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 Trigonometry-basics/684448: Solve the triangle using the given information. a=7cm b=4cm c=5cm How do I find the angles? Law of cosines? Please provide all steps.1 solutions Answer 424099 by jim_thompson5910(28504)   on 2012-11-24 20:50:24 (Show Source): You can put this solution on YOUR website!a^2 = b^2 + c^2 - 2*b*c*cos(A) 49 = 4^2 + 5^2 - 2*4*5*cos(A) 49 = 16 + 25 - 40*cos(A) 49 = 41 - 40*cos(A) 49 - 41 = -40*cos(A) 8 = -40*cos(A) 8/(-40) = cos(A) -1/5 = cos(A) cos(A) = -1/5 A = arccos(-1/5) A = 101.536959 So the angle A is roughly 101.536959 degrees. I'll let you find angles B and C
 Trigonometry-basics/684424: Solve the triangle using the given information. A=105degrees b=12 c=9 I'm pretty sure you need to use law of sines: because your given two sides and one angle. But I don't know how to start. Please provide full steps1 solutions Answer 424085 by jim_thompson5910(28504)   on 2012-11-24 18:56:10 (Show Source): You can put this solution on YOUR website!You use the law of cosines actually to find the length of 'a' a^2 = b^2 + c^2 - 2*b*c*cos(A) a^2 = 12^2 + 9^2 - 2*12*9*cos(105) a^2 = 225 - 216*cos(105) a^2 = 225 - 216*(-0.258819) a^2 = 280.904904 a = sqrt(280.904904) a = 16.76021789 Now that you know that a = 16.76021789 b = 12 c = 9 You can use the law of sines to find angles B and C. I'll show you how to find angle B and I'll let you find angle C sin(B)/b = sin(A)/a sin(B)/12 = sin(105)/16.76021789 sin(B)/12 = 0.9659258/16.76021789 sin(B)/12 = 0.0576321 sin(B) = 12*0.0576321 sin(B) = 0.6915852 B = arcsin(0.6915852) B = 43.7557225 So the angle B is roughly 43.7557225 degrees I'll let you find angle C Note: there are 2 ways to find angle C, you can use the fact that A+B+C = 180 (ie all angles must add to 180) or you can use the law of sines again.
 Triangles/684164: right angled triangles/triangles that have the same angles have _____?1 solutions Answer 423951 by jim_thompson5910(28504)   on 2012-11-23 17:57:47 (Show Source): You can put this solution on YOUR website!right angled triangles/triangles that have the same angles have __proportional corresponding sides__
 Percentage-and-ratio-word-problems/684161: If the ratio of buses to passengers is 1 to 17 and there are 51 passengers, how many buses are there?1 solutions Answer 423946 by jim_thompson5910(28504)   on 2012-11-23 17:36:30 (Show Source): You can put this solution on YOUR website!1/17 = x/51 1*51 = 17x 51 = 17x 51/17 = x 3 = x x = 3 So there are 3 buses.
 Equations/684156: Show that the points A (3,-5), B (-3,-1) and C (7,1) are vertices of an isosceles triangle. Find the area? Help pls. with graph and solution!1 solutions Answer 423939 by jim_thompson5910(28504)   on 2012-11-23 17:14:35 (Show Source): You can put this solution on YOUR website!Hint: Find the distance between * Points A and B * Points B and C * Points A and C if two of those distances are the same, then you have an isosceles triangle You can use the distance formula to do the above distance formula: ------------------------------------------------------- To find the area, you can use hero's or herons formula, which can be seen at the link below (if you forget it) http://www.mathsisfun.com/geometry/herons-formula.html Let me know if you need more help with this. Thanks.
 Linear-systems/684152: how do i solve 2x-3y=6 2x-y=7 substitution method linear systems 1 solutions Answer 423937 by jim_thompson5910(28504)   on 2012-11-23 16:56:39 (Show Source): You can put this solution on YOUR website!Hint: Solve the second equation for y 2x-y=7 -y = -2x+7 y = 2x-7 Then plug this into the first equation 2x-3y=6 2x-3(2x-7) = 6 2x-6x+21 = 6 -4x+21 = 6 I'll let you finish. Solve for x. Then use the solution for x to find the solution for y.
