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# Recent problems solved by 'ewatrrr'

ewatrrr answered: 10675 problems
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 Quadratic-relations-and-conic-sections/622704: Graph (x+1)^2/9 + (y+3)^2/25 = 11 solutions Answer 391539 by ewatrrr(10682)   on 2012-06-21 09:31:47 (Show Source): You can put this solution on YOUR website! ``` Hi, Ellipse C(-1,-3) Vertices(-1,2),(-1,-8) and (2,-3),(-4,-3) See below descriptions of various conics Standard Form of an Equation of a Circle is where Pt(h,k) is the center and r is the radius Standard Form of an Equation of an Ellipse is where Pt(h,k) is the center. (a positioned to correspond with major axis) a and b are the respective vertices distances from center and ±are the foci distances from center: a > b Standard Form of an Equation of an Hyperbola opening right and left is: where Pt(h,k) is a center with vertices 'a' units right and left of center and foci units right and left of center along y = k Standard Form of an Equation of an Hyperbola opening up and down is: where Pt(h,k) is a center with vertices 'b' units up and down from center, and foci units units up and down from center, along x = h the vertex form of a Parabola opening up(a>0) or down(a<0), where(h,k) is the vertex. The standard form is , where the focus is (h,k + p) the vertex form of a Parabola opening right(a>0) or left(a<0), where(h,k) is the vertex. The standard form is , where the focus is (h +p,k ) ```
 Angles/622687: four times the angle is equal to twice its supplement find the angle 1 solutions Answer 391538 by ewatrrr(10682)   on 2012-06-21 09:21:26 (Show Source): You can put this solution on YOUR website! ``` Hi, four times the angleis equal to twice its supplement 4x = 2(180° - x) 6x = 360° x = 60° (supplement is 120°) ```
 logarithm/622684: Express the logarithm in terms of log2M and log2N: log2 (M/N)7 1 solutions Answer 391523 by ewatrrr(10682)   on 2012-06-21 08:29:56 (Show Source): You can put this solution on YOUR website! ``` Hi, ______________________________________________________________________ ***** ****** ```
 Length-and-distance/622430: find the other endpoint when given the following points: endpoint: (-4,3) midpoint: (6,3) endpoint: (5,0) midpoint: (-3,-5) endpoint: (4,1) midpoint: (3,0)1 solutions Answer 391388 by ewatrrr(10682)   on 2012-06-20 14:07:06 (Show Source): You can put this solution on YOUR website! ``` Hi, Note: Midpoint Pt(x,y): ( , ) endpoint: (-4,3) midpoint: (6,3) (-4 + x)/2 = 6 and (3+y)/2 = 3 Pt(16,3) endpoint: (5,0) midpoint: (-3,-5) endpoint: (4,1) midpoint: (3,0) ```
 test/622425: A rug is to fit in a room so that a border of consistent width is left on all four sides. If the room is 9 feet by 25 feet and the area of the rug is 57 square feet, how wide will the border be? Answers I can choose from: 3ft 4ft 5ft 5.5ft Thank you!1 solutions Answer 391387 by ewatrrr(10682)   on 2012-06-20 14:03:22 (Show Source): You can put this solution on YOUR website! ``` Hi, A rug is to fit in a room so that a border of consistent width is left on all four sides. If the room is 9 feet by 25 feet and the area of the rug is 57 square feet, how wide will the border be? (9-2x)(25-2x) = 57ft^2 9*25 - 68x + 4x^2 = 57 4x^2 - 68x +168 = 0 x^2 - 17x + 42 = 0 Factoring (x - 14)(x-3) = 0 x = 3' the width of the border. (throwing out 14 for the border) CHECKING our Answer*** 3 * 19 = 57ft^2 ```
