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Graphs/409457: still not sure of this answer. graph (-2,5) slope of -1 I know the formula is y=mx+b so would that be y=-1x+5 so then -1x+5-1x+5 x= -5 or am i way off?? 1 solutions Answer 288205 by solver91311(16868)   on 2011-02-15 12:01:47 (Show Source): You can put this solution on YOUR website! Way off is putting it mildly. is the slope-intercept form, where is the slope and is the -coordinate of the -intercept -- that is, the point where the graph intersects the -axis. But here the given point is which has a non-zero -coordinate and is therefore certainly NOT a point on the -axis. Hence, is NOT the -intercept, and . What you are trying to use is a formula that is inappropriate to the situation. Furthermore, I think that using any formula at all is inappropriate to what this question is asking you to do. Step 1: Plot the point . Step 2: Recognize that a slope of -1 means that whenever the value increases by some amount, the value decreases by that same amount. You can also go the other way and increase when decreasing , if such pleases you. Step 3: Starting at the point plotted in step 1, move to the right some number of units, stop, and then move down that same number of units. (Alternatively, move to the left some number of units and then up that same number of units) Plot the new point. Step 4: Draw a line that passes through the two plotted points. Done. Now if you want the equation of the line you just graphed, that is another story and definately NOT what the question asked you to do. But here is the process: Since you are given an arbitrary point that is not the -intercept and the slope, use the point-slope form of an equation of a line: where are the coordinates of the given point and is the given slope. John My calculator said it, I believe it, that settles it

Polynomials-and-rational-expressions/409452: Given the quadratic function f(x) = x^2 – 6x + 9, find a value of x such that f(x) = 25. This is what I have: x^2 - 6x + 9 = 25 x^2 - 6x - 16 = 0 x^2 - 8x + 2x -16 = 0 x(x-8) + 2(x-8) = 0 (x-8)(x+2) = 0 x = 8 1 solutions Answer 288201 by solver91311(16868)   on 2011-02-15 11:47:22 (Show Source): You can put this solution on YOUR website! Given the wording of the question, your answer is 100% correct. I say this because the question asks: "...find a value of x...", and that is precisely what you did; the fact that there is another equally valid answer to the question, namely , notwithstanding. John My calculator said it, I believe it, that settles it

Percentage-and-ratio-word-problems/409256: WHAT NUMBER IS 16% OF 70? HOW DO I WORK THIS OUT 1 solutions Answer 288146 by solver91311(16868)   on 2011-02-14 23:52:54 (Show Source): You can put this solution on YOUR website! Multiply 70 times 0.16. John My calculator said it, I believe it, that settles it

Linear-equations/409267: My question in my math book is asking this- Passes through the point (-6,5) and is parallel to the line x-2y=8 how do I solve this? I don't understand it and need help with the steps on how to do it.. 1 solutions Answer 288145 by solver91311(16868)   on 2011-02-14 23:50:24 (Show Source): You can put this solution on YOUR website! Find the slope of the given line. You can either put the equation into slope-intercept form and then determine the slope by inspection, or you can just divide the coefficient on x by the opposite of the coefficient on y. Parallel lines have equal slopes, that is: So once you have determined the slope of the given line, you have the slope of the desired line as well. Use the point-slope form of an equation of a line to write the desired equation: where are the coordinates of the given point and is the calculated slope. John My calculator said it, I believe it, that settles it

Problems-with-consecutive-odd-even-integers/409270: The sum of three consecutive integers is 450. Find the numbers 1 solutions Answer 288144 by solver91311(16868)   on 2011-02-14 23:45:22 (Show Source): You can put this solution on YOUR website! Let represent the first of the three consecutive integers. Then is the next one and is the next one after that. Solve for John My calculator said it, I believe it, that settles it

Numbers_Word_Problems/409274: the sum of two numbers is 75. The second number is 3 less than twice the first. fine the numbers 1 solutions Answer 288143 by solver91311(16868)   on 2011-02-14 23:42:09 (Show Source): You can put this solution on YOUR website! Solve for John My calculator said it, I believe it, that settles it

test/409272: If the distance between key west and cuba is 9/10 inch. What is the actual distance? 1 solutions Answer 288142 by solver91311(16868)   on 2011-02-14 23:40:41 (Show Source): You can put this solution on YOUR website! Would have been nice of you to share the map scale. Repost this problem with ALL of the information. John My calculator said it, I believe it, that settles it

