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Trigonometry-basics/295721: f(x) = -3x + 7 How do I find the inverse of this function? thank you! 1 solutions Answer 213145 by jim_thompson5910(28598)   on 2010-04-23 12:24:22 (Show Source): You can put this solution on YOUR website! Hint: First note that f(x) is basically 'y'. So . Now swap 'x' and 'y' to get . Your goal from here is to solve for 'y' to find the inverse function.

Polynomials-and-rational-expressions/295718: 9(-z+9) 1 solutions Answer 213142 by jim_thompson5910(28598)   on 2010-04-23 12:07:52 (Show Source): You can put this solution on YOUR website! Use the distributive property to get

Quadratic_Equations/295717: x^2+4x+3=0, how do i solve this 1 solutions Answer 213141 by jim_thompson5910(28598)   on 2010-04-23 12:03:23 (Show Source): You can put this solution on YOUR website! Solved by pluggable solver: Quadratic Formula Let's use the quadratic formula to solve for x: Starting with the general quadratic the general solution using the quadratic equation is: So lets solve ( notice , , and ) Plug in a=1, b=4, and c=3 Square 4 to get 16 Multiply to get Combine like terms in the radicand (everything under the square root) Simplify the square root (note: If you need help with simplifying the square root, check out this solver) Multiply 2 and 1 to get 2 So now the expression breaks down into two parts or Lets look at the first part: Add the terms in the numerator Divide So one answer is Now lets look at the second part: Subtract the terms in the numerator Divide So another answer is So our solutions are: or

Percentage-and-ratio-word-problems/295711: A shopkeeper gives two successive discounts of 8% and 12%. What is overall discount? plz hlp me ans is 33.33% 1 solutions Answer 213137 by jim_thompson5910(28598)   on 2010-04-23 11:48:34 (Show Source): You can put this solution on YOUR website! Let 'x' be the original price. If you apply an 8% discount, you're basically subtracting 8% of the original price from the original price. In other words, you're doing So after an 8% discount, the new price is dollars. Now apply the 12% discount using similar logic to get So after applying the 8% discount, then the 12% discount, the final sale price is . Subtract the coefficient from 1 to get and then multiply that result by 100 to get 19.04% So the overall discount is 19.04% --------------------------------------------- Example: Say an item originally costs $100. Apply the 8% discount to get (note: think of it as subtracting $8, 8% of $100, from $100). So after the first discount, the sale price is $92. Now apply the 12% discount to the new price of $92 to get . This means that after the two discounts, the final price is $80.96 Instead of taking two steps to find the final discount, we can take a shortcut and simply apply the overall discount of 19.04% (we should get the same answer if we did things right). So applying the discount of 19.04% to the original price of $100 gets us which is what got earlier. So this example helps support our answer. Try other values to confirm for yourself that this is the right discount. Try to incorporate real world values (ie prices you might see in the grocery store) to help you see that it works. As you can see, it's very useful to be able to combine multiple discounts into one to save time and avoid errors.

Geometry_proofs/295709: what is used to support the steps of a geometric proof? evidence based on observation or experiment? measurement and observation of many cases? postulates, definitions, given statements, and proven theorems? or steps in a geometric proff do not require support? 1 solutions Answer 213133 by jim_thompson5910(28598)   on 2010-04-23 11:34:34 (Show Source): You can put this solution on YOUR website! Well first off, geometric proofs need support, so we can quickly cross off the last choice. If they didn't need support, then we could claim anything (whether it's true or not). For the first choice, geometry doesn't really deal with experiments. So we can ignore this choice. For the second, measurement is used in geometry, but not necessarily in proofs. So we can ignore this one as well. It turns out that the answer is the third choice as geometry is essentially built on other proven theorems, axioms, and definitions.

Triangles/295703: the area of a triangle, altitude 5' base =26' 1 solutions Answer 213132 by jim_thompson5910(28598)   on 2010-04-23 11:15:57 (Show Source): You can put this solution on YOUR website! Area of triangle = (Base*Height)/2 = (26*5)/2 = 130/2 = 65 So the area of the triangle is 65 square feet.