 Linear-systems/622415: The average home price in Linden Hills, Minneapolis in 2007 was \$381,000. The average home price in Linden Hills, Minneapolis in 2011 was \$296,000 Source: http://www.zillow.com/local-info/MN-Minneapolis-home-value/r_5983/ Let year be the x variable and the home price be the y variable. Generate a linear function that relates year (x) to home price (y). Estimate what the average home price was in 2009. Estimate what the average home price will be in 2035. Discuss your answer. If this trend continues, estimate what year you would predict the average home price will reach \$250,000. Describe in your own words, what the slope of this function tells you. Give another example where you might use a linear representation to model change over time. Hint for a- f: You have two points and you are generating the equation of a line given two points. Your points are of the form (x, y) or more specifically (year, home price).1 solutions Answer 391382 by ewatrrr(10682)   on 2012-06-20 13:52:30 (Show Source): You can put this solution on YOUR website! ``` Hi, The average home price in Linden Hills, Minneapolis in 2007 was \$381,000 The average home price in Linden Hills, Minneapolis in 2011 was \$296,000 (0,381,000) (4,296,000 m = 85,000/-4 = -21,250 Generate a linear function that relates year (x) to home price (y). where x is the number of years after 2007 Estimate what the average home price was in 2009. \$338,500 Estimate what the average home price will be in 2035. -21250*28 + 381,000 If this trend continues, estimate what year you would predict the average home price will reach \$250,000. 250,000 = -21250x + 381,00 -131,000/ -21250 = x = 6.165 2007 + 7 = 2014 ```
 Probability-and-statistics/622403: The number of ways of selecting 2 boys and 2 girls from a group of 4 boys and 5 girls. 1 solutions Answer 391368 by ewatrrr(10682)   on 2012-06-20 13:22:45 (Show Source): You can put this solution on YOUR website! ``` Hi, Previously Posted The number of ways of selecting 2 boys or 2 girls from a group of 4 boys and 5 girls 4C2*5C2 = 6*10 = 60 ways ```
 Probability-and-statistics/622416: The number of ways of selecting 2 boys and 2 girls from a group of 4 boys and 5 girls 1 solutions Answer 391367 by ewatrrr(10682)   on 2012-06-20 13:22:16 (Show Source): You can put this solution on YOUR website! ``` Hi, Previously Posted The number of ways of selecting 2 boys or 2 girls from a group of 4 boys and 5 girls 4C2*5C2 = 6*10 = 60 ways ```
 Surface-area/622375: What is the sum of the measures of the interior angle of a polygon with 7 sides? 1 solutions Answer 391366 by ewatrrr(10682)   on 2012-06-20 13:17:16 (Show Source): You can put this solution on YOUR website! ``` Hi What is the sum of the measures of the interior angle of a polygon with 7 sides? Note: In general 180°(n-2) is the sum of the interior angles of a polygon with n-sides 180°(7-2) = 180*5 = 900° ```
 Numbers_Word_Problems/622412: One-fifth of a number plus one-third of the number is 140. Find the number.?1 solutions Answer 391359 by ewatrrr(10682)   on 2012-06-20 12:46:40 (Show Source): You can put this solution on YOUR website! ``` Hi, One-fifth of a numberplus one-third of the numberis 140. Question states*** || |Multiplying thru by 15 so as all denominators = 1 3x + 5x = 140*15 8x = 140*15 x = 140*15/8 x = 262.5 CHECKING our Answer*** ```
 Probability-and-statistics/622404: The number of ways of selecting 2 boys or 2 girls from a group of 4 boys and 5 girls1 solutions Answer 391355 by ewatrrr(10682)   on 2012-06-20 12:40:35 (Show Source): You can put this solution on YOUR website! ``` Hi, The number of ways of selecting 2 boys or 2 girls from a group of 4 boys and 5 girls 4C2*5C2 = 6*10 = 60 ways ```
