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solver91311 answered: 16870 problems
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Linear-equations/301408: Write the slope-intercept form of an equation of the line that passes through the given point (4,-1) and is perpendicular to the graph of 7x-2y+3 (show work) 1 solutions Answer 216099 by solver91311(16885)   on 2010-05-06 15:41:55 (Show Source): You can put this solution on YOUR website! Step 1: Find the slope of the line represented by the given equation. Since the given equation is in standard form, use the negative of the coefficient on divided by the coefficient on . Alternatively, you can solve the equation for to put the given equation into slope intercept form. Having done that, the slope of the line represented by the given equation is equal to the coefficient on . Step 2: Determine the slope of the desired line. Calculate the negative reciprocal of the slope of the given line because: Step 3: Derive an equation of the desired line using the point-slope form of the equation of a line: where is the given point and is the slope calculated in Step 2. Step 4: Solve the equation derived in Step 3 for . That is to say rearrange the equation so that is all by itself on the left side of the equals sign and everything else is on the right side. The equation will then be in the form which is the slope intercept form. I can't actually solve your problem for you because you didn't actually give us an equation of a line to work with. You wrote which is not an equation. I can't tell whether you really meant or . Besides, I don't want to deprive you of the fun and excitement of getting the answer by yourself. John

Radicals/301392: At a height of h meters, you can see V kilometers to the horizon. These numbers are related to the formula v=3.5. How far can a sailor see to the horizon from the top of a mass that is 45 m high? Round to the nearest whole number. Would the answer be 23 feet? 1 solutions Answer 216095 by solver91311(16885)   on 2010-05-06 15:05:59 (Show Source): You can put this solution on YOUR website! Go outside and stand in your front yard. Do you think you can see farther than 23 feet while you are standing on the ground? Just to give yourself a sense of proportion, a typical suburban home is somewhere between 70 and 110 feet across the front -- so if you are standing on one side of your front yard and can see all the way across to the other side of your yard, you can certainly see farther than 23 feet. Do you think you might be able to see even farther if you were 45 meters in the air? Do you think that the answer should be in feet or meters, given that the supplied dimension was in meters, or some other dimension as provided in the description of the formula? Read the first sentence of your problem again, and read it as many times as necessary until you understand that while the number associated with your answer is indeed 23, that 23 feet is absolutely incorrect. And by the way, the sailor would be at the top of a mast, not the top of a mass. Furthermore, 23 is the right number given the formula you were supplied, although gives a much more precise answer and that would round off to 24. John

Trigonometry-basics/301387: In a right triangle sin A =3/4 and c=17. find a and b... Your help will be appreciated (: 1 solutions Answer 216092 by solver91311(16885)   on 2010-05-06 14:44:42 (Show Source): You can put this solution on YOUR website! Use the Law of Sines: To determine by realizing that is right and , therefore we can write: which is to say: Next, use Pythagoras to calculate the value of You can do your own arithmetic. John

Proportions/301391: A prescription calls for 100 mg of a drug that you have in a 250 mg/ 5 ml concentration. How many ml of the liquid do you need 1 solutions Answer 216086 by solver91311(16885)   on 2010-05-06 14:32:14 (Show Source): You can put this solution on YOUR website! If 5 ml is 250 mg of the drug, then 1 ml is 50 mg of the drug, and then 2 ml must be 100 mg. John

percentage/301389: I have a question asking if a ball bounces 40% or 2.5feet what is the height the ball has been dropped from. 1 solutions Answer 216085 by solver91311(16885)   on 2010-05-06 14:30:35 (Show Source): You can put this solution on YOUR website! Let represent the original height, then Solve for John

real-numbers/301380: Two cars are traveling toward each other, starting at the same time 480km apart. If they meet after 4 hours, and one car is traveling 40 kph faster than the other, how fast is each car moving? 1 solutions Answer 216083 by solver91311(16885)   on 2010-05-06 14:28:13 (Show Source): You can put this solution on YOUR website! If the two cars went 480 km in 4 hrs, then the sum of their speeds must have been 120 km/hr. The speed of the faster car is the speed of the slower car plus 40. So the speed of the slower car plus the speed of the slower car plus 40 must be 120, which is to say the speed of the slower car plus the speed of the slower car must be 120 minus 40 or 80 km/hr, and then the speed of the slower car must be half of that, or 40 km/hr and the other car must have been going 40 plus 40 = 80 km/hr. John

real-numbers/301386: The difference between two numbers is 3. If the sum of twice the larger and the smaller is 48, find the two numbers. 1 solutions Answer 216082 by solver91311(16885)   on 2010-05-06 14:22:36 (Show Source): You can put this solution on YOUR website! I already answered this one today. See question 301383. John

