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Recent problems solved by 'edjones'

edjones answered: 7568 problems
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Triangles/81398: Height=h Base=h+7 Hypot=13 Find height and length 1 solutions Answer 72637 by edjones(7569)   on 2007-09-22 23:03:33 (Show Source): You can put this solution on YOUR website! h^2+(h+7)^2=13^2 a^2+b^2=c^2 h^2+h^2+14h+49=169 2h^2+14h-120=0 2(h^2+7h-60)=0 (h+12)(h-5)=0 h=-12 (discard) or h=5 height=5 base=5+7=12 Ed

Age_Word_Problems/99756: Mark is 3 less than 6 times Pat's age. Mark is 35 years old. How old is Pat? 1 solutions Answer 72635 by edjones(7569)   on 2007-09-22 22:32:03 (Show Source): You can put this solution on YOUR website! p=pat's age 6p-3=35 add 3 to each side: 6p=38 divide 6 into each side: p=6 1/3 y.o. Check: 6*19/3-3=35 38-3=35 true Ed

Polynomials-and-rational-expressions/98910: Could someone please show me how to solve this expression correctly? I am not getting the correct answer. 1 solutions Answer 72634 by edjones(7569)   on 2007-09-22 22:20:41 (Show Source): You can put this solution on YOUR website! Ed

Linear_Equations_And_Systems_Word_Problems/99758: Lopez spent 1/3 of his vaction money for travel and 2/5 of his vacation money for lodging. He spent $1100 for travel and lodging. What is the total amount of money he spent on his vacation? I know x + y = 1100 1/3x = 2/5y = (not sure from this point!!!) 1 solutions Answer 72630 by edjones(7569)   on 2007-09-22 21:51:22 (Show Source): You can put this solution on YOUR website! let x=vacation money 1x/3+2x/5=1100 multiply 15 times each side: 5x+6x=16500 11x=16500 divide 11 into both sides: x=$1500. Ed

Angles/99734: a linear pair where one angle measures 155 1 solutions Answer 72604 by edjones(7569)   on 2007-09-22 17:29:55 (Show Source): You can put this solution on YOUR website! a line = Ed

Length-and-distance/99730: O is the midpoint of NP; NP = 3x + 4y , NO = 2x + 3y - 5, OP = 5x - y, FIND the lengths of NO,OP, and NP. May you please show work also. N-----O-----P 1 solutions Answer 72603 by edjones(7569)   on 2007-09-22 17:26:15 (Show Source): You can put this solution on YOUR website! A) 2x+3y-5=5x-y subtract 5x and add y to each side: -3x+4y-5=0 add 5 to each side: -3x+4y=5 B) 3x+4y=2(2x+3y-5) 3x+4y=4x+6y-10 subtract 4 and 6y from each side: -x-2y=-10 Solved by pluggable solver: Solving a System of Linear Equations by Elimination/Addition Lets start with the given system of linear equations In order to solve for one variable, we must eliminate the other variable. So if we wanted to solve for y, we would have to eliminate x (or vice versa). So lets eliminate x. In order to do that, we need to have both x coefficients that are equal but have opposite signs (for instance 2 and -2 are equal but have opposite signs). This way they will add to zero. So to make the x coefficients equal but opposite, we need to multiply both x coefficients by some number to get them to an equal number. So if we wanted to get -1 and -3 to some equal number, we could try to get them to the LCM. Since the LCM of -1 and -3 is 3, we need to multiply both sides of the top equation by -3 and multiply both sides of the bottom equation by 1 like this: Multiply the top equation (both sides) by -3 Multiply the bottom equation (both sides) by 1 So after multiplying we get this: Notice how 3 and -3 add to zero (ie ) Now add the equations together. In order to add 2 equations, group like terms and combine them Notice the x coefficients add to zero and cancel out. This means we've eliminated x altogether. So after adding and canceling out the x terms we're left with: Divide both sides by to solve for y Reduce Now plug this answer into the top equation to solve for x Plug in Multiply Reduce Subtract from both sides Combine the terms on the right side Multiply both sides by . This will cancel out on the left side. Multiply the terms on the right side So our answer is , which also looks like (, ) Notice if we graph the equations (if you need help with graphing, check out this solver) we get graph of (red) (green) (hint: you may have to solve for y to graph these) and the intersection of the lines (blue circle). and we can see that the two equations intersect at (,). This verifies our answer. Check: NO) 6+10.5-5=11.5 OP) 15-3.5=11.5 NP) 9+14=23 11.5+11.5=23 Ed