Miscellaneous_Word_Problems/409276: If twice a number is divided by -5, the result is 4. Construct the equation AND then solve the equation for the number. 1 solutions Answer 288141 by solver91311(16868)   on 2011-02-14 23:39:10 (Show Source): You can put this solution on YOUR website! Multiply both sides by John My calculator said it, I believe it, that settles it

Polynomials-and-rational-expressions/409158: hi, I am solving by quadraic formula -b sqrt (b2-4ac)/(2a) x^2+2x=168 x^2+2x-168=168-168 x^2+2x-168=0 -2 +- sqrt (2^2-4(1)(-168)/(2(1)) -2 +- sqrt (4-672)/(2) -2 +- sqrt (668)/(2) This is where I am lost. It's not a perfect square, so what do I do now? I choose factors. -2 +- sqrt ((4(167))/(2) -2 +- 2 sqrt (167)/(2) common denominator of 2 -1 sqrt(167)/(2) Would you help me understand where I went wrong and how to do it right? 1 solutions Answer 288088 by solver91311(16868)   on 2011-02-14 20:21:34 (Show Source): You can put this solution on YOUR website! Sign Error: So it is a perfect square after all. John My calculator said it, I believe it, that settles it

Word_Problems_With_Coins/409090: I need help with a word problem. This is what I have so far: Joe has a collection of nickels and dimes that is worth $3.95. If the number of dimes was doubled and the number of nickels was increased by 21, the value of the coins would be $8.40. How many nickels and dimes does he have? first part: dimes value + nickles value = total amount (value of a dime)(# of dimes) + (value of a nickle)(# of nickles) = total amount (0.10)(# of dimes) + (0.05)(# of nickles) = 3.95 (0.10)(d) + (0.05)(n) = 3.95 so d = number of dimes we start with n = number of nickles we start with second part: dimes value + nickles value = total amount (value of a dime)(# of dimes) + (value of a nickle)(# of nickles) = total amount (0.10)(2*d) + (0.05)(n + 21) = 8.40 because we're supposed to have double (*2 the dimes) and 21 more nickles The two equations are then: (0.10)(d) + (0.05)(n) = 3.95 (0.10)(2d) + (0.05)(n + 21) = 8.40 1 solutions Answer 288085 by solver91311(16868)   on 2011-02-14 20:11:00 (Show Source): You can put this solution on YOUR website! What you have done so far is absolutely spot on correct, but I'm going to show you a little trick that will get rid of all of the ugly decimal coefficients so that you are much less likely to make any arithmetic errors. While it is true that a dime has a value of 0.10 dollars, it also can be said to have a value of 10 cents. Likewise a nickel is worth 5 cents. Furthermore, the total value of the coins in either situation can be said to be 395 cents or 840 cents. Now we can write the equations as: And Much tidier, no? A little manipulation gets us: Multiply the first equation by -1: Then add the two equations, term by term: And that leads us to Meaning we started with 34 dimes, and it should follow directly from that fact that we started with 11 nickels accounting for the 55 cents remaining in the $3.95. Checking our work: If we have twice the dimes, or 68 dimes, we have $6.80 in dimes and an additional 21 nickels would be 55 cents plus $1.05 or $1.60. Finally, $6.80 plus $1.60 is indeed $8.40. Ta Da! John My calculator said it, I believe it, that settles it

Mixture_Word_Problems/408947: Terry and Abigail are moving to a new house. They have 13 books on one shelf of their bookcase, but the narrow box Terry is packing can only hold a stack of 12 books. Abigail is convinced that all 13 books will fit if only they are stacked in the correct order. She tries several possible ways of stacking the books before giving up and admitting that she was wrong - only 12 books can fit. If Abigail had persisted and tried every possible way of stacking the books, how many different orders would she have had to try? 1 solutions Answer 288080 by solver91311(16868)   on 2011-02-14 19:50:02 (Show Source): You can put this solution on YOUR website! 12 ways to choose the first book, For each of these 12 ways there are 11 ways to choose the second book. 121 ways. For each of these 121 ways there are 10 ways to choose the third book. 1210 ways. And so on: You can do your own calculator work. John My calculator said it, I believe it, that settles it

Travel_Word_Problems/408948: Jim drove the 120 miles to Grandmother's house in 3 hours. He increased his speed by 10 miles per hour on the way home. How long did it take him to drive home? "Changing Rates" 1 solutions Answer 287997 by solver91311(16868)   on 2011-02-14 13:21:37 (Show Source): You can put this solution on YOUR website! To find the rate for the outbound trip, divide the distance by the time. Then add 10 mph to get the rate for the return trip. Divide the distance by this new rate to get the new time. John My calculator said it, I believe it, that settles it

