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# Recent problems solved by 'josmiceli'

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 Geometry_Word_Problems/428550: You are 90 ft from a tree. The angle of elevation from your eyes, which are 5 ft off the ground, to the top of the tree is 70 degrees. to the nearest foot, how tall is the tree?1 solutions Answer 297853 by josmiceli(9697)   on 2011-03-29 08:33:50 (Show Source): You can put this solution on YOUR website!Call the height of the tree You have a right triangle The base is 90 ft The height is The tree is 252 ft high
 Mixture_Word_Problems/428346: Assume you have sea water that weighs 64lb/ft3 and contains 35 parts per thousand (0.0035) dissolved salt by weight. How many cubic feet of the sea water would you need to place in an evaporation basin to collect 125lb of sea salt.1 solutions Answer 297767 by josmiceli(9697)   on 2011-03-28 19:55:03 (Show Source): You can put this solution on YOUR website! lbs/ft3 x ft3 x = lb ft3
 Miscellaneous_Word_Problems/428216: A hot air balloon is seen over Seven Springs simultaneously by two observers standing at two different points on the ground. ( The 2 people are facing each other and the balloon is in between them in the air.) They are 1.75 miles apart on ground level. The angles of elevation are 33 degrees and 37 degrees respectively. How high above the ground is the balloon?1 solutions Answer 297713 by josmiceli(9697)   on 2011-03-28 17:03:10 (Show Source): You can put this solution on YOUR website!Locate the point which is directly below the balloon. Call the point (C) The person who sees the balloon at 37 degrees elevation is looking higher, so that person is closer to the balloon. Call their position (A) Call the position of the other person (B) Call the position of the balloon (D) given: AB = 1.75 miles ------------ = DC / AC and, for the other person, = DC / BC ------------ .7536 = DC / AC .6494 = DC / BC ------------- DC = .7536 x AC DC = .6494 x BC ------------- .7536 x AC = .6494 x BC and Since AB = AC + BC 1.75 = AC + BC AC = 1.75 - BC -------------- .7536 x (1.75 - BC) = .6494 x BC Solve this for BC, then plug answer back into .6494 = DC / BC to get the height, DC
 Numbers_Word_Problems/428235: Salisbury High School decided to take their students on a field trip to a theme park. A total of 150 people went on the trip. Adults pay \$45.00 for a ticket and students pay \$28.50 for a ticket. How many students and how many adults went to the park if they paid a total of \$4770?1 solutions Answer 297705 by josmiceli(9697)   on 2011-03-28 16:40:59 (Show Source): You can put this solution on YOUR website!= number of students on trip = number of adults on trip given: (1) (2) (in cents) ---------------- Multiply both sides of (1) by and subtract (1) from (2) (2) (1) and, since (1) (1) There were 30 adults and 120 students check: (2) (2) OK
 Systems-of-equations/428228: My instructions are simply to "solve" the equation is 3x-(5-4x)=2(4x+2)+1 I've tried doing it and I stopped once I got -5=x+6 it didn't seem right, so I didn't finish it.1 solutions Answer 297701 by josmiceli(9697)   on 2011-03-28 16:29:01 (Show Source): You can put this solution on YOUR website! Now subtract from both sides Subtract from both sides. This is the same as adding a to both sides answer You can do a check by plugging this back into original equation: Now work from the inside of the parentheses outward OK
 Linear-equations/428225: The slope of the line that contains the points (4, 10) and (5, 13) is 3. Find the y-intercept1 solutions Answer 297699 by josmiceli(9697)   on 2011-03-28 16:15:31 (Show Source): You can put this solution on YOUR website!You can express the equation as (b is the y-intercept) Just plug in one of the points (4,10) (answer) Here's a plot:
 logarithm/428215: How do you express 4^-3=1/64 in logarithmic form? When I did this question I got log base 4 of 64 equals -3. I just wanted to be sure I was doing it right.1 solutions Answer 297697 by josmiceli(9697)   on 2011-03-28 16:09:11 (Show Source): You can put this solution on YOUR website!You're off a little You can take the log to base 4 of both sides
 Miscellaneous_Word_Problems/428211: Jack usually mows his lawn in 8 hours. marilyn can mow the same yard in 6 hours. How much time would it take for them to mow the lawn together?1 solutions Answer 297694 by josmiceli(9697)   on 2011-03-28 15:54:14 (Show Source): You can put this solution on YOUR website!You have to add their rates of mowing In words: ( 1 lawn) / (Jack's time to mow it) + (1 lawn ) / (Marilyn's time to mow it) = {1 lawn) / (Their time mowing it together) ---------------- given: Jack's rate = lawns/hour Marilyn's rate = lawns/hour ---------------- Multiply both sides by hrs or, about 3 hours and 26 minutes
 Problems-with-consecutive-odd-even-integers/428205: Name the set of 4 consecutive odd integers starting with -3.1 solutions Answer 297691 by josmiceli(9697)   on 2011-03-28 15:43:08 (Show Source): You can put this solution on YOUR website!You must count every other integer starting with an odd integers in order to get only odd integers If I call , then The set is {-3,-1,1,3}
 Equations/427920: Hii.. I'm really stuck on solving this:: 5x+3+(-x)=2x+1+2x+3 can u help me thanks1 solutions Answer 297517 by josmiceli(9697)   on 2011-03-27 20:42:29 (Show Source): You can put this solution on YOUR website! Note that , so the right side is Note that plus(minus) and minus(plus) = minus, so Now subtract from both sides Subtract from both sides This is not true, so the original equation can't be true If is subtracted from the right side, then The equation would be true for any
 Geometry_Word_Problems/427911: i dont know how to find my x and my y in this problem. you want to fence a rectangular area of your yard for a garden. you plan to use no more than 50ft of fencing. a. write a linear equation that describes the situation1 solutions Answer 297516 by josmiceli(9697)   on 2011-03-27 20:31:23 (Show Source): You can put this solution on YOUR website!If the dimensions of the yard are by , the perimeter is the distance around the yard. given: ft Divide both sides by
 Quadratic_Equations/427855: Find the area and perimeter of an 4 1/2-by-21-inch piece of paper. Area ? square inches Perimeter ? inches Please write down the steps to get the answer. Thanks1 solutions Answer 297487 by josmiceli(9697)   on 2011-03-27 18:53:01 (Show Source): You can put this solution on YOUR website!The paper is a rectangle To find area, multiply the sides in2 To find the perimeter, add up the 4 sides in in Note that area is in square inches, and perimeter is in inches
 Linear-equations/427332: During one year, the Peddys' real estate bill included \$948 for county improvements. Of this amount, \$308 went for transportation and roads. What percent did the Peddy family pay for transportation and roads? Round your answer to two decimal places1 solutions Answer 297186 by josmiceli(9697)   on 2011-03-26 11:38:17 (Show Source): You can put this solution on YOUR website!Per cent means "per one hundred" Multiply both sides by The family paid 32.49% for transportation and roads.
 Polynomials-and-rational-expressions/427325: how would you find the greatest common factor of 8ab^3 and 2ab^2? please explain.1 solutions Answer 297183 by josmiceli(9697)   on 2011-03-26 11:33:03 (Show Source): You can put this solution on YOUR website!It is the same problem as "What is the greatest common factor of 30 and 48?" 3 divides both of them, but so does 6, so that's the answer. Looking at and , I see that is a common factor, so is and . Note that will not divide into evenly. ----------------- is the common factor because and Note that there is no remainder in the divisions.