Signed-numbers/99728: 3[2(4+3)]-2 been awhile please help 1 solutions Answer 72601 by edjones(7569)   on 2007-09-22 16:36:01 (Show Source): You can put this solution on YOUR website! 3[2(4+3)]-2 inside parentheses 1st: 3[2(7)]-2 3[14]-2 42-2=40 Ed

Problems-with-consecutive-odd-even-integers/98559: This question is from textbook Algeber and Trigonometry Finbd all sets of three consecutive positive odd integers whose sum is less than 20 but greater than 10 1 solutions Answer 72600 by edjones(7569)   on 2007-09-22 16:29:16 (Show Source): You can put this solution on YOUR website! let the integers be: x, x+2, x+4 10 10<3x+6<20 10<3x+6...4<3x...x<4/3 3x+6<20...3x<14...x<14/3 sinc we are dealing with integers that must be odd: 3<=x<=3 which means that the 1st integer can only be 3. 3+5+7=15 is the only possible sequence. Ed

Geometry_Word_Problems/99702: The area of a rectangle is 54 cm2. If the length of the rectangle is 3 more than its width, find the length and width of the rectangle. 1 solutions Answer 72599 by edjones(7569)   on 2007-09-22 16:10:05 (Show Source): You can put this solution on YOUR website! L*W=A L=w+3 w(w+3)=54 w^2+3w=54 w^2+3w-54=0 Factor: (w+9)(w-6)=0 w=-9 w=6 w can't be -9 so thow -9 out. w=6 cm Check: (6+3)*6=54 true Ed

Triangles/99722: how can i create a rectangle with two sides that each measure 2 centimeters, and whose area is exactly 13 cm2? 1 solutions Answer 72598 by edjones(7569)   on 2007-09-22 16:02:12 (Show Source): You can put this solution on YOUR website! L*W=A 2x=13 x=6.5 cm each of the other sides Ed

Linear-systems/99704: three no. are in the ratio 3:4:5 if the sum of the largest and the smallest equal the sum of the third and 52, find the numbers. 1 solutions Answer 72597 by edjones(7569)   on 2007-09-22 15:51:09 (Show Source): You can put this solution on YOUR website! sum of the largest and the smallest equal the sum of the third and 52, find the numbers. the new triangle must have the sides proportional to 3:4:5 let x= the multiple of each side to make a side of the new triangle. 3x+5x=4x+52 3x+5x-4x=52 4x=52 divide 4 into each side: x=13 13*3=39 13*4=52 13*5=65 Check: 39+65=52+52 104=104 Ed

Miscellaneous_Word_Problems/99724: Please help! This word problem has me stumped. An airplane covered 15 miles of its route while decreasing its altitude by 18,000 feet. Find the slope of the airplane's line of descent. Round to the nearest hundredth. I just don't think I have enough information to get a solution. 1 solutions Answer 72596 by edjones(7569)   on 2007-09-22 15:39:48 (Show Source): You can put this solution on YOUR website! 18,000/5280=3.41 mi I drew a diagram on graph paper. I had the plane at x=0 y=3.41 at the start of decent and at x=-15 y=0 at the end. this gives us 2 points. (0,3.41) and (-15,0) slope= change in y/change in x=(3.41-0)/0-(-15)=3.41/15=.227 Ed

Triangles/99712: Hi my name is Tim and I have a question about graphing triangles. 14. The vertices of a right triangle are (-12, 8), (24, 8), and (24, -7). Find the length of the hypotenuse of the triangle (hypotenuse = side opposite the right angle). 1 solutions Answer 72594 by edjones(7569)   on 2007-09-22 15:22:39 (Show Source): You can put this solution on YOUR website! you have to use the distance formula: on one of the sides. if you put the points on graph paper it becomes obvious that 36 and 15 are the lengths of 2 of the sides. and the 3rd side is the hypotenuse. now you can use the formula above or the pythagorean theorum: a^2+b^2=c^2 36^2+15^2=c^2 1296+225=1521 sqrt(1521)=39 (one way) (another way) Ed

