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 Permutations/182009: EXPAND (g+2)(g-5) 1 solutions Answer 136619 by Earlsdon(6287)   on 2009-02-15 11:03:50 (Show Source): You can put this solution on YOUR website!Expand: Use FOIL. Combine like-terms.
 Polynomials-and-rational-expressions/181992: The Great Galaxy in Andromeda (also known as the Andromeda Galaxy or M31) is about 2.5 million light years from Earth. When we look at this galaxy today, we see light that has been traveling through space for 2.5 million years; i.e. when we look at the Andromeda Galaxy, we are seeing it as it was about 2.5 million years ago! Think about this, we are looking back in time. 1 light year is the distance that light travels in 1 year. Speed of light is 300,000 kilometers/second, find the distance that light travels from the Andromeda Galaxy to Earth in kilometers and express it in scientific notation. 1 solutions Answer 136616 by Earlsdon(6287)   on 2009-02-15 10:58:55 (Show Source): You can put this solution on YOUR website!Profound! Andromeda is light-years from earth. The speed of light is: km/sec. One light-year is (secs) X (km/sec) = km. The distance to Andromeda is: (ligh-years) X (km/light-year) = km or km.
 Miscellaneous_Word_Problems/182006: Noel is determined to get some excercise and walks to the store at a brisk rate of 4.5 mph. She meets her friend Dani at the store, and together they walk back at a slower rate of 3mph. Noel's total walking time was 1hr. How long did it take her to walk to the store? What is the distance to the store?1 solutions Answer 136614 by Earlsdon(6287)   on 2009-02-15 10:34:58 (Show Source): You can put this solution on YOUR website!You can use the formula: d = rt where d = distance, r = rate (speed), and t = time. For the trip to the store , the rate (speed) is 4.5 mph so we can write: 1) For the return trip at 3 mph, we can write: 2) Now since the distance to the store is the same as the return distance, you can write: and, since the total time for the trip was 1 hour, then: Now we can rewrite this as: and substitute it for the in equation 2) after setting equation 1) equal to equation 2). Substitute Simplify and solve for Add to both sides. Divide both sides by 7.5 hours. So it took Noel 0.4 hours or 24 minutes to walk to the store. To find the distance to the store (), substitute into either equation 1) or equation 2) and solve for the distance. Substitute miles. Noel walked 1.8 miles to the store.
 Miscellaneous_Word_Problems/181930: The temperature dropped 15 degrees from the high temperature to -6 degress C. What was the high temperature?1 solutions Answer 136549 by Earlsdon(6287)   on 2009-02-14 12:49:19 (Show Source): You can put this solution on YOUR website!Let x = the high temperature, then: Add 15 to both sides. The high temperature was 9 degrees C.
 Miscellaneous_Word_Problems/181923: An open box is to be made from a rectangular piece of tin that is 18 cm wide and 24 cm long be cutting squares of equal size from the four corners and turning up the sides. How large must a square be cut from each corner if the area of the base of the box is to be 315 sq cm?1 solutions Answer 136548 by Earlsdon(6287)   on 2009-02-14 12:43:51 (Show Source): You can put this solution on YOUR website!The area of the base of the box can be found by multiplying the sides of the base. The sides of the base are equal to the length of the sides of the original rectangular piece of tin less two times the length of the corner pieces (2x). So the area of the base of the box can be expressed as: Performing the indicated multiplication, we get: ...and this, we are told = 315 sq.cm., so we set these two things equal to get: Now you subtract 315 from both sides of this equation. You can solve this quadratic equation using the quadratic formula: where: a = 4, b = -84, and c = 117, so making the approriate substitutions, we get: or or Now as you can see, if x = 19.5, this would not make any sense because that would mean the cut-out would be larger than the side of the original rectangle! So discard that solution and take the x = 1.5 cm.
 Equations/181775: if (2a + b = 80) and (2b + a = 76) then a = ?1 solutions Answer 136370 by Earlsdon(6287)   on 2009-02-13 00:02:49 (Show Source): You can put this solution on YOUR website!If (2a+b= 80) and (2b+a = 76) then a =? 2a+b = 80 Rewrite this as b = 80-2a and substitute into the 2nd equation. 2b+a = 76 2(80-2a)+a = 76 Simplify. 160-4a+a = 76 160-3a = 76 Subtract 160 from both sides. -3a = -84 Divide both sides by -3.