 Probability-and-statistics/622408: A bag contains 17 marbles - 6 blue, 7 red, and 4 green marbles. If four marbles are drawn randomly (without replacement), determine the probability that three of them are green1 solutions Answer 391354 by ewatrrr(10682)   on 2012-06-20 12:37:13 (Show Source): You can put this solution on YOUR website! ``` Hi, A bag contains 17 marbles - 6 blue, 7 red, and 4 green marbles. If four marbles are drawn randomly (without replacement) P(3 are green) = ```
 Money_Word_Problems/622389: a man made two investments one at 8% and another at 10% if the total annual simple interest is \$1760 and the total amount invested is \$20000 how much was invested at each rate1 solutions Answer 391340 by ewatrrr(10682)   on 2012-06-20 11:42:27 (Show Source): You can put this solution on YOUR website! ``` Hi, Let x represent the amount invested at larger interest rate Question states*** .10x + .08(20000 - x) = \$1760 .02x = 1760 - 1600 .02x = 160 x = \$8000 (smount at 10%). Amount at 8% was \$12,000 And CHECKING our Answer*** \$800 + \$960 = \$1760 ```
 Travel_Word_Problems/622388: Going north with jet stream, a plane makes a 1200 mile trip in 3 hours. Going south against the jet stream, the plane makes the trip in 4 hours. Find the speed of the plane and the speed of the jet stream.1 solutions Answer 391337 by ewatrrr(10682)   on 2012-06-20 11:36:27 (Show Source): You can put this solution on YOUR website! ``` Hi, Going north with jet stream, a plane makes a 1200 mile trip in 3 hours. Going south against the jet stream, the plane makes the trip in 4 hours. D = rt or D/t = r 1200/3 = r + s 1200/4 = r - s 400 = r + s 300 = r - s 700 = 2r r = 350mph, speed of plane and speed of jet stream is 50mph (350+s = 400) ```
 Miscellaneous_Word_Problems/622386: A skating rink is 32ft x 49ft. The ply wood boards used to build it are 48 inches. Ply wood comes in 4 x 8 pieces. How many pieces of ply wood are used to build the rink?1 solutions Answer 391335 by ewatrrr(10682)   on 2012-06-20 11:30:25 (Show Source): You can put this solution on YOUR website! ``` Hi, P = The ply wood boards used to build it are 48 inches. or 4' linear length of boards needed 4' by 8' will yield pieces 4' by 4' 40.5/2 = 20.25, will need 21 pieces of plywood ```
 Linear_Equations_And_Systems_Word_Problems/622373: In a classroom there are two kinds of seats; single and double. There are twice as single seats as double seats. THe room can accomodate 76 pupils. How many each kind of seats are there?1 solutions Answer 391333 by ewatrrr(10682)   on 2012-06-20 11:19:21 (Show Source): You can put this solution on YOUR website! ``` Hi, In a classroom there are two kinds of seats; single and double. There are twice as single seats as double seats. THe room can accomodate 76 pupils. How many each kind of seats are there? Question states*** Students = Students 76 = single seats + 2(double seats) 76 = 2x + 2(x) 76 = 4x x = 19 double seats and 38 single seats CHECKING our Answer*** 38 + 2*19 = room for 76 Students ```
 Exponents/622379: A speculator bought stocks and later sold them for 19170.00, making a profit of 6.5%. How much did the stocks cost him?1 solutions Answer 391332 by ewatrrr(10682)   on 2012-06-20 11:07:49 (Show Source): You can put this solution on YOUR website! ``` Hi, A speculator bought stocks and later sold them for 19170.00, making a profit of 6.5%. How much did the stocks cost him? ```
 Points-lines-and-rays/622327: what acute angle does a line of slope -3/4 make with a horizontal line?1 solutions Answer 391329 by ewatrrr(10682)   on 2012-06-20 10:29:17 (Show Source): You can put this solution on YOUR website! ``` Hi, what acute angle does a line of slope -3/4 make with a horizontal line? tanθ = 3/4, θ ~ 36.87° ```