Polynomials-and-rational-expressions/99715: i did this problem but still am having trouble can you please slove it for me with the work shown thank you y^2-11y+30= this is the work ive done so far: y^2-6y-5y+30=0 y(y-6)-5(y-6)=0 (y-5)(y-6)=0 product =30y^2 sum= 11y -6yx-5y=30 -6y-5y=+1y 1 solutions Answer 72591 by edjones(7569)   on 2007-09-22 14:54:42 (Show Source): You can put this solution on YOUR website! y^2-11y+30=0 factor: (y-5)(y-6)=0 y=5 or y=6 comments: your initial equation lacked a zero after the = sign. Your 3rd try led to the correct answer. the rest are bad algebra. practice factoring. get it down in your mind. Ed

Polynomials-and-rational-expressions/99716: i need help with this problem can you please show me how you would solve it and its solution thank you 3a^2y^2-6a^2y+21a^2 1 solutions Answer 72590 by edjones(7569)   on 2007-09-22 14:43:48 (Show Source): You can put this solution on YOUR website! factor: there is no equation to solve. (no equal sign) Ed

Problems-with-consecutive-odd-even-integers/99717: While Michelle sat observing birds at a bird feeder, one fourth of the birds flew away when they were startled by a noise. Two birds left the feeder to go to another stationed a few feet away. Three more birds flew into the branches of a nearby tree. Four birds remained at the feeder. How many birds were at the feeder initially? 1 solutions Answer 72586 by edjones(7569)   on 2007-09-22 14:34:38 (Show Source): You can put this solution on YOUR website! let x=number of birds initially x-x/4-2-3=4 multiply 4 times each side: 4x-x-8-12=16 3x-20=16 add 20 to each side: 3x=36 divide 3 into each side: x=12 bird originally at the feeder. Check: 12-12/4-2-3=4 12-3-2-3=4 true Ed

Quadratic_Equations/99713: Could you please help me solve this equation....The directions say Solve Each Equation by making an appropriate solution...Here is the problem: x-13√x+40=0 √=Square root...Didn't know if that looked like one so I was telling you what it was... 1 solutions Answer 72584 by edjones(7569)   on 2007-09-22 14:24:46 (Show Source): You can put this solution on YOUR website! square each side: x^2+80x+1600=169x x^2-89x+1600=0 factor: (x-64)(x-25)=0 x=64 or x=25 check: 64-13sqrt(64)+40=0...64-13*8+40=0...64-104+40=0 true 25-13sqrt(25)+40=0...25-13*5+40=0...25-65+40=0 true Ed

Quadratic_Equations/99676: Given F(X) = 4X^2 - 12X, solve f(X) > 0. 1 solutions Answer 72583 by edjones(7569)   on 2007-09-22 14:02:06 (Show Source): You can put this solution on YOUR website! 4x^2-12x>0 factor: 4x(x-3)>0 4x>0...x>0 x>3 Test point method find a value of f(x) below 0, between 0 and 3, and above 3: f(-1)=16 f(1)=-8 f(4)=16 f(x)>0 when x<0 or x>3 the graph tells all. Ed

Miscellaneous_Word_Problems/99698: A home purchased for $300,000 depreciated 8% over a 1-year period. What was the value of the home after at the end of the year? A) $278,000 B) $272,000 C) $274,000 D) $276,000 I came up with $276,000 is that correct? 1 solutions Answer 72578 by edjones(7569)   on 2007-09-22 13:22:22 (Show Source): You can put this solution on YOUR website! 300000*.08=24000 300000-24000=276000 you are correct. congratulations. Ed

Linear-systems/99707: the sum of a certain even no. and the fourth even no. after it is 48. find the no. 1 solutions Answer 72577 by edjones(7569)   on 2007-09-22 13:16:02 (Show Source): You can put this solution on YOUR website! Let x, x+8 be the numbers x+x+8=48 2x+8=48 subtract 8 from each side: 2x=40 divide 2 into each side: x=20 Check x+8=28 20+28=48 Ed

Equations/99710: This question is from textbook ALGEBRA1 5-x-x=-1 1 solutions Answer 72576 by edjones(7569)   on 2007-09-22 13:09:12 (Show Source): You can put this solution on YOUR website! 5-x-x=-1 5-2x=-1 subtract 5 from each side: -2x=-6 divide -2 into each side: x=3 Check: 5-3-3=-1 5-6=-1 -1=-1 Ed