Linear-equations/295655: find f(a + h) -f (a) for the following: f(x) = 4x + 5 1 solutions Answer 213131 by jim_thompson5910(28598)   on 2010-04-23 11:13:15 (Show Source): You can put this solution on YOUR website! First compute f(a+h) and f(a). So and This means that

Coordinate-system/295683: (1) Given f(x) = 8x - 2 and g(x) = 2x - 3, find f - g 1 solutions Answer 213130 by jim_thompson5910(28598)   on 2010-04-23 11:10:33 (Show Source): You can put this solution on YOUR website! So

Radicals/295698: (-7x+2)^1/3 = (4 + 3x)^1/3 1 solutions Answer 213129 by jim_thompson5910(28598)   on 2010-04-23 11:08:55 (Show Source): You can put this solution on YOUR website! Hint: if you cube both sides, you get the equation which is a simple linear equation (and easily solvable for 'x')

Miscellaneous_Word_Problems/295700: A company produced 2,265,400 tires in one year and made a profit of 15,720,000. What was the profit of each tire? 1 solutions Answer 213128 by jim_thompson5910(28598)   on 2010-04-23 11:07:54 (Show Source): You can put this solution on YOUR website! Profit of 1 single tire = Total Profit/Number of tires = 15,720,000/2,265,400 = 6.93917189 So the profit per tire is about $6.94 (to the nearest penny)

Numeric_Fractions/295603: If 3/4 of a class is absent and 2/3 of those present leave the room. What fraction of the original class remains in the room? 1 solutions Answer 213019 by jim_thompson5910(28598)   on 2010-04-23 01:36:45 (Show Source): You can put this solution on YOUR website! "If 3/4 of a class is absent", then of the class is present. Now since "2/3 of those present leave the room", this means that 1/3 of those present remain in the room. So simply multiply by to get the number of the people who remain the room. So So of the original class remains in the room. ----------------------------------------------------------- Here's a concrete example: Say there are 600 kids. Now if "If 3/4 of a class is absent", then kids are absent and are present (in the beginning) Now because "2/3 of those present leave the room", we know that kids leave the room. Because 150 kids showed up originally, this means that kids remain. Now just compute the ratio of the remaining 50 students to the total of 600 to get which is the fraction we originally found. So this example supports our answer.

Numeric_Fractions/295607: 17 -8 1/2 = 1 solutions Answer 213018 by jim_thompson5910(28598)   on 2010-04-23 01:29:07 (Show Source): You can put this solution on YOUR website! Note: We can write 17 as since Using the note above, we can go from 17 - 8 1/2 --------- to 16 2/2 - 8 1/2 --------- Now just subtract the common parts. So and meaning that 16 2/2 - 8 1/2 --------- 8 1/2 So this also means that 17 - 8 1/2 --------- 8 1/2

Polynomials-and-rational-expressions/295525: I started submitting a question and didnt finish so I will do it again. For the following function, C computes a value, where if you add millions of dollars to the value, the result is the cost of implementing a city recycling project when x as a percent(not a decimal equivalent), citizens participate C(x)= 1.5x/100-x a.) Using this model, determine the cost if 60% of the citizens participate? b.)Using this model, find the percentage of participation that can be expected if $5 million is spent on this recycling project? Set up the equation and solve algebraically. Round to the nearest whole percent. I would appreciate help on this one, I am not sure how to do it, and would love to see it step by step. Thank you for your help 1 solutions Answer 213017 by jim_thompson5910(28598)   on 2010-04-23 01:25:07 (Show Source): You can put this solution on YOUR website! a) Just plug in x=60 to get: . So the cost is 2.25 million. b) Since we want the cost to be 5 million, we let and plug it in to get . Now we solve for 'x': Start with the given equation. Multiply both sides by 100-x. Distribute. Add 5x to both sides. Combine like terms. Divide both sides by 6.5 to isolate 'x'. Divide Now round to the nearest whole number to get So the percentage is 77% (to the nearest whole percentage)

decimal-numbers/295518: if the additive inverse of 7 is added to the multiplicative inverse of 1/2, what is the sum? 1 solutions Answer 213016 by jim_thompson5910(28598)   on 2010-04-23 01:17:48 (Show Source): You can put this solution on YOUR website! the additive inverse of 7 is -7 and the multiplicative inverse of 1/2 is 2. So add these two numbers together to get: -7+2=-5

Equations/295604: 5/8=v/7 Solve the following proportion for v, round your answer to the nearest tenth 1 solutions Answer 213015 by jim_thompson5910(28598)   on 2010-04-23 01:16:43 (Show Source): You can put this solution on YOUR website! Start with the given ratio Multiply both sides by 7 Multiply So our answer is which in decimal form is

Square-cubic-other-roots/295601: ∛(-1/64)simplify 1 solutions Answer 213014 by jim_thompson5910(28598)   on 2010-04-23 01:12:15 (Show Source): You can put this solution on YOUR website! So

