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# Recent problems solved by 'lwsshak3'

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 Quadratic-relations-and-conic-sections/629081: Find in standard form, the equation of an ellipse whose center is at (2,-1) whose major axis of length 10 is along the y-axis, and whose minor axis of length 8 is along the x-axis.1 solutions Answer 396023 by lwsshak3(6522)   on 2012-07-17 01:48:26 (Show Source): You can put this solution on YOUR website!Find in standard form, the equation of an ellipse whose center is at (2,-1) whose major axis of length 10 is along the y-axis, and whose minor axis of length 8 is along the x-axis. ** Given equation is that of an ellipse with a vertical major axis. Its standard form: , a>b, (h,k)=(x,y) coordinates of center. .. Given center: ((2,-1) Given length of vertical major axis=10=2a a=5 a^2=25 given length of minor axis=8=2b b=4 b^2=16 Equation:
 Rational-functions/628883: What are the asymptotes of the graph of y = 2 divided by x+18?1 solutions Answer 395926 by lwsshak3(6522)   on 2012-07-16 16:43:41 (Show Source): You can put this solution on YOUR website!What are the asymptotes of the graph of y = 2 divided by x+18? ** To find the asymptote of a rational expression, set the denominator =0, then solve for x. At this value of x, the function becomes undefined for given problem, 2/(x+18). x+18=0 x=-18 equation of asymptote: x=-18
 Mixture_Word_Problems/628920: As part of flight training, a student pilot was required to fly to an airport and then return. The average speed on the way to the airport was 125 mph, and the average speed returning was 218.75. Find the distance between the two airports if the total flying time was 8.25 hours.1 solutions Answer 395921 by lwsshak3(6522)   on 2012-07-16 16:34:56 (Show Source): You can put this solution on YOUR website!As part of flight training, a student pilot was required to fly to an airport and then return. The average speed on the way to the airport was 125 mph, and the average speed returning was 218.75. Find the distance between the two airports if the total flying time was 8.25 hours. ** let x=distance between airports travel time=distance/speed .. LCD:125*218.75 218.75x+125x=8.25*125*218.75 343.75x=8.25*125*218.75 x=656.25 distance between airports=656.25 miles
 Expressions-with-variables/628948: Having a problem figuring out this algebra. Any help will be appreciated thanks (4+8i)(4-8i)1 solutions Answer 395910 by lwsshak3(6522)   on 2012-07-16 16:10:17 (Show Source): You can put this solution on YOUR website!Having a problem figuring out this algebra. Any help will be appreciated thanks (4+8i)(4-8i) ** You should recognize this the factored form of the difference of two squares which go like this: (a+b)(a-b)=a^2-b^2 .. (4+8i)(4-8i) =4^2-(8i)^2 =16-64i^2 i^2=-1 =16+64 =80
 Problems-with-consecutive-odd-even-integers/628881: a wire is attached to a cell phone tower at a point 210 feet above the ground. company policy requires the slope of the wire to be (7/3). Hw far from the base of the tower does the wire attach to the ground?1 solutions Answer 395906 by lwsshak3(6522)   on 2012-07-16 15:47:57 (Show Source): You can put this solution on YOUR website!a wire is attached to a cell phone tower at a point 210 feet above the ground. company policy requires the slope of the wire to be (7/3). Hw far from the base of the tower does the wire attach to the ground? ** let x=distance from base of tower to where wire attaches to the ground Slope is always expressed as a ratio, ∆y/∆x=change in y/change in x We then apply this ratio to the given problem. 210/x=7/3 7x=3*210 x=630/7=90 distance from base of tower to where wire attaches to the ground=90 ft
