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Recent problems solved by 'josmiceli'

josmiceli answered: 9651 problems
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Miscellaneous_Word_Problems/738955: From her house, Ann drove to her grandmother's at an average speed of 60 miles per hour. She returned over the Same route at average speed of 45 miles per hour. If ann spent 7 hours traveling, how many miles is Ann's grandmother's house from her house? I have no idea what to do? 1 solutions Answer 450978 by josmiceli(9654)   on 2013-04-17 21:37:10 (Show Source): You can put this solution on YOUR website! Let = her time in hrs for the 1st trip = her time for the trip back Let = distance to grandmother's house ---------------- (1) (2) -------------------- Substitute (1) into (2) (2) (2) (2) (2) and (1) (1) (1) The distance to grandmother's house is 180 mi check: (2) (2) (2) (2) OK

test/738900: I am a new student and the SOLs are very close and I'm very lost! Now were working on factoring numbers the problems 3x^2-9x+6 1 solutions Answer 450957 by josmiceli(9654)   on 2013-04-17 19:26:52 (Show Source): You can put this solution on YOUR website! factor: Set it equal to zero Divide both sides by Note that and ----------------------- This leads me to the solution ---------------------- There is the more drawn-out way, also You know the solution will look like where both of and can be positive or negative. --------------------------- Expanding: ------------------------------------- You are given: ---------------- This shows how I got my solution

Travel_Word_Problems/738838: Your boat goes 20 MPH full throttle. You are going downstream at full throttle, 20 MPH. The river is flowing at 10 MPH. The river is straight and there is a straight road beside the river. How fast will a car have to travel to keep up with the boat? 20 MPH or 30 MPH? Thanks 1 solutions Answer 450936 by josmiceli(9654)   on 2013-04-17 17:41:41 (Show Source): You can put this solution on YOUR website! The speed of the current gets added to the speed of the boat, so mi/hr A car beside the boat would also have to travel at mi/hr

Linear-equations/738845: Jesse’s Catering charges a flat delivery fee of $30, plus $15.25 per person served. Bob’s Catering uses the equation C = 12.50 + 17.60p to determine the cost to serve p people. An office building needs to cater a meal for 20 people. Which statement is true? Jesse’s Catering will cost $27.15 more than Bob’s Catering. Jesse’s Catering will cost $27.15 less than Bob’s Catering. Jesse’s Catering will cost $29.50 more than Bob’s Catering. Jesse’s Catering will cost $29.50 less than Bob’s Catering. 1 solutions Answer 450932 by josmiceli(9654)   on 2013-04-17 17:35:43 (Show Source): You can put this solution on YOUR website! Jesse's equation: (1) Bob's Equation: (2) ---------------------- There are 20 people (1) (1) (1) -------------- (2) (2) (2) ----------------- The last choice is correct Jesse’s Catering will cost $29.50 less than Bob’s Catering.

Linear-systems/738782: Glenn is a chemist with Gemco Pharmaceutical. He needs to prepare 40 gallons of a 15% hydrochloric acid solution find the amount of a 12% solution and the amount of a 20% solution he should mix to get this solution. Again, i know how to solve a system of equations, but i dont know how to translate this problem, please help. 1 solutions Answer 450913 by josmiceli(9654)   on 2013-04-17 14:01:54 (Show Source): You can put this solution on YOUR website! Let = gallons of 12% solution needed Let = gallons of 20% solution needed -------------- (1) (2) ---------------------------- (2) (2) (2) Multiply both sides of (1) by and subtract (1) from (2) (2) (1) and, since (1) (1) 25 gallons of 12% solution are needed 15 gallons of 20% solution are needed check: (2) (2) (2) OK

Trigonometry-basics/738771: the hypotenuse of an isosceles right triangle is one meter longer than either of its legs. find the exact length of each side. 1 solutions Answer 450912 by josmiceli(9654)   on 2013-04-17 13:39:51 (Show Source): You can put this solution on YOUR website! If it's isosceles, then both legs are equal Let = length of one of the legs Use quadratic formula answer ------------------------ check: OK

Travel_Word_Problems/738657: You can travel 40 mi on your motorbike in the same time it takes your friend to travel 15 mi on his bicycle. If your friend rides his bike 20 mi/h slower than you ride your motorbike, find the speed for each bike. 1 solutions Answer 450885 by josmiceli(9654)   on 2013-04-17 08:33:50 (Show Source): You can put this solution on YOUR website! Let = speed for motorbike in mi/hr = speed for bikein mi/hrLet = the time for both in hrs -------------- Equation for motorbike: (1) Equation for bike: (2) -------------------- (2) Substitute (1) into (2) (2) (2) (2) -------------- (1) (1) (1) (1) The motorbike travels at 32 mi/hr The bike travels at 12 mi/hr ------------------- check: (2) (2) (2) (2) OK