Radicals/295600: √(12w^4 ) Rewrite the following in simplified radical form, assume that all variables represent positive real numbers 1 solutions Answer 213013 by jim_thompson5910(28598)   on 2010-04-23 01:11:19 (Show Source): You can put this solution on YOUR website! Start with the given expression. Factor into Factor into Break up the square root using the identity . Take the square root of to get . Take the square root of to get . Rearrange and multiply the terms. ================================================== Answer: So simplifies to In other words, where

Graphs/295333: (3,4)m = -1/4 Need to write this as an equation 1 solutions Answer 212841 by jim_thompson5910(28598)   on 2010-04-22 14:10:10 (Show Source): You can put this solution on YOUR website! Hint: The general equation of any line is , where 'm' is the slope. Since the point (3,4) lies on the line, we know that when x=3, y=4. In addition, we're given the slope . Plug all of these values into the equation given above to get and then solve for 'b'

Volume/295334: The area of a circle depends on the radius. Use the equation A(r) = r2 to compute A(6). 1 solutions Answer 212839 by jim_thompson5910(28598)   on 2010-04-22 14:08:27 (Show Source): You can put this solution on YOUR website! The equation should be which means that (which is approximate)

Functions/295296: I am working on functions (fractions/ division) but I am stumped. Any help is appreciated. compute and then simplify the quantity f (a + h) − f (a): f(x)=2/x+1 thank you 1 solutions Answer 212837 by jim_thompson5910(28598)   on 2010-04-22 14:06:08 (Show Source): You can put this solution on YOUR website! First, let's compute , we do this by simply replacing each 'x' with 'a+h' and simplifying. So Similarly, doing the same for gets us This then means that So the goal now is to simplify Take note that the LCD is . So multiply the first fraction by to get Now multiply the second fraction by to get Combine the fractions: Distribute: And finally combine like terms: So in the end,

Quadratic_Equations/295332: Solve using the quadratic formula. Could someone please help me with this? I appreciate it. 1 solutions Answer 212833 by jim_thompson5910(28598)   on 2010-04-22 13:57:45 (Show Source): You can put this solution on YOUR website! Start with the given equation Add 23 to both sides. Solved by pluggable solver: Quadratic Formula Let's use the quadratic formula to solve for x: Starting with the general quadratic the general solution using the quadratic equation is: So lets solve ( notice , , and ) Plug in a=1, b=-10, and c=23 Negate -10 to get 10 Square -10 to get 100 (note: remember when you square -10, you must square the negative as well. This is because .) Multiply to get Combine like terms in the radicand (everything under the square root) Simplify the square root (note: If you need help with simplifying the square root, check out this solver) Multiply 2 and 1 to get 2 So now the expression breaks down into two parts or Now break up the fraction or Simplify or So the solutions are: or

Equations/295330: Find all real soultions. x^2+30x + 200 = 0 x^2 + 3x + 1 = 0 X^2- 6x + 1 = 0 3x^2 + 7x + 4 = 0 1 solutions Answer 212832 by jim_thompson5910(28598)   on 2010-04-22 13:54:20 (Show Source): You can put this solution on YOUR website! # 1 Solved by pluggable solver: Quadratic Formula Let's use the quadratic formula to solve for x: Starting with the general quadratic the general solution using the quadratic equation is: So lets solve ( notice , , and ) Plug in a=1, b=30, and c=200 Square 30 to get 900 Multiply to get Combine like terms in the radicand (everything under the square root) Simplify the square root (note: If you need help with simplifying the square root, check out this solver) Multiply 2 and 1 to get 2 So now the expression breaks down into two parts or Lets look at the first part: Add the terms in the numerator Divide So one answer is Now lets look at the second part: Subtract the terms in the numerator Divide So another answer is So our solutions are: or ====================== # 2 Solved by pluggable solver: Quadratic Formula Let's use the quadratic formula to solve for x: Starting with the general quadratic the general solution using the quadratic equation is: So lets solve ( notice , , and ) Plug in a=1, b=3, and c=1 Square 3 to get 9 Multiply to get Combine like terms in the radicand (everything under the square root) Simplify the square root (note: If you need help with simplifying the square root, check out this solver) Multiply 2 and 1 to get 2 So now the expression breaks down into two parts or Now break up the fraction or Simplify or So the solutions are: or

Exponents/295263: n2*n3 1 solutions Answer 212831 by jim_thompson5910(28598)   on 2010-04-22 13:52:38 (Show Source): You can put this solution on YOUR website! which means that

Graphs/295261: Construct a truth table for (~p q) ↔ p 1 solutions Answer 212830 by jim_thompson5910(28598)   on 2010-04-22 13:52:03 (Show Source): You can put this solution on YOUR website! You're missing the symbol that goes in between the ~p and q. Please repost with the correct symbol.