Quadratic_Equations/408949: What does it mean when you need to find the "sum" of the solutions to an equation? the equation is 8x squared + 6x + 1. 1 solutions Answer 287996 by solver91311(16868)   on 2011-02-14 13:19:47 (Show Source): You can put this solution on YOUR website! The same thing it means to find the sum of any set of things -- add them. This is a quadratic equation, therefore it has two elements in its solution set (or, at worst, a single element with a multiplicity of 2). Solve the equation for its two roots and add them. John My calculator said it, I believe it, that settles it

Polynomials-and-rational-expressions/408282: Hi, I finished this equation and would like to know if you would check my answer. My textbook answer is says 1 but I got 1 (1)(11). I would like to know how to do the problem correctly. Thanks. (c+5)/(7)+(c-3)/(4)=(5)/(14) common demoninator 28 and multiply by it. 28 (c+5)/(7)+ 28(c-3)/(4)= 28(5)/(14) 4c+5+7c-3=10 11c+2=10 -2 +2 (11c)/(11c)=12/11 c=1 (1)/(11) 1 solutions Answer 287681 by solver91311(16868)   on 2011-02-12 21:31:50 (Show Source): You can put this solution on YOUR website! You have the right idea, but you misapplied the process of applying the common denominator. You need to review the Distributive Property: John My calculator said it, I believe it, that settles it

Probability-and-statistics/408081: 6. Each day a quality engineer selects a random sample of 100 bolts from the day’s production, measures their lengths, and computes a 95% confidence interval for the mean length of all the bolts manufactured that day. What is the probability that more than 15 of the confidence intervals constructed in the next 250 days will fail to cover the true mean? 7. On a certain day, a large number of fuses were manufactured, each rated at 15A. A sample of 75 fuses is drawn from the day’s production, and 17 of them were found to have burnout amperages greater than 15A. a. Find a 95% confidence interval for the proportion of fuses manufactured that day whose burnout amperage is greater than 15A. b. Find a 98% confidence interval for the proportion of fuses manufactured that day whose burnout amperage is greater than 15A. c. Find the sample size needed for a 95% confidence interval to specify the proportion to within ±0.05 d. Find the sample size needed for a 98% confidence interval to specify the proportion to within ±0.05 e. If a 95% confidence interval is computed each day for 200 days, what is the probability that more than 192 of the confidence intervals cover the true proportions? 8. A random sample of 400 electronic components manufactured by a certain process are tested, and 30 are found to be defective. a. Let p represent the proportion of components manufactured by this process that are defective. Find a 95% confidence interval for p. b. How many components must be sampled so that the 95% confidence interval will specify the proportion defective to within ±0.02? 9. A chemist made 8 independent measurements of the melting point of tungsten. She obtained a sample mean of 3410.14oC and a sample standard deviation of 1.018oC. a. Find a 95% confidence interval for the melting point of tungsten b. Find a 99% confidence interval for the melting point of tungsten c. If the eight measurements had been 3409.76, 3409.80, 3412.66, 3409.79, 3409.76, 3409.77, 3409.80, and 3409.78, would the confidence intervals found in parts (a) and (b) be valid? Explain. 1 solutions Answer 287538 by solver91311(16868)   on 2011-02-12 00:44:13 (Show Source): You can put this solution on YOUR website! Go back and read the instructions for posting. John My calculator said it, I believe it, that settles it

Evaluation_Word_Problems/408079: I have two questions to ask here, the first is: 1) Pip can run four times as fast as she walks. One day she walked for 3 hours and ran for 2 hours. If she covered 55km altogether. How fast did she walk? The second one is: 2) How many litres of 15% sugar solution must be added to 5 lires of 10$ sugar solution to make a 12% sugar solution? Please Help! 1 solutions Answer 287537 by solver91311(16868)   on 2011-02-12 00:43:09 (Show Source): You can put this solution on YOUR website! If you have two questions, go back and make two posts. Read the instructions, "One question per post" Let represent the walking rate. Then is the running rate. Since distance equals rate times time, the distance walked must be and the distance ran must be . The sum of these distances is 55, so: Solve for John My calculator said it, I believe it, that settles it

Coordinate-system/408004: Sketch the region given by the set. {(x,y)/0 ** Please note, that the < is equal to or less than (underlined) 1 solutions Answer 287536 by solver91311(16868)   on 2011-02-12 00:29:11 (Show Source): You can put this solution on YOUR website! Did you mean: ? If so, graph the horizontal line with a solid line. You already have the line because that is the -axis. Shade the area between the two lines. The boundaries are solid lines because of the "or equals" part of John My calculator said it, I believe it, that settles it