Quadratic_Equations/99678: Given f(x)=x^2 * (x-7) - 16 * (x-7), solve f(x) is greater than or equal to 0 . Express your answer using interval notation. 1 solutions Answer 72575 by edjones(7569)   on 2007-09-22 12:59:44 (Show Source): You can put this solution on YOUR website! x^2 * (x-7) - 16 * (x-7)>=0 x^3-7x^2-16x+112>=0 factor (x-7)(x-4)(x+4)>=0 X[-4,4]U[7,infinity) Ed

Linear_Equations_And_Systems_Word_Problems/99672: Translate the following statement into an algebraic equation. Let x represent the number. 7 more than a number is 19 1 solutions Answer 72538 by edjones(7569)   on 2007-09-21 22:52:36 (Show Source): You can put this solution on YOUR website! x=19+7

Polynomials-and-rational-expressions/99634: Could someone please help me with this expression. I have tried but dont think I am doing it correctly. Simplify and assume x represents a positive number. 1 solutions Answer 72537 by edjones(7569)   on 2007-09-21 22:51:43 (Show Source): You can put this solution on YOUR website! Ed

Square-cubic-other-roots/99652: Perform the indicated division. Rationalize the denominator if necessary. Then simplify each radical expression. 6 - sqrt(20) divided by 2 1 solutions Answer 72535 by edjones(7569)   on 2007-09-21 22:44:48 (Show Source): You can put this solution on YOUR website! (6 - sqrt(20))/2 (6-2sqrt(5))/2 3-sqrt(5) Ed

Finance/99648: Can you help me simplify the following leaving the answer in index form please. 4m^8x2m^2/6m^5 or 4mx10 to the eight x 2m squared divided by 6m to the power of 5 1 solutions Answer 72501 by edjones(7569)   on 2007-09-21 20:42:24 (Show Source): You can put this solution on YOUR website! add the exponents when multiplying like numbers. subtract the exponents when dividing like numbers. 4m^8x2m^2/6m^5 8x^10/6m^5=4x^5/3 Ed

Radicals/99643: I need to solve this problem and I can'tfigure it out: square root of x^2-15=square root of 2x 1 solutions Answer 72498 by edjones(7569)   on 2007-09-21 20:33:34 (Show Source): You can put this solution on YOUR website! sqrt(x^2-15)=sqrt(2x) square both sides: x^2-15=2x x^2-2x-15=0 (x-5)(x+3)=0 x=-3 or x=5 Ed

Triangles/99635: Could someone please show me how to get the altitude of a triangle? I cant seem to remember the formula to solve. Please help me. Side A 13 Side B 13 Bottom 10 1 solutions Answer 72490 by edjones(7569)   on 2007-09-21 19:50:32 (Show Source): You can put this solution on YOUR website! The altitude divides the isoscoles triangle into 2 equal right triangles. let a=altitude b=10/2=5 c=13 a^2+b^2=c^2 5^2+a^2=13^2 a^2=169-25=144 altitude=12 Ed

Quadratic_Equations/99597: The width of a rectangular gate is 2 meters(m) larger than it's height. The diagonal brace measures sqrt 6m. Find the width and height. 1 solutions Answer 72486 by edjones(7569)   on 2007-09-21 19:29:45 (Show Source): You can put this solution on YOUR website! a^2+b^2=c^2 h^2+(h+2)^2=6 h^2+h^2+4h+4=6 2h^2+4h-2=0 h=.414214... m height(quadratic formula below) h+2=2.414214... m width check: .414214...^2+2.414214...^2=6 Ed Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc) Quadratic equation (in our case ) has the following solutons: For these solutions to exist, the discriminant should not be a negative number. First, we need to compute the discriminant : . Discriminant d=32 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 0.414213562373095, -2.41421356237309. Here's your graph:

Functions/99622: f(x)=(x+3)squared, f(4) 1 solutions Answer 72477 by edjones(7569)   on 2007-09-21 18:13:12 (Show Source): You can put this solution on YOUR website! f(4)=(4+3)^2=7^2=49 Ed

Exponents/99524: the area of aquare field is 60025 m. square. A man cycles along its boundary at 18 km/hr. I how much time will he return at the starting point. 1 solutions Answer 72392 by edjones(7569)   on 2007-09-21 00:50:58 (Show Source): You can put this solution on YOUR website! t=time s=speed d=distance m =.245 km (1 side of the field) perimeter = 4*.245=.980 km t=d/s t=.980/18=49/900 hr 49/900*60=49/15 min= 3 min 16 sec Ed