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Expressions-with-variables/340028: write an expression for the pattern 10+1,10+2,10+3... 1 solutions Answer 243681 by solver91311(16872)   on 2010-09-07 18:03:35 (Show Source): You can put this solution on YOUR website! John My calculator said it, I believe it, that settles it

Radicals/340013: Please help by multiplying: (6+√7)(6-√7) 1 solutions Answer 243679 by solver91311(16872)   on 2010-09-07 18:02:34 (Show Source): You can put this solution on YOUR website! Just use FOIL like multiplying any pair of binomials. Hint: This is a conjugate pair, so the result will be the difference of two squares. John My calculator said it, I believe it, that settles it

Quadratic_Equations/340006: How do you know if a quadratic equation will have one, two, or no solutions? How do you find a quadratic equation if you are only given the solution? Is it possible to have different quadratic equations with the same solution? Explain. Provide your classmate’s with one or two solutions with which they must create a quadratic equation. 1 solutions Answer 243678 by solver91311(16872)   on 2010-09-07 17:59:30 (Show Source): You can put this solution on YOUR website! The first part of your question is easy. There are ALWAYS two solutions, if you count the multiplicity. The Fundamental Theorem of Algebra says so. However, evaluate the discriminant to determine the nature of the roots. For any quadratic polynomial equation of the form: Find the Discriminant, and evaluate the nature of the roots as follows: No calculation quick look: If the signs on and are opposite, then guaranteed. Two real and unequal roots. If is a perfect square, the quadratic factors over . One real root with a multiplicity of two. That is to say that the trinomial is a perfect square and has two identical factors. A conjugate pair of complex roots of the form where is the imaginary number defined by +----------+----------+----------+----------+----------+----------+----------+ is a solution of the quadratic equation: if and only if is a factor of the quadratic polynomial: So, just take your given solution, whatever it is, and form a binomial factor by subtracting from x. Do this for each of your solutions. If you are told there is only one solution, say, out loud, "Ok, there is a pair of identical solutions" and create two identical factors. If you are given one irrational solution, remember that irrational solutions always come in conjugate pairs. If you are given as a solution, then you know that must also be a solution. The conjugate trick works for complex roots (the ones that involve that you get when ) also. Once you have your two factors, multiply them together using our old friend FOIL, and set the result equal to zero. That will give you one possible quadratic equation with the given roots. +----------+----------+----------+----------+----------+----------+----------+ It is most assuredly possible. In fact, for any pair of solutions, real or otherwise, there is a set of quadratic equations with infinite elements. If is the solution set of the quadratic equation Then is the solution set of every quadratic equation of the form: where John My calculator said it, I believe it, that settles it

Distributive-associative-commutative-properties/339996: is 3+(m*10)=3+(10m) commutative property of addition, multiplication, or associative property of addition or multiplication.? 1 solutions Answer 243673 by solver91311(16872)   on 2010-09-07 17:30:13 (Show Source): You can put this solution on YOUR website! When you commute to work, you go from one place to the other, i.e. work to home. The and the moved from one place to the other, and the and the are multiplicands -- that is, they are multiplied together. John My calculator said it, I believe it, that settles it

logarithm/339999: 6 loga m + 9 loga n Both the a's should be lowered down. Any advice on solving this? 1 solutions Answer 243672 by solver91311(16872)   on 2010-09-07 17:26:38 (Show Source): You can put this solution on YOUR website! Depends on what you mean by "solve" it. John My calculator said it, I believe it, that settles it

Linear-equations/340001: the equation c=35h+60 describes a painter's charge c, for a job that takes h hours. which statement is true 1 solutions Answer 243671 by solver91311(16872)   on 2010-09-07 17:25:38 (Show Source): You can put this solution on YOUR website! Gee, did you expect us just to guess what the statements are? John My calculator said it, I believe it, that settles it

Expressions-with-variables/339993: three times the sum of x and y increased by twice the sum of x and y 1 solutions Answer 243670 by solver91311(16872)   on 2010-09-07 17:24:24 (Show Source): You can put this solution on YOUR website! Fascinating. What did you want to do with it? Did you read and understand the part of the instructions for posting questions on this site that says you need to give a clear and complete explanation of what it is you want? Does it make any sense to you at all when we tell you we aren't mind-readers? John My calculator said it, I believe it, that settles it