 Probability-and-statistics/622341: A jar contains seven coins: a dime, 2 quarters, and 4 nickels. One coin is taken from the jar at random. What is the probability that the coin taken is a nickel?1 solutions Answer 391326 by ewatrrr(10682)   on 2012-06-20 10:05:28 (Show Source): You can put this solution on YOUR website! ``` Hi, 7 coins: 1 dime, 2 quarters and 4 nickels One coin is taken from the jar at random. P(nickel) = ```
 Probability-and-statistics/622343: A bag has ten marbles in it. Three of them are green, one of them is red, five of them are yellow, and one of them is blue. If one marble is taken out of the bag randomly, what is the probability that it will either be green or red?1 solutions Answer 391325 by ewatrrr(10682)   on 2012-06-20 10:03:43 (Show Source): You can put this solution on YOUR website! ``` Hi, 10 marbles: 3 green, 1 red, 5 yellow and 1 blue If one marble is taken out of the bag randomly P(green 'or' red) = P(green) + P(red) = ```
 Probability-and-statistics/622345: There are three green, three blue and three white marbles in a jar. What is the probability of drawing first a white marble and then a blue marble, without replacing the first marble into the jar?1 solutions Answer 391324 by ewatrrr(10682)   on 2012-06-20 10:00:18 (Show Source): You can put this solution on YOUR website! ``` Hi, 9 marbles: 3 green, 3 blue, 3 white without replacement P(white, then blue) = ```
 Linear-systems/622357: 3x-2y=0, x+2y=8 1 solutions Answer 391322 by ewatrrr(10682)   on 2012-06-20 09:51:15 (Show Source): You can put this solution on YOUR website! ``` Hi, 3x-2y=0, Green y = (3/2)x x+2y=8 Blue y = (-1/2)x + 4 4x = 8 x = 2 and y = 3 (6-2y = 0, 2y = 6, y = 3) Ordered pair (2,3) is the solution to this system fo Equations ```
 Numbers_Word_Problems/622361: find a four-digit whole number that satisfies the following conditions: the number is less than 1,300, the sum of the digits is 14, none of the digits are equal, and the digits in the tens place and ones place are consecutive numbers.1 solutions Answer 391320 by ewatrrr(10682)   on 2012-06-20 09:44:03 (Show Source): You can put this solution on YOUR website! ``` Hi, four-digit whole number <1300, sum of digits 1s 14 1 2 x 3 1 +2 + x +3= 14 x = 8 1283 would satisfy the conditions ```
 Linear-systems/622360: Find the midpoint coordinates of the segment that connects the following given points: (4, -3) and (0, -3) (4, 4) and (4, 0) (7, -7) and (9, -7) (-3, 4) and (-8, 4) (-4, 2) and (-4, 0) (2, 6) and (2, 2) (-18.7, -19.9) and (-10.5, -6.3) (8, a + 7) and (5, a + 11) (d - 5, -4) and (d - 3, -6) (-4, -8) and (-4, -13) (-14, -17) and (-10, -30) (-21, 21.9) and (-17.8, 20.2) 1 solutions Answer 391319 by ewatrrr(10682)   on 2012-06-20 09:39:35 (Show Source): You can put this solution on YOUR website!``` Hi, Note: Midpoint Pt(x,y): ( , ) for ex: (-3, 4) and (-8, 4) Midpoint is (-11/2,4) (8, a + 7) and (5, a + 11) midpoint is (13/2, (a + 9)) (-14, -17) and (-10, -30) midpoint is (-12, -47/2) ```
 Linear-equations/622354: Use the information provided to write the vertex form equation of each parabola. Vertex at origin, focus: (0, -1/4) 1 solutions Answer 391318 by ewatrrr(10682)   on 2012-06-20 09:34:31 (Show Source): You can put this solution on YOUR website! ``` Hi, the vertex form of a Parabola opening up(a>0) or down(a<0), where(h,k) is the vertex. The standard form is , where the focus is (h,k + p) Parabola with Vertex at origin, focus: (0, -1/4) 4py = x^2 and p = -1/4, y = -x^2 ```