 Miscellaneous_Word_Problems/181769: This question is from textbook saxon algebra 2 A jar contains 10 marbles: 3 red, 1 blue, and 6 green. The red marbles are numbered 1-3, the blue is numbered 4, and the green are numbered 5-10. Find the probability that a marble drawn from the jar is odd or green.1 solutions Answer 136366 by Earlsdon(6287)   on 2009-02-12 23:51:50 (Show Source): You can put this solution on YOUR website!The probability of drawing a marble that is odd or green (an inclusive event)is expressed by: P(odd or green) = P(odd) + P(green) - P(odd and green) and this can be written as: P(odd or green) = P(odd) + P(green) - P(odd)*P(green) P(odd or green) = 5/10 + 5/10 - (5/10)*(5/10) = 1-(25/100) = 1-(1/4) = 3/4 So the probability of drawing a marble that is odd or green is 3/4 or 75%
 Expressions-with-variables/181768: This question is from textbook saxon algebra 2 Identify any excluded values. Then simplify the expression. 9x^3-27x^2 over 12x-36 I identified the excluded value as x=3. I don't know what to do from here. Help!1 solutions Answer 136364 by Earlsdon(6287)   on 2009-02-12 23:27:13 (Show Source): You can put this solution on YOUR website!You are correct on the excluded value of x = 3 because that's the value of x that would make the denominator zero and this, of course, is a no-no in math. Now to simplify: Factor from the numerator and factor from the denominator. Cancel the indicated factors. Reduce the fraction to...
 Polynomials-and-rational-expressions/181773: Can you help me wtih this problem? Factor by grouping: 1-n-m+nm1 solutions Answer 136362 by Earlsdon(6287)   on 2009-02-12 23:17:25 (Show Source): You can put this solution on YOUR website!Factor by grouping: Group as shown, and remember to change the sign (+ to -) in the last term: Factor the m in the second group. Now factor the (1-n) ...and you're done!
 real-numbers/181564: This question is from textbook introductory algebra The name of this book is "Introductory Algebra" By Keedy/Bittinger.6th edition. The page number is 102 problem #37. I am homeschooling my daughter and am having some trouble solving this problem. Thanks for any help you might can offer. 3{[7(x-2)+4]-[2(2x-5)+6]} If you could please help to solve this and also explain what the different parentheses mean.. thank you so much J.T1 solutions Answer 136164 by Earlsdon(6287)   on 2009-02-11 18:24:40 (Show Source): You can put this solution on YOUR website!You can't really "solve" an expression such as you have here but you certainly can "simplify" it, so we'll show how that's done. 3{[7(x-2)+4]-[2(2x-5)+6]} The different parentheses don't have any particular meaning and are used only as a grouping symbol. To simplify this expression, start on the inner parentheses (), then go on to the curly brackets {}, then to the square brackets []. 3{[7(x-2)+4]-[2(2x-5)+6]} Apply the "distributive property" on 7(x-2) = 7x-14 and 2(2x-5)=4x-10, to get: 3{[7x-14+4]-[4x-10+6]} Now simplify the quantities inside the square brackets [] 3{[7x-10]-[4x-4]} Now you can combine the insides of the two square brackets and, of course, remember to change the sign of the second group. 3{7x-10-4x+4} Combine like-terms inside the curly brackets {}. 3{3x-6} Finally, apply the distributive property to get: 9x-18 as the answer.
 Rational-functions/180741: This question is from textbook Saxon Algebra 2 A 20-centimeter straw is placed so that it fits exactly at a 60 degree angle to the base in a glass. How tall is the glass to the nearest centimeter? (The hypotenuse is 20cm) 1 solutions Answer 135506 by Earlsdon(6287)   on 2009-02-07 17:30:19 (Show Source): You can put this solution on YOUR website!Let the height of the glass = h. Using the sine function: Sin(a) = h/c where a = 60 degrees and c is the hypotenuse. cm The glass is 17 cm. tall.
 Travel_Word_Problems/180733: Variation Problem Disregarding wind resistance, the distance a body falls from rest varies directly as the square of the time it falls. If a skydiver falls 64ft in 2 seconds, how far will he fall in 10 seconds?1 solutions Answer 135505 by Earlsdon(6287)   on 2009-02-07 17:24:06 (Show Source): You can put this solution on YOUR website!Write the equation of variation: where d = distance in feet and t = time in seconds. k = the constant of variation. To find the value of k, substiute d = 64 ft. and t = 2 secs. Divide both sides by 4. The equation is now: Substitute t = 10 secs. feet.