Miscellaneous_Word_Problems/339923: A ball is thrown straight upward at an initial speed of 136 feet per seconds. From Physics it is known that, after t seconds, the ball reaches a height h feet given by the formula h=-16t2+136t. Answer the following questions: 1. The ball reaches the height of 26.56nft after t1=____________seconds and t2=___________seconds (with t1≤t2). 2. Does it reach the height of 389 feet ? (Y or N) 3. The greatest height reached by the ball is ____________________feet. 4. The ball reaches the highest point after t=_________seconds. 5. The ball hits the ground after t=__________seconds 1 solutions Answer 243625 by solver91311(16872)   on 2010-09-07 15:59:37 (Show Source): You can put this solution on YOUR website! Set the function equal to the specific height you wish to find the time for and the solve the resulting quadratic equation. The two roots will answer both parts of question 1. Question 2. Answer question 3 first. If the answer to question 3 is greater than or equal to 389, then the answer to question 2 is Yes, otherwise it is no. Question 3. First answer Question 4. Substitute the value from question 4 into the function to calculate the maximum height. Question 4. Use the formula for the x-coordinate of the vertex of a parabola. . Question 5. Set the function equal to zero and solve for . You are looking for the non-zero root here. John My calculator said it, I believe it, that settles it

Angles/339924: if the measure of an angle is represented by 4X, hte measure of its supplement is represented by? 1 solutions Answer 243616 by solver91311(16872)   on 2010-09-07 15:48:31 (Show Source): You can put this solution on YOUR website! the supplement of is given by John My calculator said it, I believe it, that settles it

Numbers_Word_Problems/339925: the sum of three consecutive odd integers is 165? What are the intergers? 1 solutions Answer 243613 by solver91311(16872)   on 2010-09-07 15:45:00 (Show Source): You can put this solution on YOUR website! Let represent the first odd integer. Then the next consecutive odd integer is , and the one after that is The sum of the three is 165: Solve for John My calculator said it, I believe it, that settles it

Miscellaneous_Word_Problems/339928: A ball is thrown straight upward at an initial speed of 149 feet per second. h=-16⁢t2+149⁢t When does the ball reach the highest point? 1 solutions Answer 243609 by solver91311(16872)   on 2010-09-07 15:40:57 (Show Source): You can put this solution on YOUR website! is only true if the ball was launched from the ground at 149 feet per second initial velocity. Typically when you throw something upward, the ball is above the ground by a distance that is in proportion to the thrower's height. Be that as it may, the function describes a parabola opening downward. The maximum height is reached at the value of for the vertex of the parabola. Use where and By the way, 149 feet per second is roughly 101.5 miles per hour, very close to the top speed of a pitched baseball. Find me the guy who can throw a ball straight up at that velocity. John My calculator said it, I believe it, that settles it

Linear-equations/339900: Find the equation for (4,2) (1,3) 1 solutions Answer 243595 by solver91311(16872)   on 2010-09-07 15:22:41 (Show Source): You can put this solution on YOUR website! Do you mean "Find an equation that represents the line passing through the points..."? Use the two-point form of an equation of a straight line: where and are the coordinates of the given points. John My calculator said it, I believe it, that settles it

Expressions-with-variables/339902: Is it possible to subtract this any further? 1 solutions Answer 243552 by solver91311(16872)   on 2010-09-07 13:57:01 (Show Source): You can put this solution on YOUR website! The best you can do is: Which may or may not be a simplification depending on your application. John My calculator said it, I believe it, that settles it

Evaluation_Word_Problems/339814: Find a formula that calculates the number of songs S that can be stored on x gigabytes. 1 solutions Answer 243550 by solver91311(16872)   on 2010-09-07 13:54:48 (Show Source): You can put this solution on YOUR website! Where represents the average length of a song in gigabytes. John My calculator said it, I believe it, that settles it

Systems-of-equations/339885: I am not sure how to set up this problem: The average monthly high temperature (in degrees Fahrenheit) in Cincinnati for the first 10 months of the year can be modeled by the equation where x = 1 corresponding to January. What month is the high temperature most likely to be close to 75 degrees? Thank you so much (I am encouraged to use a TI84 graphing calculator, but that is new to me so I am having trouble with that as well.) Beth 1 solutions Answer 243548 by solver91311(16872)   on 2010-09-07 13:45:48 (Show Source): You can put this solution on YOUR website! The "right" way to do this is to set your function equal to 75 and solve for . Your function is a bit odd in that you have two terms, which lead me to suspect that you have a small typo and that you really meant: And using the equation solver at QuickMath.com, you get April if you use your rendering, and March if you use mine. Can't say which is more correct since I don't really know the climate in Cincinnati. But then I got to digging a little deeper and found that there is something very, very wrong with your model. Even using your rendering of the exponents, the average high temperature in September (month 9) would be 253 degrees. Get your model right and let me know, we'll talk about where you need to go from here. John My calculator said it, I believe it, that settles it

percentage/339891: What percent of 460 is 138? 1 solutions Answer 243542 by solver91311(16872)   on 2010-09-07 13:22:36 (Show Source): You can put this solution on YOUR website! Divide 460 by 138 and then move the decimal point two places to the right. John My calculator said it, I believe it, that settles it

