use if his car continues to consume gas at the same rate? Round to the nearest gallon.))) 1 solutions Answer 107434 by Fombitz(13828)   on 2008-07-02 15:56:44 (Show Source): You can put this solution on YOUR website! Set up a ratio. 7 gallons is to 200 miles as x gallons is to 1300 miles. Mathematically, that is, To the nearest gallon, that would be 46 gallons.

Equations/147022: Add or subtract the fractions. Express the answer in simplest form: A: [4/(x-2)]+[3/x^2-x-2] B: [4y/(y^2+6y+5)]-[2y/(y^2-1)] 1 solutions Answer 107404 by Fombitz(13828)   on 2008-07-02 10:39:25 (Show Source): You can put this solution on YOUR website! A: Remember, to add or subtract fractions you need a common denominator. Luckily, So you can multiply, the first term by (x+1)/(x+1) to get it done. A: A: A: A: B: Let's look at both denominators and factor them. First term denominator: Second term denominator: Multiply the first term by (y-1)/(y-1) and then multiply the second term by (y+5)/(y+5) to get the common denominator (y+1)(y-1)(y+5). B: B: B: B:

Graphs/147063: Hello, I need help solving equation like the following: 0.7(3x + 4) ≥ 1.3 – (x+2) I know I remove the parentheses by multiplying 2.1x + 2.8 ≥ -1.3x? + -2.6 I am not sure if I multiply –x and -2 by 1.3 if so, I have I add 1.3x to each side and get 3.4x and subtract 2.8 from each side and get 3.4x ≥ - 5.4 Divide both sides by 3.4 X = -5.4 OR 1.6 rounded. I know this is incorrect but where did I go wrong? 3.4 Thank you for your help. 1 solutions Answer 107403 by Fombitz(13828)   on 2008-07-02 10:11:36 (Show Source): You can put this solution on YOUR website! Left hand side is OK, but what happened on the right hand side? To get rid of the decimals, multiply both sides by 10. I'll let you take it from there. If you get stuck again, re-post a question.

Money_Word_Problems/147066: Examine the rise in gasoline prices from 1997 to 2006. The price of regular unleaded gasoline in January 1997 was $1.26 and in January 2006 the price of regular unleaded gasoline was $2.31 (Bureau of Labor Statistics, 2006). Use the coordinates (1997, 1.26) and (2006, 2.31) to find the slope (or rate of change) between the two points. Describe how you arrived at your answer 1 solutions Answer 107402 by Fombitz(13828)   on 2008-07-02 10:07:44 (Show Source): You can put this solution on YOUR website! The slope or rate of change would be the change in gas price (in dollars) divided by the change in time (years in this case). In equation form, where GP is gas price and Y is year. The units of the rate of change are $/year. On average, the price of gas from 1997 to 2006 rose almost 12 cents per year.

Graphs/147067: Show the graph for f(x)=(x-2)^2 Thank you 1 solutions Answer 107401 by Fombitz(13828)   on 2008-07-02 10:02:09 (Show Source): You can put this solution on YOUR website!