 Exponents-negative-and-fractional/427202: I need to graph these two linear equations x+y=9 and x-y=31 solutions Answer 297083 by josmiceli(9697)   on 2011-03-25 20:49:29 (Show Source): You can put this solution on YOUR website! and Here's the plot:
 Quadratic_Equations/427200: I am trying to find a way to solve this problem. A gravel path of equal width is to be built around a 8' by 8' square garden. How wide can the path be if there is enough gravel for 80 square ft?1 solutions Answer 297082 by josmiceli(9697)   on 2011-03-25 20:45:14 (Show Source): You can put this solution on YOUR website!You are putting 80 square feet around square feet Adding these, square feet. These combined areas have to be a square, since the path surrounds a square. ft is a side of the square. The path width is The path is 2 ft wide check: OK
 Quadratic_Equations/427167: what are the solutions to the equation x^2+7x=-121 solutions Answer 297066 by josmiceli(9697)   on 2011-03-25 19:23:17 (Show Source): You can put this solution on YOUR website! To complete the square, take 1/2 of the coefficient of , square it, and add it to both sides take the square root of both side and ---------- You can check by plugging in for and then for
 percentage/427175: Cece scored a 78 on her first math test. She scored an 84 on her second test. What is the percent increase, rounded to the nearest tenth, from Cece’s first score to her second score?1 solutions Answer 297065 by josmiceli(9697)   on 2011-03-25 19:06:25 (Show Source): You can put this solution on YOUR website!The increase is Let = percent gain 7.7 percent increase
 Money_Word_Problems/427050: Company A sold 14.7 million dollars of electronics equipment in 2000 and its sales have increased by 2.1 million dollars each year. Company B sold 19.4 million dollars of electric equipment in 2000 and its sales have increased by 1.7 million each year. 1) Let A (t) and B (t) repesent the sales (in millions of dollars) by company A and compnay B, respectively, at t years since 2000. Find equations for A and B. 2) Predict when sales at the companies will be equal. What will that sales be?1 solutions Answer 297004 by josmiceli(9697)   on 2011-03-25 13:03:54 (Show Source): You can put this solution on YOUR website!Let = sales for the year Let = the year Plot Sales on the vertical axis and the year on the horizontal You are given a point (2000,14.7) for company A. I'll call it (0,14.7) The rate of increase, or slope is millions/year To get the equation: (in millions) ------------------------- For company B, the point is (0,19.4), and the slope is millions/year ------------------------ To find where the lines intersect (equal amount of sales), Subtract B's equation from A's If the data is year-end data, then this figure means 9 months into 2012, or September 2012 Hope I got it right
 test/426991: Evaluate (-x)2 and-x2 when x=31 solutions Answer 296966 by josmiceli(9697)   on 2011-03-25 08:27:16 (Show Source): You can put this solution on YOUR website! -------------
 Age_Word_Problems/426990: When Tim started football 3 years ago, his coach was twice his age. Currently, Tim's coach is 10 years older than him. How old is Tim now? 1 solutions Answer 296965 by josmiceli(9697)   on 2011-03-25 08:24:01 (Show Source): You can put this solution on YOUR website!Let = Tim's age now Let = Coach's age now ----------------------- given: (1) (2) ---------------- Substitute (2) into (1) (1) (1) (1) Tim is 13 now check: (1) This is 10 years older than Tim is now
 Linear_Equations_And_Systems_Word_Problems/426987: A box has a volume of 100 cubic cm and the area of the bottom of the box is 50 square cm. Find the height of the box?1 solutions Answer 296962 by josmiceli(9697)   on 2011-03-25 08:13:35 (Show Source): You can put this solution on YOUR website!Given: cm3 cm2 -------------- cm3 cm3 cm
 Travel_Word_Problems/426915: Nestor finished a 42-kilometer race in 1 hour and 45 minutes. What was his average speed in kilometers per hour? Please explain how to get the answer. Thanks, Sparrow1 solutions Answer 296879 by josmiceli(9697)   on 2011-03-24 21:41:40 (Show Source): You can put this solution on YOUR website!You need an answer in km/hr, so you must covert 1 hour and 45 minutes to hours To convert minutes to hours, the units are: (minutes) x (hours/minute) = hours Plugging in numbers: , so there are hours in minutes Speed is (distance) / (time) km/hr km/hr km/hr