 Quadratic_Equations/180786: Connect English With Mathematics and graphing Lines 3. For each of the following, write a word or phrase that has the opposite meaning. a) decreased b) subtracted c) less than d) minus e) added to f) more than Sorry, because my english is not good help me pleaseeee and thank you very much.1 solutions Answer 135503 by Earlsdon(6287)   on 2009-02-07 17:04:59 (Show Source): You can put this solution on YOUR website!a) Decreased...Increased. b) Subtracted...Added. c) Less than...More than. d) Minus...Plus. e) Added to...Subtracted from. f) More than...Less than.
 Rational-functions/180756: This question is from textbook Saxon Algebra 2 HELP!!! Divide x^2+4x over x+3 then divide by (8x^4+32x^3) 1 solutions Answer 135475 by Earlsdon(6287)   on 2009-02-07 11:33:33 (Show Source): You can put this solution on YOUR website! Invert the second divisor and multiply: Factor where possible: Cancel as indicated: Cancel an x: =
 Linear-equations/180685: Here is the question: 2x+y=4 I have to find the y intercept of this equation. Is the y intercept of this equation 4?1 solutions Answer 135416 by Earlsdon(6287)   on 2009-02-06 20:37:00 (Show Source): You can put this solution on YOUR website!Yes it is! To see this, put the equation into the "slope-intercept" form: y = mx+b where m = slope and b = y-intercept. subtract 2x from both sides of the equation. compare this with: and The slope is -2 and the y-intercept is 4.
 Linear-systems/180678: Could you please help me solve this, I have been trying for two days and I am not understanding what I am doing wrong. Thank you soooo much!!!! THe directions state to solve each by substitution and determine whether the equation is independent, dependent, or inconsistent. 2y=x+6 (this is the first part) -3x+2y=-2 (this is the second part) 1 solutions Answer 135414 by Earlsdon(6287)   on 2009-02-06 20:31:04 (Show Source): You can put this solution on YOUR website!Solve the system of equations: 1) 2) Substitute equation 1) for the 2y in equation 2). 2a) Simplify and solve for x by comining the x's. 2a) Subtract 6 from both sides of the equation. 2a) Divide both sides by -2. 2a) Now substitute this value of x into either one of the original equations to find y. Let's use equation 1). Substitute x = 4. Divide both sides by 2. The solution is: (4, 5) which is the intersection point of the two lines represented by the two linear equation.
 Radicals/180663: If a = -1 and b=2, then Square root 80a^4b/5b is equal to?1 solutions Answer 135406 by Earlsdon(6287)   on 2009-02-06 18:33:27 (Show Source): You can put this solution on YOUR website!You really should use parentheses to clearly describe the problem! Is it: or or Evaluate: if and or
 Expressions-with-variables/180270: x+5(squarerootx)-10=2(squarerootx)1 solutions Answer 135127 by Earlsdon(6287)   on 2009-02-04 20:49:31 (Show Source): You can put this solution on YOUR website!Solve for x: First subtract from both sides. Now add 10 to both sides. Next, subtract x from both sides to leave the by itself. Now square both sides. Subtract 9x from both sides. Factor the trinomial. Apply the zero product rule. or so... or But notice that while x = 4 is a valid root, x = 25 is an "extraneous" root introduced during the process by squaring, so x=25 does not work.
 Equations/180286: Word problem: Find two consecutive even integers such that the smaller integer subtracted from twice the larger gives a difference of 10. find the two even integers. I go the answers just by trial and error as: 6 & 8 but is there a formula to use for this problem? thanks1 solutions Answer 135120 by Earlsdon(6287)   on 2009-02-04 20:32:31 (Show Source): You can put this solution on YOUR website!Let x = the smaller even integer and x+2 = the next consecutive even integer. 2(x+2)-x = 10 "...the smaller integer subtracted from twice the larger integer gives a difference of 10." 2x+4-x = 10 x+4 = 10 x = 6 and x+2 = 8 The two consecutive even integers are 6 and 8.
 Inequalities/180222: The problem is not in my textbook,it is on a worksheet. f/-2<-8 f over negative 2 is less than negative 81 solutions Answer 135055 by Earlsdon(6287)   on 2009-02-04 16:57:26 (Show Source): You can put this solution on YOUR website!Solve for f: Multiply both sides by -2, and don't forget to reverse the inequality symbol.