Sequences-and-series/301383: The difference between two numbers is 3. If the sum of twice the larger and the smaller is 48, find the two numbers. 1 solutions Answer 216081 by solver91311(16885)   on 2010-05-06 14:21:18 (Show Source): You can put this solution on YOUR website! So represents the larger number and is equal to We are given that: But, by substitution: So Check: Answer checks. John

Linear-equations/301076: how do you solve y=2x and y=x+1 1 solutions Answer 215887 by solver91311(16885)   on 2010-05-05 19:47:35 (Show Source): You can put this solution on YOUR website! You have two expressions equal to . Set them equal to each other. Since Solution set is the ordered pair: John

Money_Word_Problems/300978: I need help with this word math problem. In a collection of nickels, dimes, and quarters, there are twice as many dimes as nickels, and fewer quarters than dimes. If the total value of the coins is $4.50, how many of each type of coin are there? 1 solutions Answer 215856 by solver91311(16885)   on 2010-05-05 17:45:46 (Show Source): You can put this solution on YOUR website! Impossible to derive a unique answer to this one. You left out how many fewer quarters there are than dimes. The number of quarters ranges from The number of dimes ranges from and is divisible by 2 And the number of nickels is half of the dimes. The difference between the number of dimes and number of quarters is a number divisible by 3. John

Equations/300884: The process of solving an equation by writing it in the form and then taking the square root of each side is called solving by________________________the__________________. Hello, I was really hoping that someone could help me with this. Thanks in advance. 1 solutions Answer 215847 by solver91311(16885)   on 2010-05-05 17:28:26 (Show Source): You can put this solution on YOUR website! Completing the square John

Polynomials-and-rational-expressions/300845: Please help me solve this equation. I am not sure how to solve it with a cubed variable. Does it follow a regular FOIL pattern? 6x^3 +5x^2 +11 also, t^3 + 6t-4 1 solutions Answer 215807 by solver91311(16885)   on 2010-05-05 13:47:25 (Show Source): You can put this solution on YOUR website! The first thing you need to learn is proper terminology. 1. An equation has an equals sign ("=") in it. Neither of your expressions has an equals sign, so neither of your expressions is an equation. 2. You can't solve anything that is not an equation. You can simplify, evaluate, or factor, but you cannot solve. Now as to the two expressions you presented, it turns out that neither has any rational factors, neither can be simplified any more than they already are, and you did not present any values to substitute for the variables so as to be able to do an evaluation of the expressions. And the answer to your question about pattern is no, cubics do not, in general, follow the "FOIL" pattern. John

Polynomials-and-rational-expressions/300848: Jack usually mows his lawn in 5 hours. Marilyn can mow the same lawn is 3 hours. How much time would it take to mow the lawn together? 1 solutions Answer 215800 by solver91311(16885)   on 2010-05-05 13:11:52 (Show Source): You can put this solution on YOUR website! General answer to "Two People Working Together Problems" If A can do a job in x time periods, then A can do of the job in 1 time period. Likewise, if B can do the same job in y time periods, then B can do of the job in 1 time period. So, working together, they can do of the job in 1 time period. Therefore, they can do the whole job in: time periods. John

Expressions-with-variables/300849: Solve the problem: A square board has a perimeter which is 7 times the length of a side, decreased by 12. Find the length of the side. 1 solutions Answer 215799 by solver91311(16885)   on 2010-05-05 13:09:48 (Show Source): You can put this solution on YOUR website! Just solve for John

Complex_Numbers/300834: I am looking for a general solution to a complex number raised to a complex power. I recall that Euler had a solution, but I can't recall what it was. However, it was in the form of (something here) + i (something here), and used logarithms heavily (as is an Euler trademark). Any help will be greatly appreciated. Thanks. 1 solutions Answer 215795 by solver91311(16885)   on 2010-05-05 13:07:42 (Show Source): You can put this solution on YOUR website! To calculate : Let taking the sign appropriately so that Let Then John

test/300843: Mr. jones is visiting his son at college. After driving 180 miles he has completed 5/8 of the trip. How long is the total trip? 1 solutions Answer 215789 by solver91311(16885)   on 2010-05-05 12:39:36 (Show Source): You can put this solution on YOUR website! Let represent the total trip distance. Then: Just solve for . John