 Polynomials-and-rational-expressions/628931: i don't understand how to do a polynomial equation, particularly ones with exponents higher then 2 like x^3+9x^2+23x+15=01 solutions Answer 395899 by lwsshak3(6522)   on 2012-07-16 15:28:54 (Show Source): You can put this solution on YOUR website!i don't understand how to do a polynomial equation, particularly ones with exponents higher then 2 like x^3+9x^2+23x+15=0 ** f(x)=x^3+9x^2+23x+15=0 You can try to factor the expression by grouping, but if this is difficult like given equation, then you must use the rational roots theorem as follows: Using synthetic division: ...0..|.....1......9.......23.......15 .-1..|.....1.... .8.......15........0 (-1 is a root) f(x)=(x+1)(x^2+8x+15)=(x+1)(x+5)(x+3) zeros are: -5,-3, -1 note: you can always check your answer on a graphics calculator like a TI-83+
 Quadratic-relations-and-conic-sections/628918: A focal point of the elipse ((x+3)^2)/16)+(y-1)^2)/4)=1 is: a.) (-1,1) b.) (-3-2 radical 3, 1) c.) (-7,1) d.) 3+2 radical 3, 1) * note: when ever i have entered the equation in to graph it it keeps saying 1/16 (x+3) but that is not correct it is x+3^2 all over 16. I have worked it some way but I dont know how to continue it. I have: Centre: (-3,1) a=16 b=3 c=15.716 but i dont know how to find the focal point. 1 solutions Answer 395895 by lwsshak3(6522)   on 2012-07-16 15:09:27 (Show Source): You can put this solution on YOUR website!Find a focal point of the ellipse: ((x+3)^2)/16)+(y-1)^2)/4)=1 This is an equation of an ellipse with horizontal major axis: Its standard form: (x-h)^2/a^2+(y-k)^2/b^2=1, (a>b), (h,k)=(x,y) coordinates of center For given ellipse: center(-3,1) a^2=16 a=√16=4 b^2=4 b=√4=2 c^2=a^2-b^2=16-12=4 c=√4=2 Foci: (Both focal points)=(-3±c,1)=(-3±2,1)=(-5,1) and (-1,1) answer a is the correct answer
 Travel_Word_Problems/628911: a chemist added 2L of water to 8L of a 48% nitric acid solution. What is the acid concentration of the new solution?1 solutions Answer 395887 by lwsshak3(6522)   on 2012-07-16 14:23:38 (Show Source): You can put this solution on YOUR website!a chemist added 2L of water to 8L of a 48% nitric acid solution. What is the acid concentration of the new solution? ** let x=acid concentration of new solution 48%*8=x(10+2)=12x 12x=3.84 x=3.84/12=.32 acid concentration of new solution=32%
 Radicals/627877: How do you simplify √16x^5 + y^4 + z^21 solutions Answer 395692 by lwsshak3(6522)   on 2012-07-15 03:15:12 (Show Source): You can put this solution on YOUR website!How do you simplify √16x^5 + y^4 + z^2 =4x^2√x+y^4+z^2 that is all you can do
 Rational-functions/627661: find all zeros of the following polynomial write the polynomial in factored form f(x) = 7x^3-x^2+7x-11 solutions Answer 395690 by lwsshak3(6522)   on 2012-07-15 02:51:32 (Show Source): You can put this solution on YOUR website!find all zeros of the following polynomial write the polynomial in factored form f(x) = 7x^3-x^2+7x-1 factor by grouping f(x) =x^2(7x-1)+(7x-1) f(x) = (7x-1)(x^2+1)=0 7x-1=0 x=1/7 or x^2+1=0 x^2=-1 x=±√-1=± zeros: 1/7 and two non-real zeros, ±i
 Polynomials-and-rational-expressions/628330: Solve the polynomial inequality and graph the solution set on a real number line. Express the solution set in interval notation. x^3-4x^2-16x+64<01 solutions Answer 395688 by lwsshak3(6522)   on 2012-07-15 02:36:24 (Show Source): You can put this solution on YOUR website!Solve the polynomial inequality and graph the solution set on a real number line. Express the solution set in interval notation. x^3-4x^2-16x+64<0 factor by grouping x^2(x-4)-16(x-4)<0 (x-4)(x^2-16)<0 (x-4)(x+4)(x-4)<0 number line <....-....-4.....+.....4....+.....> solution: (-∞,-4)
 Angles/628524: two angles are supplementary. one angle is 40degrees more than four times the other. find the measures of the angle. its complement and its supplement1 solutions Answer 395687 by lwsshak3(6522)   on 2012-07-15 02:21:00 (Show Source): You can put this solution on YOUR website!two angles are supplementary. one angle is 40degrees more than four times the other. find the measures of the angle. its complement and its supplement ** let x=one of two supplementary angles 180-x=other supplementary angle .. 180-x=4x+40 5x=140 x=28 180-x=152 90-x=62 .. measure of the angle=28º Its complement=62º Its supplement=152º