Expressions-with-variables/295317: Perform the operation and simplify the answer. Hi, I need help with this. Thank you. 1 solutions Answer 212829 by jim_thompson5910(28598)   on 2010-04-22 13:51:01 (Show Source): You can put this solution on YOUR website! Start with the given expression. Multiply EVERY term by the inner LCD 8 to clear out the inner fractions. Note: because we're multiplying every term by the same number, we have not changed the fraction. Also, not much more simplification can be done after this step. So where

Finance/295322: A mixture of 8% disinfectant solution is to be made from 10% and 7% disinfectant solutions. How much of each solution should be used if gallons of 8% solution are needed? 1 solutions Answer 212828 by jim_thompson5910(28598)   on 2010-04-22 13:48:24 (Show Source): You can put this solution on YOUR website! You're missing the total number of gallons. Please repost with the entire problem.

Rational-functions/295320: I am in algebra 2 this year. also i am really bad at any math. i need help on how to factor and foil x2 - 6x + 9. i dont undrestand any of this. it looks like it is in another language. thank you caitlin 1 solutions Answer 212827 by jim_thompson5910(28598)   on 2010-04-22 13:47:12 (Show Source): You can put this solution on YOUR website! Solved by pluggable solver: Factoring using the AC method (Factor by Grouping) In order to factor , first multiply the leading coefficient 1 and the last term 9 to get 9. Now we need to ask ourselves: What two numbers multiply to 9 and add to -6? Lets find out by listing all of the possible factors of 9 Factors: 1,3,9, -1,-3,-9, List the negative factors as well. This will allow us to find all possible combinations These factors pair up to multiply to 9. 1*9=9 3*3=9 (-1)*(-9)=9 (-3)*(-3)=9 note: remember two negative numbers multiplied together make a positive number Now which of these pairs add to -6? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -6 |||| First Number | Second Number | Sum 1 | 9 | 1+9=10 3 | 3 | 3+3=6 -1 | -9 | -1+(-9)=-10 -3 | -3 | -3+(-3)=-6 We can see from the table that -3 and -3 add to -6. So the two numbers that multiply to 9 and add to -6 are: -3 and -3 So the original quadratic breaks down to this (just replace with the two numbers that multiply to 9 and add to -6, which are: -3 and -3) Replace with Group the first two terms together and the last two terms together like this: Factor a 1x out of the first group and factor a -3 out of the second group. Now since we have a common term we can combine the two terms. Combine like terms. ============================================================================== Answer: So the quadratic factors to which can also be written as since the factors repeat themselves Notice how foils back to our original problem . This verifies our answer.

Complex_Numbers/294966: divide the complex numbers and write the final answer in the form a+bi -10+i ______ 2+i I appreciate any help =D Thank you =D 1 solutions Answer 212627 by jim_thompson5910(28598)   on 2010-04-21 18:00:18 (Show Source): You can put this solution on YOUR website! Start with the given expression. Multiply the fraction by . Combine the fractions. FOIL the numerator. FOIL the denominator. Multiply. Replace with -1. Combine like terms. Break up the fraction. Reduce. So which is in standard form where and

Linear-equations/294832: Find the slope and Y-intercept of the given function equation: x=-2 I think it is slope is undefined and their is no y-intercept, is that correct? 1 solutions Answer 212571 by jim_thompson5910(28598)   on 2010-04-21 13:58:00 (Show Source): You can put this solution on YOUR website! You are 100% correct. Good job.

expressions/294824: 25(x-4)+3x=77-2(x-3) 1 solutions Answer 212570 by jim_thompson5910(28598)   on 2010-04-21 13:47:37 (Show Source): You can put this solution on YOUR website! Solved by pluggable solver: Linear Equation Solver Start with the given equation. Distribute. Combine like terms on the left side. Combine like terms on the right side. Add to both sides. Add to both sides. Combine like terms on the left side. Combine like terms on the right side. Divide both sides by to isolate . Reduce. ---------------------------------------------------------------------- Answer: So the solution is

Quadratic_Equations/294776: 6) Complete the square x2 – 12x 7) Complete the square x2 – 2x = 8 8) Complete the square x2 – 5x = –6 1 solutions Answer 212553 by jim_thompson5910(28598)   on 2010-04-21 11:54:49 (Show Source): You can put this solution on YOUR website! 6) Simply take half of -12 (the x coefficient) to get -6 and square it to get 36. Now add and subtract this value to get . From here, factor to get . So which means that