Age_Word_Problems/339866: please help me with this word problem! when katie is twice as old as she is now,she will be three times as old as she was three years ago. how old is she now? please can you help me! many thanks 1 solutions Answer 243540 by solver91311(16872)   on 2010-09-07 13:21:19 (Show Source): You can put this solution on YOUR website! Let represent Katie's age now. Three years ago she was . When she is twice as old as she is now she will be and that is equal to three times what she was three years ago, or . So: Solve for John My calculator said it, I believe it, that settles it

Exponents/339875: How do I solve with x as power? 2^x+4 = 4(16^x) 1 solutions Answer 243534 by solver91311(16872)   on 2010-09-07 13:15:06 (Show Source): You can put this solution on YOUR website! Use logarithms. Any base will do in the final analysis, but the arithmetic will be neater in this case if you use base 2. First, I will make the assumption that you mean: as opposed to: First note that Hence your equation becomes: Now take the base 2 logarithm of both sides: Use the following laws of logarithms to simplify the equation: Next note that So: But also recall that: So we can say: and then: Which you can solve by ordinary means. John My calculator said it, I believe it, that settles it

Exponential-and-logarithmic-functions/339871: How do I solve with a fraction as power? x^3/4 = -8 1 solutions Answer 243524 by solver91311(16872)   on 2010-09-07 12:51:27 (Show Source): You can put this solution on YOUR website! Take the cube root of both sides: Raise both sides to the fourth power: Or, if you happen to be a arithmetic masochist, Raise both sides to the fourth power: Take the cube root of both sides: Bear in mind if you try to work this backwards from the solution to get the original problem, you are going to end up with an either/or situation because: John My calculator said it, I believe it, that settles it

Radicals/339869: Can you please show me the correct graph for the following equation: y=log_4(x+2) thank u 1 solutions Answer 243521 by solver91311(16872)   on 2010-09-07 12:43:58 (Show Source): You can put this solution on YOUR website! Vertical asymptote: John My calculator said it, I believe it, that settles it

Equations/339857: d=x/x-w i don't understand this problem and x-w is over x not x/x Thanks 1 solutions Answer 243518 by solver91311(16872)   on 2010-09-07 12:27:17 (Show Source): You can put this solution on YOUR website! Do you mean: ? What is it you don't understand? What have you been asked to do with this relationship? John My calculator said it, I believe it, that settles it

Equations/339862: IF b and c are positive numbers and 1/b = b/c = c/8 then b+c = ?? (A)4 (B)6 (C)7 (D)8 (E)9 Could you explain the above problem. Thanks 1 solutions Answer 243517 by solver91311(16872)   on 2010-09-07 12:21:36 (Show Source): You can put this solution on YOUR website! Cross-multiply: Then Cross-multiply: Substitute: Multiply by Take the cube root: Substitute: Hence and John My calculator said it, I believe it, that settles it

Volume/339860: A box with a square base has a surface area (including the top) of 3m^2. Express the volume V of the box as a function of the width w of the base 1 solutions Answer 243515 by solver91311(16872)   on 2010-09-07 12:14:11 (Show Source): You can put this solution on YOUR website! No can do. You would be able to do this if the box were perfectly cubical, that is: . But since you only guaranteed that the base of the box was square, i.e. , any Volume function would have to include both AND as variables. John My calculator said it, I believe it, that settles it

Travel_Word_Problems/339858: A truck enters a highway driving 60 mph. A car enters the highway at the same place 8 minutes later and drives 75 mph in the same direction. From the time the car enters the highway, how long will it take the car to pass the truck? 1 solutions Answer 243514 by solver91311(16872)   on 2010-09-07 12:08:50 (Show Source): You can put this solution on YOUR website! 60 miles per hour is one mile per minute. If the car enters the highway 8 minutes after the truck passes, the truck has to be 8 miles ahead. The first 60 mph of the car's speed is used in just keeping up with the truck, so the additional 75 - 60 = 15 mph is what is used to catch up to the truck. How long does it take a car going 15 mph to go 8 miles? John My calculator said it, I believe it, that settles it