Polynomials-and-rational-expressions/738487: 3-(5x-4)-9x=21 I don't know what to do! I tried to solve this way: -5x-9x=21-3+4 -14x=22 x= -22/14 but this isn't right... please help 1 solutions Answer 450831 by josmiceli(9654)   on 2013-04-16 20:29:01 (Show Source): You can put this solution on YOUR website! Multiply both sides by ----------- Your problem was dealing with Remember that (-) x (-) = (+), so ----------- Check the answer: OK

test/738493: A broken pipe was leaking 1 2/3 gal water per minute. It took mr. Wrench 10 1/2 min to stop the leak. How much water was wasted? ( answer in fraction form) 1 solutions Answer 450830 by josmiceli(9654)   on 2013-04-16 20:10:58 (Show Source): You can put this solution on YOUR website! ( 1 2/3 ) x ( 10 1/2 ) ( gal/min)( min ) ( 10 + (2/3)*10 + 1*( 1/2 ) + (2/3)*(1/2) 10 + 20/3 + 1/2 + 1/3 10 + 40/6 + 3/6 + 2/6 10 + 45/6 10 + 7 + 3/6 17 1/2 answer

logarithm/738480: Solve the logarithmic equation. log x + log(x + 48) = 2 1 solutions Answer 450828 by josmiceli(9654)   on 2013-04-16 20:03:20 (Show Source): You can put this solution on YOUR website! The key is to make the substitution ( by inspection ) ( disregard ) ----------- Check: OK cannot be an answer because the expession would make no sense. There cannot be a log which will gives you a negative number.

Polynomials-and-rational-expressions/738468: What polynomial function with rational coefficients works for the given roots: 3i and √6 1 solutions Answer 450826 by josmiceli(9654)   on 2013-04-16 19:46:10 (Show Source): You can put this solution on YOUR website! The imaginary roots always come in pairs, so There are roots , and

test/738372: Please tell me how I can solve this problem. Write the standard form of the equation of the parabola with axis of symmetry x=-1, vertex at (-1, 5) and where f(0)= 3. Graph the equation. 1 solutions Answer 450794 by josmiceli(9654)   on 2013-04-16 16:29:33 (Show Source): You can put this solution on YOUR website! When the form of the equation is The x-coordinate of the vertex is at , so ----------- So far I have ------------ You are given the point ( -1,5 ), so Now I have Also given the point (3,0) and, since and -------------- The equation is: -------------- check: Is the vertex at (-1,5) ? OK Does it go through (3,0) ? OK

Graphs/738122: A car dealer has 22 vehicles on his lot. If 8 of the vehicles are vans and 6 of the vehicles are red, and 10 vehicles are neither vans nor red, how many red vans does he have on his lot? (venn diagram) 1 solutions Answer 450685 by josmiceli(9654)   on 2013-04-15 22:19:53 (Show Source): You can put this solution on YOUR website! There are 2 intersecting circles. 1 circle is all vehicles that are vans The 2nd circle is all vehicles that are red ------------ 10 vehicles are outside these 2 circles, so 22 minus 10 is 12 vehicles that are inside the 2 circles. ------------ The vehicles that are in the intersection of the circles are counted twice: Once as being a van, and again as being red. ------------ Instead of 8 plus 6 = 14 vehicles, there are 22 minus 10 = 12 So, I can say there are 6 that are vans, but not red ones, there are 2 red vans, and there are 4 red vehicles that are not vans, and 6 + 2 + 4 = 12, as it should be. ------------- So the answer is 2 red vans

Money_Word_Problems/737961: Collin earns $75 for 6 hours of work. at that rate, how many hours would she have to work to earn $ 500? 1 solutions Answer 450611 by josmiceli(9654)   on 2013-04-15 17:20:50 (Show Source): You can put this solution on YOUR website! His rate of pay is dollars / hr in units: ( dollars ) /( dollars / hr ) = hrs It will take 40 hrs to earn $500

Travel_Word_Problems/737839: what fraction of 80m is 1km? 1 solutions Answer 450582 by josmiceli(9654)   on 2013-04-15 12:50:42 (Show Source): You can put this solution on YOUR website! km = m 1 km is 12.5 times 80 m

Travel_Word_Problems/737833: Walking at 3/4 of her usual speed, Molly arrives at her destination 2.5 hours late. What is her usual time for walking this distance? 1 solutions Answer 450581 by josmiceli(9654)   on 2013-04-15 12:42:40 (Show Source): You can put this solution on YOUR website! I will say that usually her motion equation is (1) When she walks at 3/4 her usual speed, her equation is: (2) -------------------------- The only units given are hours I can say unit, miles or what ever, so (1) (2) -------------------------- (2) Substitute (1) into (2) (2) (2) (2) (2) (2) and, since (1) (1) (1) (1) Her usual time is 7.5 hrs check: (2) (2) (2) (2) Hope I got it