 Equations/180041: I know the answer to my question, because I kept multiplying, but I don't know howto show my work as a stratey. The question is. In a math class of 26 students, each girl drew a triangle and each boy drew a rectangle. There were 92 slides in all. How may girls and how many boys were in the class. The answer I came up with was 16 girls and 11 boys.1 solutions Answer 134909 by Earlsdon(6287)   on 2009-02-03 20:31:02 (Show Source): You can put this solution on YOUR website!Let B = the number of boys and G = the number of girls. B+G = 26 "The number of students is 26" The girls drew triangles, each of which has three sides, so the total number of sides from the triangles is: 3*G The boys drew rectangles each of which has four sides, so the total number of sides from the rectangles is: 4*B Now you can write two equations as follows: 1) B+G = 26 Rewrite this as: B = 26-G and substitute for B in equation 2). 2) 4*B+3*G = 92 which is the total number of sides. 4(26-G)+3*G = 92 Simplify and solve for G. 104-4G+3G = 92 Subtract 104 from both sides. -G = -12 Divide through by -1 to make positive. G = 12 To find the number of boys (B): B = 26-G B = 26-12 B = 14 So the number of boys is 14 and the number of girls is 12 Check: B+G = 26 14+12 = 26 26 = 26 OK! 4*B+3*G = 92 4*14+3*12 = 92 56+36 = 92 92 = 92 OK!
 Exponential-and-logarithmic-functions/179676: 12 with a power of X = 527 -how would u solve this? 1 solutions Answer 134594 by Earlsdon(6287)   on 2009-02-01 21:10:15 (Show Source): You can put this solution on YOUR website!You would use logarithms to solve this kind of problem. Take the log of both sides. Apply the power rule to the left side. Now divide both sides by Evaluate using your calculator.
 Rational-functions/179673: I really need help with this equation with rational exponents. This problem is not from a text book, it is from a worksheet. (x-5)raised to the two-third power +3(x-5)raised to the one-third power-4=0 ( I couldn't figure out how to write this problem using the formula plotting system.) I have no idea how to work this problem. Please help!!!1 solutions Answer 134593 by Earlsdon(6287)   on 2009-02-01 21:02:17 (Show Source): You can put this solution on YOUR website!You can temporarily chang variables to facilitate solving problems like this: You can rearrange this as: Let's substitute to give us: Factor this: from which: or Replacing the variable: we get: or so... If Raise each side to the third power. but so... Add 5 to both sides. and... Cube both sides. Add 5 to both sides.
 Travel_Word_Problems/179599: A rock is thrown from the top of a building. The distance is feet, between the rock and the ground "t" seconds after it is thrown is given by d=16t^2+64X+128 what is the maximum height that the rock reaches?1 solutions Answer 134521 by Earlsdon(6287)   on 2009-02-01 15:20:40 (Show Source): You can put this solution on YOUR website!Your problem statement seems to have some anomalies in it! The standard formula for the height (as a function of time) of an object propelled upwards from an initial height of with an initial velocity of is given by: where g (the constant of acceleration due to gravity) is 32 ft/sec^2, so your formula should look like: Your formula also shows two different varaibles. t and x. So, back to the problem but starting with the correct formul, (the d in your problem will work just as well as the h(t)) we have: First, we'll find the time, t, at which the height, d, is at its maximum. The graph of the quadradtic equation that we have here is a parabola that opens downward (signified by the negative first term) so its maximum will occur at the vertex of the parabola, and this is given by: where a = -16 and b = 64, so... } secs. To find the maximum height, we substitute the time, t=2secs into the original equation and solve for d. feet. The rock will reach a maximum height of 192 feet.
 Polynomials-and-rational-expressions/179602: Complete the factoring 2x^5+10x^4-12x^3 = 2x^3(x-1)( )1 solutions Answer 134516 by Earlsdon(6287)   on 2009-02-01 14:50:11 (Show Source): You can put this solution on YOUR website!Factor: Factor the trinomial on the right side.