Probability-and-statistics/339819: Suppose that you are playing a game of Scrabble and the remaining letters in the bag are ADKNSTVZ. If it is your turn to play and there is a C available for use on the board and you have a BXLE, needing to draw 3 letters, what is the chance that you will draw the needed AND to create the word CANDLE? (HINT: Consider how many ways you can draw 3 letters from a bag of 8). 1 solutions Answer 243513 by solver91311(16872)   on 2010-09-07 12:04:52 (Show Source): You can put this solution on YOUR website! You need to calculate: Where is the number of combinations of things taken at a time and is calculated by Which will give you the denominator of your probability fraction, i.e. the total number of possible outcomes. Since only one of those outcomes is a success according to the parameters of your problem, the numerator of the probability fraction is 1. John My calculator said it, I believe it, that settles it

Equations/339853: If I have a part of a house that measures 17'x21.6', the total house is 2162 sq feet. what percentage is that part to the entire house? 1 solutions Answer 243512 by solver91311(16872)   on 2010-09-07 11:58:56 (Show Source): You can put this solution on YOUR website! Multiply 17 times 21.6. Divide the result by 2162. Move the decimal point two places to the right. John My calculator said it, I believe it, that settles it

Functions/339840: Find the domain of the function. g(x)=6/1-8x 1 solutions Answer 243511 by solver91311(16872)   on 2010-09-07 11:55:43 (Show Source): You can put this solution on YOUR website! Step 1: Set the denominator of your rational function equal to zero and solve. Step 2: The domain of your function is then all real numbers except the numbers discovered in step 1. John My calculator said it, I believe it, that settles it

Mixture_Word_Problems/339842: I have 3 problems that I am stuck on. Here is the first question. Many fruit drinks are actually only 5% real fruit juice. If you let 2 oz. of water evaporate from 12 oz. of a drink that is 5% fruit juice, what is the percent concentration of the result? Is there a formula for evaporation? .12 ____ - x = 2(.02 x .05) .05 Is this how you get started. Thanks for your help 1 solutions Answer 243510 by solver91311(16872)   on 2010-09-07 11:43:28 (Show Source): You can put this solution on YOUR website! Sorry, but your "this is how you get started" makes no sense whatsoever. If you do the indicated arithmetic, you get an answer of about 2.4 percent. If you start with a given concentration and then remove some of the water you must end with a greater concentration. If you begin with 12 ounces of a 5% solution, then 0.05 times 12 = 0.6 oz is the amount of pure fruit juice you have and that means you began with 11.4 oz of water. Reducing the water by 2 oz leaves 9.4 oz of water added to the 0.6 oz of pure fruit juice that wasn't reduced at all gives you 10 oz of mixture. 0.6 divided by 10 = 0.06 = 6%. And that makes sense. John My calculator said it, I believe it, that settles it

Expressions-with-variables/339846: i need help finding t2 in the following equation: 230=100*(t2-25) thanks 1 solutions Answer 243504 by solver91311(16872)   on 2010-09-07 11:27:02 (Show Source): You can put this solution on YOUR website! That depends a great deal on whether your "t2" means or . Next time, use "t_2" to mean or "t^2" to mean . John My calculator said it, I believe it, that settles it

Polygons/339844: If length of one side of a regular polygon is 25% of its perimeter, then polygon has how many sides? (a) 3 (b) 4 (c) 5 (d) 8 (e) 25 1 solutions Answer 243503 by solver91311(16872)   on 2010-09-07 11:20:41 (Show Source): You can put this solution on YOUR website! Divide 25% of the perimeter into 100% of the perimeter, which is to say divide 1 by 0.25 -- which has the same answer as the question: "How many quarters (25-cent pieces) in one dollar?" John My calculator said it, I believe it, that settles it

Travel_Word_Problems/339834: an object is dropped from an initial height of x feet. the objects height at any time t. on seconds , is given by h=-16t^2+s. How long does it take for an object dropped from 300 feet to hit the ground ? 1 solutions Answer 243501 by solver91311(16872)   on 2010-09-07 11:17:06 (Show Source): You can put this solution on YOUR website! If you are going to drop your object from an initial height of feet, then you need to use the function: On the other hand, if you insist on using then you must drop your object from an initial height of feet. In point of fact, it will serve you well to learn the more general function for the height of an object in feet acted upon by gravitational force near the surface of planet Earth. Where is time in seconds, is initial velocity in feet per second, and is the initial height in feet. is the acceleration due to gravity near the Earth in feet per second per second divided by 2. For your problem: (the object was merely dropped, not thrown), , (since we want to know the time when the object hits the ground, i.e. height = zero), and is what we want to determine. Plug in the values we know: A little algebra: Now all you need to do is solve the quadratic for the positive root (We can't go back in time, now can we?). Let me know what you find out. John My calculator said it, I believe it, that settles it