 Polynomials-and-rational-expressions/628523: factorise by using factor theorum :- y^3-7y+6 (please show its steps also)1 solutions Answer 395686 by lwsshak3(6522)   on 2012-07-15 02:07:11 (Show Source): You can put this solution on YOUR website!factorise by using factor theorum :- y^3-7y+6 (please show its steps also) ** f(y)=y^3-7y+6 Use rational roots theorem to solve: (with synthetic division) ...0..|...-1......0......-7.......6............ ...1..|.....1......1......-6......0 (1 is a root) f(y)=(y-1)(y^2+y-6) f(y)=(y-1)(y+3)(y-2)
 Polynomials-and-rational-expressions/628515: i have a problem of this question factorize it a3-13a+12????? plz help me.1 solutions Answer 395685 by lwsshak3(6522)   on 2012-07-15 01:50:42 (Show Source): You can put this solution on YOUR website!i have a problem of this question factorize it a3-13a+12. ** f(a)= a3-13a+12 Use rational roots theorem to solve: (with synthetic division) ...0..|.....1......0......-13.......12............ ...1..|.....1......1......-12........0 (1 is a root) f(a)=(a-1)(a^2+a-12) f(a)=(a-1)(a+4)(a-3)
 Mixture_Word_Problems/628519: how much each of 20% and 80% alcohol should be added to get 5 gallons of a 50% alcohol mixture1 solutions Answer 395684 by lwsshak3(6522)   on 2012-07-15 01:38:58 (Show Source): You can put this solution on YOUR website!how much each of 20% and 80% alcohol should be added to get 5 gallons of a 50% alcohol mixture ** let x=amt of 20% alcohol to add 5-x=amt of 80% alcohol to add .. 20%x+80%(5-x)=50%*5 .2x+4-.8x=2.5 .6x=1.5 x=2.5 5-x=2.5 .. amt of 20% alcohol to add=2.5 gal amt of 80% alcohol to add=2.5 gal
 Angles/628520: What is the measures of two complementary angles such that the larger angle is six less than twice the smaller angle? My solution is: Complementary angle= 90 2x-6=90 2x=90+6 2x=96 1/2(2x)=(96)1/2 x=48 Small Complementary Angle = 48 Larger Complementary Angle = 961 solutions Answer 395680 by lwsshak3(6522)   on 2012-07-15 01:31:05 (Show Source): You can put this solution on YOUR website!What is the measures of two complementary angles such that the larger angle is six less than twice the smaller angle? ** let x=larger of two complementary angles 90-x=smaller of two complementary angles .. x=2(90-x)-6 x=180-2x-6 3x=174 x=58 90-x=32 larger of two complementary angles=58º smaller of two complementary angles=32º
 Money_Word_Problems/628394: A woman invests money in two funds that yield an annual total income of \$86. One fund pays an annual return of 7%, and the other pays a return of 8%. How much is invested in the fund yielding 7% if the total annual amount invested at the start of the year is \$1200.001 solutions Answer 395618 by lwsshak3(6522)   on 2012-07-14 17:41:48 (Show Source): You can put this solution on YOUR website!A woman invests money in two funds that yield an annual total income of \$86. One fund pays an annual return of 7%, and the other pays a return of 8%. How much is invested in the fund yielding 7% if the total annual amount invested at the start of the year is \$1200.00 ** let x=amt invested in 7% fund 1200-x=amt invested in 8% fund .. .07x+.08(1200-x)=86 .07x+96-.08x=86 .01x=10 x=1000 1200-x=200 amt invested in 7% fund=\$1000
 Quadratic_Equations/628443: steps to solve x^4 + 2x^2-15=01 solutions Answer 395614 by lwsshak3(6522)   on 2012-07-14 17:16:40 (Show Source): You can put this solution on YOUR website!steps to solve x^4 + 2x^2-15=0 factor (x^2+5)(x^2-3)=0 x^2+5=0 x^2=-5 x=±√-5 x=±(√5) i or x^2-3=0 x^2=3 x=±√3 two real roots: ±√3 two imaginary or non-real roots: ±(√5) i