 Percentage-and-ratio-word-problems/426908: The ratio of apples in Barbara's store to those in Mark's store was 8:1. Barbara gave half her apples to Mark, and then Mark had 6 more apples than Barbara. How many apples did Barbara have first?1 solutions Answer 296874 by josmiceli(9697)   on 2011-03-24 21:33:22 (Show Source): You can put this solution on YOUR website!Let = number of apples Mark started with = Number Barbara started with given: Barbara started with 48 apples check: Barbara gives 24 to Mark Now Mark has 30 This is 6 more than Barbara's OK
 Coordinate-system/426862: What is the slope of a line that contains the coordinate points (7,-3) and (-2,5)?1 solutions Answer 296848 by josmiceli(9697)   on 2011-03-24 20:22:41 (Show Source): You can put this solution on YOUR website!The slope is (change in y) / (change in x), so given: (7,-3) and (-2,5) slope = slope =
 Money_Word_Problems/426856: Juan goes to a bank and gets change for a \$50 bill consisting of all \$5 bills and \$1 bills. There are 22 bills in all. How many of each kind are there?1 solutions Answer 296846 by josmiceli(9697)   on 2011-03-24 20:19:03 (Show Source): You can put this solution on YOUR website!Let = number of \$5 bills Let = number of \$1 bills given: (1) (2) ---------------- (1) By substitution: (2) and (1) There are 7 \$5 bills and 15 \$1 bills
 Polynomials-and-rational-expressions/426739: The initial velocity of a rocket shot straight upward is 40 ft/sec. The height of the rocket after t seconds is given by the formula h(t) = -16t(squared) + 40 t. What is the maximum height the rocket reaches? When will it land? Show and explain work.1 solutions Answer 296822 by josmiceli(9697)   on 2011-03-24 18:27:49 (Show Source): You can put this solution on YOUR website! The maximum height occurs at where To find the max height, The max height is 25 ft It will land when There are 2 ways for h(t) to be zero, ( at takeoff), and The rocket will land in 2.5 sec check answer: OK Here's a plot:
 Unit_Conversion_Word_Problems/426490: A car traveled 281 miles in 4 hours 41 minutes. What was the average speed of the car in miles per hour? Please show me how did you get the answer. Thank you. 1 solutions Answer 296673 by josmiceli(9697)   on 2011-03-24 03:11:53 (Show Source): You can put this solution on YOUR website!You just need to express 4 hrs 41 min in terms of hours. Then you will have an answer in miles/hour The simplest expression, since 41 has no divisors is hours + (min/(min/hr) = hrs The average speed is 60 mi/hr Note that is not a conversion, it is just another way to express hrs
 logarithm/426485: How to simplify log2(0.5)^4?. I tryed it and my answer wasn't right. My answer was 1, -4, -0.90 and 21 solutions Answer 296671 by josmiceli(9697)   on 2011-03-24 02:56:34 (Show Source): You can put this solution on YOUR website!It's a little confusing the way you present it Is it: or is it I'm guessing it's the first one The general rule is: , so note that From the above rule, this is so, the whole thing is: answer
 test/426456: Hi i really need help with my homework. I dont know how to do this problem. "Through point (3,1) with the same slope as line 2x-3y=1"1 solutions Answer 296645 by josmiceli(9697)   on 2011-03-23 23:45:43 (Show Source): You can put this solution on YOUR website!First, get the equation into the form In this form, = slope given: Subtract from both side Divide both sides by Any line parallel to this one will also have So far you have for the new line It goes through (3,1), so I can plug this x and y into equation to get So, the equation is answer Check: Does it go through (3,1)? OK
 Equations/426458: what is the first step in solving the equation x + 78 = 1351 solutions Answer 296642 by josmiceli(9697)   on 2011-03-23 23:33:35 (Show Source): You can put this solution on YOUR website! You always want to get the unknown by itself, so subtract from both sides. ( anything you do to one side, you must do to the other) answer