Equations/737783: How many liters of a 10% saline solution must be mixed with 20 liters of a 15% saline solution to make a 12% saline solution? 1 solutions Answer 450562 by josmiceli(9654)   on 2013-04-15 09:59:56 (Show Source): You can put this solution on YOUR website! Let = liters of 10% solution needed = liters of salt in 10% solution liters of salt in 15% solution ------------------- 30 liters of 10% solution are needed check: OK

Graphs/737772: please explain to me: find an equation of the line that has x-intercept (2,0) and is perpendiclar to 4x+3y=6 1 solutions Answer 450560 by josmiceli(9654)   on 2013-04-15 09:51:13 (Show Source): You can put this solution on YOUR website! First realize that ANY line which is perpendicular to thr given line will have the same slope, so that is the 1st thing to find. ---------------- The equation is in the standard form. Put it into the slope-intercept form which is The will be the slope of this line. ---------------- ------------------- Now find the slope that is perpendicular to this slope The formula is , so ------------------ So far, you have: You just need to find ------------------------ You given the point (2,0) also, so just plug this x and y into the equation and solve for ------------- The complete equation is: ------------------- Check: does it go through (2,0)? OK Here is the plot of both lines:

Rectangles/737623: Please help me to solve this problem. Thank you so much The hypotenuse of a right triangle is 4 meters more than the length of the longer leg. The shorter leg is 20 meters. Find the length of the longer leg. 1 solutions Answer 450472 by josmiceli(9654)   on 2013-04-14 21:07:17 (Show Source): You can put this solution on YOUR website! Shorter leg = Longer leg = Hypotenuse = given: ------------ The longer leg is 48 m ------------ check: OK

Travel_Word_Problems/737631: Mary walks at 4 mph. sarah jogos 10 mph. if they both leave the school at 8 am going along the same path in the same direction, at what time will they be 9 miles apart? 1 solutions Answer 450462 by josmiceli(9654)   on 2013-04-14 20:18:59 (Show Source): You can put this solution on YOUR website! Let = Sarah's distance when they are 9 mi apart = Mary's distance when they are 9 mi apart Let = time in hrs passed after 8 AM when they are 9 mi apart ------------- Sarah's equation: (1) Mary's equation: (2) ------------ (2) By substitution: (2) (2) (2) ' 8 AM + 3/2 hrs = 9:30 AM check: (1) (1) and (2) (2) (2) OK

Travel_Word_Problems/737528: A red car is traveling at 55 mph. A blue car is traveling at 65 mph. The cars are 305 miles apart. The cars started at the same spot at different times. The cars have been driving for 5 hours. Which system of equations could be used to solve for the total driving time of the red car (r) and the total driving time of the blue car (b)? 1 solutions Answer 450418 by josmiceli(9654)   on 2013-04-14 16:22:29 (Show Source): You can put this solution on YOUR website! Let = distance red car has traveled = distance blue car has traveled = time for red car = time for blue car ----------------------- One of the cars must have been traveling for hrs, the other for less time ----------------------- red car: (1) blue car: (2) --------------------- (2) = By substitution: The red car had to be the one traveling for , since is too much, so hrs The red car drove for 5 hrs, the blue car drove for 6/13 hrs check: (1) (1) (1) and (2) (2) (2) OK

Travel_Word_Problems/737518: a private plane traveled from seattle to a rugged wilderness at an average of 132 mph. On the return trip, the average speed was 231 mph. If the total traveling time was 7 hours, how far is Seattle from the wideness? 1 solutions Answer 450400 by josmiceli(9654)   on 2013-04-14 15:53:33 (Show Source): You can put this solution on YOUR website! Let = the one-way distance the plane flies Let = the time in hours for the 1st trip = the time for the return trip ------------- 1st trip: Return trip: By substitution: and The distance from Seattle to wilderness is 588 mi check: OK

Linear-equations/737497: I'm not even certain how to begin to start this, I thought the formula for solving it might be A=10t-19944 but I can't figure out if it's right or not. -- A certain mountain has an elevation of 19,944 feet. In 1918, the glacier on this peak covered 10 acres. By 2003 this glacier had melted to only 1 acre. A: Assume that this glacier melted at a constant rate each year. Find this yearly rate. B: Use your answer from part (a) to write a linear equation that gives the acreage A of this glacier t years past 1918 1 solutions Answer 450396 by josmiceli(9654)   on 2013-04-14 15:32:12 (Show Source): You can put this solution on YOUR website! (a) The rate of melting is ( change in acres ) / ( years passed ) Rate = Rate = ------------- (b) , where = acres covered = time in years = slope from part (a) = -intercept, where ( I am saying that 1918 is ) In 1918, -------------- check: when acre OK