 Equations/628439: Write your solution using set builder notation. Please show all of your work. solve -11x-24<9-2(5x-9)1 solutions Answer 395611 by lwsshak3(6522)   on 2012-07-14 17:04:20 (Show Source): You can put this solution on YOUR website!Write your solution using set builder notation. Please show all of your work. solve -11x-24<9-2(5x-9) -11x-24<9-10x+18 -x<24+27 -x<51 x>-51 {x|x>-51}
 Rate-of-work-word-problems/628433: When a stone is dropped into a deep well, the number of seconds t until the sound of a splash is heard is given by the formula T=√x/4+x/1100 where x is the depth of the well in feet. If it takes 9 seconds to hear a splash, how deep (to the nearest foot) is the well?1 solutions Answer 395610 by lwsshak3(6522)   on 2012-07-14 16:56:43 (Show Source): You can put this solution on YOUR website!When a stone is dropped into a deep well, the number of seconds t until the sound of a splash is heard is given by the formula T=√x/4+x/1100 where x is the depth of the well in feet. If it takes 9 seconds to hear a splash, how deep (to the nearest foot) is the well? T=√x/4+x/1100 9=√x/4+x/1100 LCD:4*1100 1100√x+4x=9*4*1100=39600 1100√x+4x-39600=0 275√x+x-9900=0 let u=√x u^2=x .. u^2+275u-9900=0 Solve by following quadratic formula: a=1, b=275, c=9900 ans: u=32.2=√x square both sides x≈1037 ft
 absolute-value/628379: |-11|+5²=50y-|+31|-49y1 solutions Answer 395605 by lwsshak3(6522)   on 2012-07-14 16:20:23 (Show Source): You can put this solution on YOUR website!|-11|+5²=50y-|+31|-49y The absolute value of any number is always positive. 11+5²=50y-31-49y 11+25=50y-31-49y y=11+25+31=67
 Travel_Word_Problems/628310: a car leaves Rockford, Il at teh rate of 65mph bound for Madison,WI. At the same time, a truck leaves Madison bound for Rockford at the rate of 55 mph. If the cities are 72 miles apart how long will it take for the car and truck to meet?1 solutions Answer 395546 by lwsshak3(6522)   on 2012-07-14 03:51:25 (Show Source): You can put this solution on YOUR website!a car leaves Rockford, Il at teh rate of 65mph bound for Madison,WI. At the same time, a truck leaves Madison bound for Rockford at the rate of 55 mph. If the cities are 72 miles apart how long will it take for the car and truck to meet? ** let x=distance car traveled 72-x=distance truck traveled travel time=distance/speed 65/x=55/(72-x) 55x=65*72-65x 120x=65*72 x=65*72/120=39 mi 72-x=33 mi travel time=39/65=0.6 hr or 36 min time car and truck met: 36 min
 Points-lines-and-rays/628163: The perimeter of a rectangle is 28 cm. if the length of a diagonal is 10 cm, find the length and width of the rectangle.1 solutions Answer 395545 by lwsshak3(6522)   on 2012-07-14 03:32:47 (Show Source): You can put this solution on YOUR website!The perimeter of a rectangle is 28 cm. if the length of a diagonal is 10 cm, find the length and width of the rectangle. ** let x=length of rectangle let y=width of rectangle 2x+2y=perimeter=28 x+y=14 y=14-x by pythagorean theorem: x^2+y^2=10^2=100 x^2+(14-x)^2=100 x^2+196-28x+x^2=100 2x^2-28x+196=100 2x^2-28x+96=0 x^2-14x+48=0 (x-8)(x-6)=0 x=8 or x=6 length of rectangle: 8 cm width of rectangle: 6 cm
 Linear-equations/628304: Consider the line 8x-7y=-1, find the equation of the line that is parallel to this line and passes through the point (1,3). Find the equation of the line that is perpendicular to this line and passes through the point (1,3)1 solutions Answer 395544 by lwsshak3(6522)   on 2012-07-14 03:13:17 (Show Source): You can put this solution on YOUR website!Consider the line 8x-7y=-1, find the equation of the line that is parallel to this line and passes through the point (1,3). Find the equation of the line that is perpendicular to this line and passes through the point (1,3) ** Standard form of equation for a straight line: y=mx+b, m=slope, b=y-intercept Original line: 8x-7y=-1 7y=8x+1 y=8x/7+1/7 slope=8/7 .. Perpendicular line: slope:-7/8 (negative reciprocal of slope of original line. Equation: y=-7x/8+b solving for b using given point (1,3) 3=-7*1/8+b b=3+7/8=31/8 equation: y=-7x/8+31/8 .. Parallel line: slope: 8/7 (same as slope of original line) Equation: y=8x/7+b solving for b using given point (1,3) 3=8*1/7+b b=3-8/7=13/7 equation: y=8x/7+13/7 see graph below as a visual check: red line:original blue line: parallel green line: perpendicular