 Functions/622355: I have to solve this algebraically, not by using a graph: A parabola has a vertex (8, 3) and one x intercept of 5. Determine the coordinates of the other x- intercept. 1 solutions Answer 391317 by ewatrrr(10682)   on 2012-06-20 09:25:50 (Show Source): You can put this solution on YOUR website! ``` Hi, solving algebraically: Parabola with V(8,3) and passing thru (5,0) y = a(x -8)^2 + 3 0 = a(5-8)^2 + 3 -3/9 = a y = (-1/3)(x-8)^2 + 3 0 = (-1/3)(x-8)^2 + 3 -3 = (-1/3)(x-8)^2 (x-8)^2 = 9 (x-8) = ± 3 x = 5 and x = 11 (11,0) are the coordinates of the other x- intercept. ```
 Linear-systems/622349: Could someone please double check my work please, f. What is the profit made from selling 20 tiles per month?(answer- worth 3 points - must show work) P(20)=-20^2+(33*20)-200 P(20)=400+660-200 P(20)=460 The profit made from selling 20 tile sets per month is \$460.00 g. What is the profit made from selling 25 tiles each month?(answer- worth 3 points - must show work) P(25)=-25^2+(33*25)-200 P(25)=625+825-200 The profit made from selling 25 tile sets is \$1250.1 solutions Answer 391314 by ewatrrr(10682)   on 2012-06-20 09:17:26 (Show Source): You can put this solution on YOUR website! ``` Hi, Re: TY Note: Graph demonstrates Profit Peaks at ~16 tiles and then decreases as more tiles are sold Careful, the (-1) stays in effect P(x)= (-1)x^2 + 33x - 20 P(20)= (-1)20^2+(33*20)-200 P(20)= -400+660-200 = 60 P(25)= (-1)25^2+(33*25)-200 P(25)= - 625+825-200 = 0 ```
 Linear-equations/622350: what is the slope of y= 5x 1 solutions Answer 391308 by ewatrrr(10682)   on 2012-06-20 09:04:54 (Show Source): You can put this solution on YOUR website! ``` Hi, y = x y = mx + b |Standard slope-intercept form m = 5/1 = 5 (Note: in this case b = 0) ```
 Linear-systems/622346: If the profit equation is P=-x^2+33x-200, what would be the profit on 25 tile sets?1 solutions Answer 391307 by ewatrrr(10682)   on 2012-06-20 09:01:17 (Show Source): You can put this solution on YOUR website! ``` Hi, If the profit equation is P(x)= -x^2+33x-200 |Idea is to replace x with 25 and then find P(25) ```
 Linear-systems/622320: use the confficient to define w/c system hand one sol'vn infinitely many or no solution 1) 2x+y=10 2x-3y=5 2) 4y-6x=1 2y-3x=4 3) x+y=2 2x+2y=4 4) 4x+5y=12 2x-y=6 5) y=3x-5 -6x+2y=-101 solutions Answer 391304 by ewatrrr(10682)   on 2012-06-20 08:40:08 (Show Source): You can put this solution on YOUR website! ``` Hi, 3) x+ y=2 2x+2y=4 5) y=3x-5 -3x +y =-5 -6x+2y=-10 | 3) and 5) The systems are identical Lines, Infinite amount of Solutions 2) 4y-6x=1 2y-3x=4 | multiplying 2nd thru by -2, 0 ≠ -7 NO solution 1) 2x+y=10 2x-3y=5 (4.375,1.25) 4) 4x+5y=12 2x-y=6 (3,0) ```
 Linear-equations/622335: The amount of water in a wading pool by given by the function w(t)=30+5t, where "t" is time in minutes and t= 0 corresponds to when a faucet is turned on to add water to the pool. a. What is the rate of change of the water in the pool? b. Is this an increasing or decreasing function? c. How much water is in the pool an hour after the faucet has been turned on?1 solutions Answer 391303 by ewatrrr(10682)   on 2012-06-20 08:23:53 (Show Source): You can put this solution on YOUR website! ``` Hi, The amount of water in a wading pool by given by the function w(t)=30+t, where "t" is time in minutes and t= 0 corresponds to when a faucet is turned on... using Gallons a. What is the rate of change of the water in the pool? 5gal/min b. Is this an increasing or decreasing function? c. How much water is in the pool an after the faucet has been turned on? ```