Miscellaneous_Word_Problems/408070: a) Marie left her briefcase at home and had to return to get it. State which point represents when she turned back around to go home and explain how you arrived at that conclusion. b) Marie also had to wait at the railroad tracks for a train to pass. How long did she wait? 1 solutions Answer 287535 by solver91311(16868)   on 2011-02-12 00:18:44 (Show Source): You can put this solution on YOUR website! Must be a duck because ice cream has no bones. (Makes as much sense as you utterly nonsensical question). John My calculator said it, I believe it, that settles it

Miscellaneous_Word_Problems/408076: Bob is offered a salary of $160 a week and 2% commission on total sales or a straight 11% on total sales. What do total sales need to be for the 11% to be a better offer? 1 solutions Answer 287534 by solver91311(16868)   on 2011-02-12 00:12:17 (Show Source): You can put this solution on YOUR website! Let represent weekly sales. Then with the minimum salary his earnings are: And his earnings on straight commission: We want to know the value of such that: Solve the inequality for John My calculator said it, I believe it, that settles it

Numbers_Word_Problems/408075: Lily and Sara each had an equal amount of money at first. After Lily spent $18 and Sara spent $25, Lily had twice as much as Sara. How much money did each have at first? 1 solutions Answer 287533 by solver91311(16868)   on 2011-02-12 00:07:09 (Show Source): You can put this solution on YOUR website! Solve for John My calculator said it, I believe it, that settles it

Complex_Numbers/408067: 1)how to Find the complex conjugate of (3+5i)/(1+2i) 2)how to Find all the seventh roots of (3+4i). 1 solutions Answer 287532 by solver91311(16868)   on 2011-02-12 00:01:42 (Show Source): You can put this solution on YOUR website! One question per post, please. I presume you mean find the complex conjugate of the denominator so that you can rationalize. The conjugate of a complex fraction doesn't make any sense. The conjugate of a complex number is In order to rationalize your denominator, you need to multiply your fraction by 1 in the form of the conjugate of the denominator divided by itself. Remember the product of two conjugates is the difference of two squares and that John My calculator said it, I believe it, that settles it

Linear-equations/408071: The function, p(d) = 1 + d/33, gives the pressure, in atmospheres (atm), at a depth d in the sea (d is in feet). Note that p(0) = 1 atm, p(33) = 2, and so on. Find the pressure at 120 feet. The pressure at 120 feet is ___ atm. (type an integer or a simplified fraction) 1 solutions Answer 287529 by solver91311(16868)   on 2011-02-11 23:44:39 (Show Source): You can put this solution on YOUR website! Substitute 120 in place of d in the function and then do the arithmetic. John My calculator said it, I believe it, that settles it

Length-and-distance/408016: What is an equation of the line that passes through the point (-2, 5) and is perpendicular to the line whose equation is y = 1/2x + 5? 1. y = 2x + 1 2. y = -2x + 1 3. y = 2x + 9 4. y = -2x - 9 1 solutions Answer 287528 by solver91311(16868)   on 2011-02-11 23:43:11 (Show Source): You can put this solution on YOUR website! Parallel lines have slopes that are negative reciprocals so you can eliminate two of the answers immediately. Of the remaining two answers, only one of them forms a true statement if you substitute the coordinate values of the point through which the perpendicular must pass. John My calculator said it, I believe it, that settles it