 Rate-of-work-word-problems/628309: The frame on a picture is 28 cm by 32 cm outside and is of uniform width. What is the width of the frame if 192 cm^2 of the picture shows?1 solutions Answer 395543 by lwsshak3(6522)   on 2012-07-14 02:36:01 (Show Source): You can put this solution on YOUR website!The frame on a picture is 28 cm by 32 cm outside and is of uniform width. What is the width of the frame if 192 cm^2 of the picture shows ** let w=width of the frame Area of frame+picture=28*32=896 Area of frame=896-192=704=length*w=2*(28+32)*w w=704/2*(28+32)=704/120≈5.87 width of the frame≈5.87 cm
 logarithm/627566: Hello! I need help solving 2 equations involving Logarithms. How do I correctly graph the equation bellow on the same coordinate plane? Question #1: F(x)= 2^-x and G(x)= 4^x Question #2: How do I solve/or rewrite this equation as a single quantity? log^2 (x) + log^2 (x+2) = log^2 (x +6) Please help me! LOL -Cass1 solutions Answer 395481 by lwsshak3(6522)   on 2012-07-13 17:28:18 (Show Source): You can put this solution on YOUR website!Hello! I need help solving 2 equations involving Logarithms. How do I correctly graph the equation bellow on the same coordinate plane. .. Question #1: F(x)= 2^-x and G(x)= 4^x .. For F(x)=2^-x=1/2^x Domain: (-∞,∞) Range: (0,∞) Horizontal asymptote: x-axis or y=0 .. For F(x)=4^x Domain: (-∞,∞) Range: (0,∞) Horizontal asymptote: x-axis or y=0 See graph below: Green curve is 4^x and red curve is 2^-x or 1/2^x Note that both curves have a y-intercept=1 (2^0=1) Also note both functions are always >0 .. Question #2: How do I solve/or rewrite this equation as a single quantity? log^2 (x) + log^2 (x+2) = log^2 (x +6) log^2[ (x) (x+2)] = log^2 (x +6) x(x+2)=x+6 x^2+2x=x+6 x^2+x-6=0 (x+3)(x-2)=0 x=-3 (reject, x>0) or x=2
 logarithm/626914: Describe the following characteristics of the logarithmic function y = logax. 1) Domain 2) Range 3) x-intercept 4) Horizontal asymptote 5) Vertical asymptote 6) General shape1 solutions Answer 395473 by lwsshak3(6522)   on 2012-07-13 16:41:07 (Show Source): You can put this solution on YOUR website!Describe the following characteristics of the logarithmic function y = logax. 1) Domain: (0,∞) 2) Range: (-∞,∞) 3) x-intercept: 1 4) Horizontal asymptote: none 5) Vertical asymptote: y-axis or x=0 6) General shape: starting from (0,-∞) curve becomes less negative until it crosses the x=axis at (1,0), at which point the curve becomes increasingly positive to ∞. Number line: <...-....1...+.....>
 logarithm/628156: Write the expression as a single logarithm with a coefficient of 1. Assume all variable expressions represent positive real numbers. ln(6x + 7) − ln y − 8 ln z + (1/2)ln w = ?1 solutions Answer 395468 by lwsshak3(6522)   on 2012-07-13 16:15:41 (Show Source): You can put this solution on YOUR website!Write the expression as a single logarithm with a coefficient of 1. Assume all variable expressions represent positive real numbers. ln(6x + 7) − ln y − 8 ln z + (1/2)ln w ln(6x + 7) −(ln y + 8 ln z) + (1/2)ln w ln[(6x+7)(w^1/2)/ y*z^8]
 logarithm/628158: Write the expression as a single logarithm with a coefficient of 1. Assume all variable expressions represent positive real numbers. logb(3x) + logb(y + 4) + logb(y + 2) − logb(y2 + 6y + 8) = ?1 solutions Answer 395464 by lwsshak3(6522)   on 2012-07-13 15:58:01 (Show Source): You can put this solution on YOUR website!Write the expression as a single logarithm with a coefficient of 1. Assume all variable expressions represent positive real numbers. logb(3x) + logb(y + 4) + logb(y + 2) − logb(y^2 + 6y + 8) logb(y^2 + 6y + 8)=log[(y+4)(y+2)] logb[(3x(y+4)(y+2))/(y+4)(y+2)] (y+4)(y+2) cancels out, leaving: logb(3x)