test/300841: a square has a perimeter of 24 cm if the sides of the square are increased by 4 times what happens to the perimeter 1 solutions Answer 215788 by solver91311(16885)   on 2010-05-05 12:37:19 (Show Source): You can put this solution on YOUR website! The perimeter of any figure is just the sum of the measures of the sides, hence the perimeter of a square is simply four times the measure of one of the sides. but if you increase the measure of the sides by a factor of four, then each side now measures , and the perimeter becomes: Hence the new perimeter is 4 times larger than the original perimeter: John

test/298121: if the sum of a number and six is doubled the result is nine less than the number find the number 1 solutions Answer 214542 by solver91311(16885)   on 2010-04-28 21:47:20 (Show Source): You can put this solution on YOUR website! Let represent the number. The sum of the number and six: . The sum of the number and six doubled. . "Is" means equals. Nine less than the number So, Solve for John

Money_Word_Problems/298124: Use A=P(1+r)^t to find the interest rate r. round to the nearest hundreth, if necessary. $8000 (P) grows to $8487 (A) in 2 years (t). Assume that interest is compounded annually. I am lost on this problem.... I know that it is 8487=8000(1+r)^2 8487/8000= (1+r)^2 then I get really confused on this step. please help. 1 solutions Answer 214541 by solver91311(16885)   on 2010-04-28 21:42:44 (Show Source): You can put this solution on YOUR website! So far, so good. Now just take the square root of both sides. Ordinarily, you would consider both the positive and negative square roots, but in this context the negative square root doesn't make much sense -- stick with the positive. And then add -1 to both sides A little calculator work and you are through. John

Square-cubic-other-roots/298116: x-25 divided by the square root of x -5? 1 solutions Answer 214539 by solver91311(16885)   on 2010-04-28 21:35:20 (Show Source): You can put this solution on YOUR website! A truly fascinating little expression. The piquancy of the radical in the denominator is particularly enticing. So what did you want to do with this? This a place to do mathematics, it is NOT the Psychic Hot Line. Don't force us to guess what you want. John

Polynomials-and-rational-expressions/298081: Please help me solve this problem. I need to find the product of (x+6)cubed. Not sure how to type the exponent 3 1 solutions Answer 214538 by solver91311(16885)   on 2010-04-28 21:31:19 (Show Source): You can put this solution on YOUR website! Use the caret mark (^ - shift-6) to indicate raising to a power. Your problem would be correctly rendered (x + 6)^3 In general, Even more in general, Where is the number of ways to choose things taken at a time and is equal to John

Age_Word_Problems/298112: A lady is three times as old as her daughter. 8 years ago the product of their ages was 112. find their present ages. 1 solutions Answer 214533 by solver91311(16885)   on 2010-04-28 21:13:30 (Show Source): You can put this solution on YOUR website! Let represent the daughter's age now. Then represents the mother's age now, represents the mother's age 8 years ago, and represents the daughter's age 8 years ago. The product of their ages 8 years ago is then: and this is equal to 112, so: which is to say The quadratic factors to: So or You can safely exclude the negative root since that would mean that the mother would have been -4 15 months before her daughter was born. The other answer is the correct value for the daughter's age now. Check: Daughter is Mom is Eight years ago daughter was and mom was . John

Linear-equations/298100: linear functions that satisfies the given conditions: f(0)= 2, f(9)=5 1 solutions Answer 214532 by solver91311(16885)   on 2010-04-28 20:57:36 (Show Source): You can put this solution on YOUR website! If , then the point is on the graph of the function. Likewise if , then the point is on the graph of the function. Now that you have two points, use the two-point form of the equation of a line to write your equation. John

Polygons/295864: How many different (noncongruent) convex quadrilateral can you make on a 3-by-3 dot grid, using the dots as vertices? 1 solutions Answer 213278 by solver91311(16885)   on 2010-04-23 20:34:43 (Show Source): You can put this solution on YOUR website! Number your dots, left to right, then top to bottom. You can make a square with 1,2,4,5. But that is congruent to any other square with side measuring 1. You can make a larger square with 1,3,7,9. There is obviously only one of those that can be made. You can make a rectangle with 1, 3, 4, 6. You can make a parallelogram with 2,3,4,5. All other parallelograms of this size are congruent. You can make a larger parallelogram with 2, 3, 7, and 8 You can make a trapezoid with 2, 3, 4, 6 You can make a larger trapezoid with 3, 4, 7, 9 So, two squares, a rectangle, two parallelograms, and two trapezoids (or trapeziums if you are British) for a total of 7. John