Travel_Word_Problems/737488: if your friend lives 90 miles away and you need to be at their house in 120 minutes, how fast do you need to drive up there in miles per hour? 1 solutions Answer 450391 by josmiceli(9654)   on 2013-04-14 15:15:48 (Show Source): You can put this solution on YOUR website! In terms of units: ( miles / minutes ) x ( minutes / hour ) = miles / hour mi/hr

Linear_Equations_And_Systems_Word_Problems/737422: eggs are sold in boxes. a small box holds 6 eggs a large box holds 12 eggs hina buys x small boxes of eggs hina also buys 4 less of the large boxes of eggs than the small boxes. find, in terms of x, the total number of eggs in the large boxes that hina buys find in terms of x the total number of eggs that hina buys give your answer inits simplest form 1 solutions Answer 450367 by josmiceli(9654)   on 2013-04-14 11:04:49 (Show Source): You can put this solution on YOUR website! = totyal number of eggs in large boxes = total number of eggs

Linear-equations/737409: Dear tutor, For the problem: Write an equation of the line that passes through the given point and is parallel to the given line (18,2), 3y=x-12 I went through these steps: changed the equation to slope-intercept form: y=1/3x-4 Then plugged in the x and y variables from the point and the slope and solved for b: y=mx+b 2=1/3(18)+b b=-4 And ended up getting the equation y=1/3x-4, which is the same as the original! Is this correct or did I do something wrong? Thanks for the help! 1 solutions Answer 450362 by josmiceli(9654)   on 2013-04-14 10:58:02 (Show Source): You can put this solution on YOUR website! It looks like the point ( 18,2 ) is on the given line ----------- The line is parallel to itself, so the answer is OK

Word_Problems_With_Coins/737413: Please help me solve this word problem with steps. Thank You Andy has 27 coins made up of quarters and half dollars, and their total value is $9.00. How many quarters does he have? 1 solutions Answer 450359 by josmiceli(9654)   on 2013-04-14 10:45:27 (Show Source): You can put this solution on YOUR website! Let = number of quarters Let = number of half dollars --------------- (1) (2) ( in cents ) -------------------------------- (2) Subtract (1) from (2) (2) (1) and (1) (1) There are 18 quarters and 9 half dollars

Miscellaneous_Word_Problems/737403: It's for a venn diagram A school offers hockey and basketball. The result of a survey of 300 students showed: 120 play hockey only 90 play basketball only 30 don't play anything How many play both bastekball and hockey Thank you 1 solutions Answer 450354 by josmiceli(9654)   on 2013-04-14 10:34:19 (Show Source): You can put this solution on YOUR website! It's much easier if you draw 2 intersecting circles Then you have to label the parts of the circles the problem is talking about. ---------------- One circle is labeled H and contains all those who play hockey The other circle is labeled B and contains all those who play basketball ------------------------- The intersection of the 2 circles is those who play both sports ------------------------- Everything outside the 2 circles is those who play neither sport. There are there ------------------------- The area of the H circle that doesn't include the intersection is those who only play hockey There are of these ------------------------- The area of the B circle that doesn't include the intersection is those who only play Basketball There are of these ------------------------- The only area left is the intersection of the 2 circles which is those who play both sports ------------------------- Add what you have so far There are students total, so 60 students play both sports

Exponents/737299: what expressions is equivalent to x to the power of 6 and x to the power of 2 1 solutions Answer 450274 by josmiceli(9654)   on 2013-04-13 19:35:24 (Show Source): You can put this solution on YOUR website!

Miscellaneous_Word_Problems/737286: Christine and Peter earn a combined annual income of $190,500. If Christine earns $30,500 per year more than Peter, what are their individual annual salaries? 1 solutions Answer 450273 by josmiceli(9654)   on 2013-04-13 19:33:04 (Show Source): You can put this solution on YOUR website! Let = Peter's salary = Christine's salary Peter's salary is $80,000 Christine's is $110,500

Mixture_Word_Problems/737244: how many milliliters of a 17% alcohol solution must be added to 52 mL of a 8% alcohol solution to make a 13% alcohol solution? I did: .15x + .04(42)=.08(42+x) .15x + 1.68=3.36+.08x -.08x -.08x .07x+1.68=3.36 -1.68 -1.68 .07x=1.68 x=24 Then I filled in x: .08(42+24) 66(.08)=5.28 1 solutions Answer 450255 by josmiceli(9654)   on 2013-04-13 16:55:51 (Show Source): You can put this solution on YOUR website! I'll try my method and see if it agrees Let = ml of 17% solution needed ml of alcohol in 8% solution --------------- 65 milliliters of a 17% alcohol solution must be added check: OK