Miscellaneous_Word_Problems/408057: Hi there, My question: For this linear equation y=-(2/3) x+30 I have to graph the x and y intercepts, and determine the heigth of the laser beam when the laser is 30 feet from the building... For this linear equation y=-(2/3) x+30 A1} the Y axis represents the height (above ground) in feet. A2} the X axis represents the distance (from the building) measured in feet. This problem has asked me to interpret the results graphically. I have graphed the following values: The x intercept or the point where the value crosses the x axis represents the point where the laser beams touches the ground. The y intercept, the point where the value crosses the y axis which represents the laser starting point or point where man is located. A3} in the equation y=-(2/3) x+30 y=mx+b format (slope intercept) (b) Represents the height of the window (x)Represents the point where the light intercepts the ground. A4} I solved this question by first drawing a grid, starting at the window point (0, 30)Then I used my slope of -2/3 to determine the value of 42 feet out from the building when the lights beam intercepts the ground. (42, 0) I have found the light to be 42feet out (x value), 30feet high(y value) by using (rise over run) or slope of -2/3. A5} Quadrant 2 is the only relevant quadrant for this problem. If we were doing a standard graphed linear equation, we would include quad. 1, 2 and 3 but since we are not including the area under the ground quad 3 is excluded, and since the beam is directional, quad 1 is also excluded. Quad four is also excluded because in either scenario, the plotted points are never on that plane/ quadrant. A graph was a very good representation of the light because it clearly shows the path the light took to the ground, in a way that brings the problem to life. The graph gave a pictorial representation for each value. Y isn’t simply Y its now, the point where the light originated from. And x has a pictorial value as well; X is the place where the beam intersects the ground. My work was returned to me because I did not find the x value correctly, I do not know how to go about finding this. I have graphed this problem but was not able to send a copy so that you could see my work, x y=-(2/3)x+30 -1 30 2/3 0 30 1 29 1/3 I need to know what the height is in feet when the laser beam is 30 feet away from the building... Thank you so much for your help! Take care Maranda 1 solutions Answer 287526 by solver91311(16868)   on 2011-02-11 23:36:57 (Show Source): You can put this solution on YOUR website! You are way way way over thinking this thing. Take your equation and substitute 0 in place of x. Do the arithmetic. The value you get for y is the height of the window. Take the original equation and substitute 0 in place of y. Do the arithmetic. The value you get for x is the distance from the building where the beam hits the ground. John My calculator said it, I believe it, that settles it

Polynomials-and-rational-expressions/408066: how many grains of sand are in a one quart mason jar? 1 solutions Answer 287523 by solver91311(16868)   on 2011-02-11 23:24:30 (Show Source): You can put this solution on YOUR website! Depends on how coarse the sand is. John My calculator said it, I believe it, that settles it

Coordinate-system/408058: y = -3 -3x need the x and y intercepts thanks 1 solutions Answer 287522 by solver91311(16868)   on 2011-02-11 23:23:18 (Show Source): You can put this solution on YOUR website! Substitute 0 for x. Solve for the resulting value of y = b. Then the y-intercept is (0,b). Then substitute 0 for y. Solve for the resulting value of x = a. Then the x-intercept is (a,0) John My calculator said it, I believe it, that settles it

Travel_Word_Problems/407879: how far have you traveled if you ran 15 minutes at 5 miles per hour 1 solutions Answer 287406 by solver91311(16868)   on 2011-02-11 12:13:32 (Show Source): You can put this solution on YOUR website! Distance equals rate times time if everything is in compatible units. That is to say miles equals miles per hour times hours, or feet equals feet per second times seconds, or kilometers equals kilometers per hour times hours. You have a time in minutes and a rate in miles per hour. You either have to convert the given number of minutes to an equivalent number of hours, then multiply and get a number of miles. Or you could convert miles per hour to miles per minute which would also give you the same answer. Hint: There are 60 minutes in 1 hour. So 15 minutes is hour. Or 5 mph is miles per minute. John My calculator said it, I believe it, that settles it

Travel_Word_Problems/407877: Noan and Ben are running in the Walker Street Fun Run. Noah runs at 7 mph, Ben at 5 mph. If they start at the same time, how long (in minutes) will it be before they are 1/6 mile apart? 1 solutions Answer 287400 by solver91311(16868)   on 2011-02-11 12:05:07 (Show Source): You can put this solution on YOUR website! Exactly the same amount of time it would take the faster guy to go mile at the difference between the two speeds. Time equals distance divided by rate. mile divided by 2 mph is hour. You need the answer in minutes, so convert hour to minutes. John My calculator said it, I believe it, that settles it

Exponents-negative-and-fractional/404515: (6-i)/(6+3i) 1 solutions Answer 285872 by solver91311(16868)   on 2011-02-05 01:41:50 (Show Source): You can put this solution on YOUR website! Rationalize the denominator by multiplying both numerator and denominator by the conjugate of the denominator. John My calculator said it, I believe it, that settles it

Inequalities/404513: Please help me with solving this inequality and please show me how you came up with the answer: 5+3x<7 Thank You 1 solutions Answer 285870 by solver91311(16868)   on 2011-02-05 01:19:11 (Show Source): You can put this solution on YOUR website! Add -5 to both sides. Multiply both sides by John My calculator said it, I believe it, that settles it

Triangles/403949: How many right triangles might have a hypotenuse that measures 4x+5 in inches? And legs that measure 3x+13 inches and x inches? What are the dimensions of the triangle? 1 solutions Answer 285543 by solver91311(16868)   on 2011-02-03 17:11:54 (Show Source): You can put this solution on YOUR website! Factor or use the quadratic formula. Exclude any negative root. John My calculator said it, I believe it, that settles it