Complex_Numbers/295818: The complex number 2+i is a root of , where p is real. Explain why 2-i is another root and find the third root. 1 solutions Answer 213264 by solver91311(16885)   on 2010-04-23 19:34:45 (Show Source): You can put this solution on YOUR website! Because complex roots ALWAYS come in conjugate pairs. Therefore if is a root of a polynomial equation, then is also a root of that same polynomial equation. Guaranteed. If is the root of a polynomial equation, then is a factor of the polynomial. Since you know two of the roots of the equation, you know two of the factors of the polynomial, namely: and So, step one is to multiply these two factors together. I'll leave that as an exercise for the student. Hint: The product of two conjugates is the difference of two squares. And don't forget The next step is to divide the original polynomial by the quadratic trinomial you just derived in the previous step. Use polynomial long division. See http://www.purplemath.com/modules/polydiv2.htm if you need a refresher on the process. You will need to select an appropriate value for so that you end up with a zero remainder. The quotient you obtain will be the third factor. Good luck. John

Radicals/295840: how do you solve 1 solutions Answer 213258 by solver91311(16885)   on 2010-04-23 19:17:11 (Show Source): You can put this solution on YOUR website! I'm going to presume you mean But what do you mean by "how do you solve"? There is nothing to solve. This is just a function definition. If you want to know the value of the independent variable, , that produces a particular value of the function, , you are going to have to share that particular value with us. If you want to graph the function, you should say so. Graphing the function is not "solving" anything. So what is it you really want to do here? John

Finance/295827: Math obviously is not my strong point especially when it comes to compound interest. If I invest $1000 on May 18th in a savings account that pays 10% interest compounded every month, and I invest $1000 (on the same day) in an account which pays 10% interest that is compounded continuously: (a) Which will be worth more in one year? (b) By how much? Eric 1 solutions Answer 213255 by solver91311(16885)   on 2010-04-23 19:11:17 (Show Source): You can put this solution on YOUR website! Obvious to whom? For an investment of at interest per year (as a decimal) compounded times per year for years. For an investment of at interest per year (as a decimal) compounded continuously for years. Note: is the base of the natural logarithms. "Inv ln" does the trick quite nicely on the Windows built-in calculator in Scientific mode. The rest is just calculator work. Whichever comes out larger is the answer to a) and the difference between the two is the answer to b) John

Radicals/295834: What is the square root of x^14? 1 solutions Answer 213251 by solver91311(16885)   on 2010-04-23 18:56:51 (Show Source): You can put this solution on YOUR website! Remember the rule for rational exponents: So John

Square-cubic-other-roots/295835: Solve and check for extraneous solutions. 3sqrt(w+1)=6 I came up with w=35/3. I don't think that's correct and I'm not sure what I'm doing wrong 1 solutions Answer 213247 by solver91311(16885)   on 2010-04-23 18:52:13 (Show Source): You can put this solution on YOUR website! Well, let's see how correct your answer is: And after rationalizing the denominator, Ok, so back to the drawing board. Square both sides Multiply both sides by Check: Checks. John

Human-and-algebraic-language/295751: Not understanding how to put this question in an algebraic expression! Mike made $9,000 last year from an extra job. He invested part of the money at a 9% annual rate of interest and the rest of it at 8%. At the end of the year, he made a total of $770 in interest. How much was invested at the 8%? 1 solutions Answer 213186 by solver91311(16885)   on 2010-04-23 15:15:41 (Show Source): You can put this solution on YOUR website! Let represent the amount invested at 8%. Then, since the rest of his money was invested at 9%, the amount invested at 9% was The amount of money he earned on the 8% investment was then , and the amount of money he earned on the 9% investment was . Since the total amount that he earned was $770, you can say: Now just solve for . John

Trigonometry-basics/295736: A tower is 200 ft tall. To the nearest degree, find the angle of elevation from a point 50ft away from the base of the tower to the top of the tower. 1 solutions Answer 213173 by solver91311(16885)   on 2010-04-23 14:27:18 (Show Source): You can put this solution on YOUR website! The tangent of an angle is the measure of the opposite side of the triangle divided by the adjacent side of the triangle. So, you want to know the angle who's tangent is , or The calculator, in Degrees mode, says: or degrees, to the nearest degree. John