 Triangles/179555: Hi. In math class we are doing word problems with right triangles. Here is the problem: Suppose a roller coaster's height is 105 feet off the ground. The distance on the ground from the start of the hill to the top of the hill is 200 feet. How fat do you actually travel on the roller coaster's track?1 solutions Answer 134508 by Earlsdon(6287)   on 2009-02-01 12:13:09 (Show Source): You can put this solution on YOUR website!It would help you if you were to draw a diagram of the situation in which the right triangle's height represents the height of the roller coaster (105 ft.) and the triangle's base represents the roller coaster's distance from the start of the hill to the top of the hill (200ft.). To answer the question "How far do you actually travel on the roller coaster's track?", you need to find the length of the hypotenuse of the right triangle. This can be done using the Pythagorean theorem: where c is the hypotenuse and a and b are the lengths of the other two legs. So... Substitute a = 200ft. and b = 105ft. Take the square root of both sides of the equation. Using your calculator, you get... Rounding to the nearest foot, you get... c = 226 feet as the distance actually traveled on the roller coaster's track.
 Quadratic_Equations/179560: 3. Walt made an extra \$12,000 last year from a part-time job. He invested part of the money at 7% and the rest at 9%. He made a total of \$970 in interest. How much was invested at 7%? 1 solutions Answer 134505 by Earlsdon(6287)   on 2009-02-01 11:55:17 (Show Source): You can put this solution on YOUR website!Let x = the amount Walt invested at 7%, so the remainder (\$12000-x) was invested at 9%. The interest earned on these two amounts can be expressed as: (7%)(x) + (9%)(\$12000-x) and the sum of these two amounts is given as \$970.00 Now you can write the equation that will allow you to so;ve for x, the amount invested at 7%. First, change the percentages to their decimal equivalents: (7% = 0.07) and (9% = 0.09) Simplifying this, you'll get: Combine the x-terms. Subtract 1080 from both sides of the equation. Finally, divide both sides by -0.02 \$5,500.00 was invested at 7% while \$12000-\$5500 = \$6,500.00 was invested at 9%
 Square-cubic-other-roots/179561: Squareroot of 2x+3=2 Thank you1 solutions Answer 134503 by Earlsdon(6287)   on 2009-02-01 11:35:45 (Show Source): You can put this solution on YOUR website!Solve for x: Square both sides of the equation. Subtract 3 from both sides. Finally, divide both sides by 2.
 Numeric_Fractions/178857: Could you please help me with some fractions. These ones are to convert the improper fractions to mixed numbers: 1) 28/4 2) 10/3 3) 6/2 4) 50/13 Thank you in advance.I'm an older student and I haven't done fractions in a long time. Elle 1 solutions Answer 133820 by Earlsdon(6287)   on 2009-01-27 21:14:18 (Show Source): You can put this solution on YOUR website!Convert the improper fractions to mixed numbers: 1) Perform the indicated division (The numerator (28) divided by the denominator (4)). 2) Perform the indicated division. + or 3 1/3 3) Perform the indicated division. 4) Perform the indicated division. + or 3 11/13
 Numeric_Fractions/178859: Could you please show me how to do these fractions.These ones you have to change each fraction to an equivalent fraction: 1) 3/4 = --/16 ?=-- 2)1/12 = --/48 ? = -- 3) 5/6 = --/30 ? = -- 4) 3/8 = --/64 ? = -- Thank you for your help1 solutions Answer 133817 by Earlsdon(6287)   on 2009-01-27 21:06:46 (Show Source): You can put this solution on YOUR website!Convert to equivalent fractions: 1) Multiply both sides by 16. Simplify the left side. Cancel as indicated. , so... 2) Multiply both sides by 48. Simplify the left side. Cancel as indicated. so... 3) Multiply both sides by 30. Simplify the left side. Cancel as indicated. so... 4) Multiply both sides by 64. Simplify the left side. Cancel as indicated. so...
 Functions/178280: This question is from textbook college algebras Thank you in advance for your help. I do not understand what I need to do to find f^-1 and verify that (f o f^-1)(x)=x and (f^-1 o f )(x)=x the equation is f(x)=x/x+1 for x>-11 solutions Answer 133241 by Earlsdon(6287)   on 2009-01-24 15:58:15 (Show Source): You can put this solution on YOUR website!Verify that and for: for First, you'll need to find Start with the given function: Substitute for Now exchange x and y. Next, solve this for y. Multiply both sides by Expand the left side. Subtract xy from both sides. Factor the y from the right side. Divide both sides by Now replace the with Now you are in a position to find: Substitute recalling that Notice that where there is an x on the left side, it's replaced with on the right side. Now we'll simplify the right side. Invert and multiply. Do you think you can manage to show that ?