 Points-lines-and-rays/684131: Write an equation for the line that is parallel to the given line and passes through the given point. y = x + 8; (4, 10) A. y = x B. y = x + 6 C. y = x – 6 D. y = x + 6 1 solutions Answer 423927 by jim_thompson5910(28504)   on 2012-11-23 16:16:24 (Show Source): You can put this solution on YOUR website!y = x + 8 ----> m = 1, b = 8 ------------------------------------------------------- y = mx+b y = 1x + b y = x + b 10 = 4 + b 10-4 = b 6 = b b = 6 ------------------------------------------------------- y = mx+b y = 1x + 6 y = x + 6 So the answer is choice B
 Graphs/684114: Describe in words how you would obtain the graph of y = 3(x-4)^2 from transmission of the graph y = x^2 make sketches of both parabolas on the same set of axis. can you please explain this to me? thanks in advance1 solutions Answer 423911 by jim_thompson5910(28504)   on 2012-11-23 14:41:46 (Show Source): You can put this solution on YOUR website!Step 1) Start with the graph of y = x^2 (shown in green) ========================================================================== Step 2) Shift it 4 units to the right to get y = (x-4)^2 (shown in blue) ========================================================================== Step 3) Then vertically stretch it by a factor of 3 to get y = 3(x-4)^2 (shown in purple) ========================================================================== For the sake of comparison, here are the two graphs y = x^2 (in green) and y = 3(x-4)^2 (in blue) and finally, here is the graph of just 3(x-4)^2 (in green)
 Equations/684045: Find the slope and angle inclination of a line passing through A(7,-5) and B(4,4)? Please answer.. I'm begging..1 solutions Answer 423908 by jim_thompson5910(28504)   on 2012-11-23 14:11:22 (Show Source): You can put this solution on YOUR website!Note: is the first point . So this means that and . Also, is the second point . So this means that and . Start with the slope formula. Plug in , , , and Subtract from to get Subtract from to get Reduce So the slope of the line that goes through the points and is The angle of inclination is theta = arctan(rise/run) theta = arctan(3/1) ... note: make the rise positive theta = 71.56505 So the angle of inclination is roughly 71.56505 degrees
 Radicals/684043: How to solve this : (sqrt (2x-1))*(sqrt (2x-1))1 solutions Answer 423907 by jim_thompson5910(28504)   on 2012-11-23 14:10:18 (Show Source): You can put this solution on YOUR website!(sqrt (2x-1))*(sqrt (2x-1)) = (sqrt (2x-1))^2 (sqrt (2x-1))*(sqrt (2x-1)) = 2x-1
 test/684068: 1 solutions Answer 423906 by jim_thompson5910(28504)   on 2012-11-23 14:09:34 (Show Source): You can put this solution on YOUR website!problem missing
 logarithm/683999: log(4)+log(x+5)=21 solutions Answer 423861 by jim_thompson5910(28504)   on 2012-11-22 20:51:18 (Show Source): You can put this solution on YOUR website!log(4)+log(x+5)=2 log(4(x+5))=2 4(x+5)=10^2 4(x+5)=100 x+5=100/4 x+5=25 x=25-5 x=20 So the solution is x=20. Don't forget to check it (I'll let you do this).
 test/683952: Dy/dx= xy/2lny1 solutions Answer 423830 by jim_thompson5910(28504)   on 2012-11-22 17:08:25 (Show Source): You can put this solution on YOUR website!dy/dx= xy/2lny dy= xy/2lny*dx 2ln(y)/y*dy= x*dx int(2ln(y)/y*dy)= int(x*dx) 2*int(ln(y)/y*dy)= int(x*dx) 2*((1/2)*ln(|y|)^2)= (1/2)x^2 + C ln(|y|)^2= (1/2)x^2 + C ln(|y|)= sqrt( (1/2)x^2 + C ) ln(|y|) = sqrt( (1/2)x^2 + C ) |y| = e^(sqrt( (1/2)x^2 + C )) y = +-e^(sqrt( (1/2)x^2 + C ))
 Trigonometry-basics/683932: Convert the rectangular equation to polar form. y = x. I'm confused because there are no numbers for y or x.1 solutions Answer 423827 by jim_thompson5910(28504)   on 2012-11-22 15:22:39 (Show Source): You can put this solution on YOUR website!The slope of y = x is 1 or 1/1. So a 45-45-90 degree triangle forms telling us that y = x makes a 45 degree angle with the x-axis. Therefore, the equation is $\large \theta = 45$ if you want the angle in degrees. Or the equation is $\large \theta = \frac{\pi}{4}$ if you want the angle in radians.
 test/683946: 1/6x+1/4x=-11 solutions Answer 423826 by jim_thompson5910(28504)   on 2012-11-22 15:18:44 (Show Source): You can put this solution on YOUR website! Start with the given equation. Multiply both sides by the LCD to clear any fractions. Distribute and multiply. Combine like terms on the left side. Divide both sides by to isolate . ---------------------------------------------------------------------- Answer: So the solution is
 Equations/683944: Solve for the zeroes: x^2+5x-61 solutions Answer 423825 by jim_thompson5910(28504)   on 2012-11-22 14:38:49 (Show Source): You can put this solution on YOUR website!x^2+5x-6 = 0 (x+6)(x-1) = 0 x+6=0 or x-1 = 0 x = -6 or x = 1 So the two solutions are x = -6 or x = 1
 test/683943: 1/8y-1/2=1/41 solutions Answer 423823 by jim_thompson5910(28504)   on 2012-11-22 14:31:04 (Show Source): You can put this solution on YOUR website!(1/8)y-1/2=1/4 8((1/8)y-1/2)=8*(1/4) y - 4 = 2 y = 2+4 y = 6
 logarithm/683940: Write the expression in terms of natural logarithms. (Express all logarithmic functions in terms of ln(x) in your answer.) log_(8.8)$$113$$1 solutions Answer 423820 by jim_thompson5910(28504)   on 2012-11-22 13:58:52 (Show Source): You can put this solution on YOUR website!log_(8.8)$$113$$ = ln(113)/ln(8.8) by the change of base formula
 Graphs/683939: Write an equation of the line with the given slope and y-intercept. slope: 7; y-intercet :4 I am thinking it will be... y=4x+7 1 solutions Answer 423818 by jim_thompson5910(28504)   on 2012-11-22 13:48:16 (Show Source): You can put this solution on YOUR website!You have it backwards and it should be
 Inequalities/683936: 1 solutions Answer 423817 by jim_thompson5910(28504)   on 2012-11-22 13:25:26 (Show Source): You can put this solution on YOUR website!Problem missing
 Linear-equations/683937: it says write the slope-intercept form of the equation of the line through the given point with the given slope. Heres the question; through:(-1,-1), slope=4 1 solutions Answer 423814 by jim_thompson5910(28504)   on 2012-11-22 13:05:54 (Show Source): You can put this solution on YOUR website! So the equation of the line is
 logarithm/683934: f(x)=√(25-x^2) Find the domain.1 solutions Answer 423812 by jim_thompson5910(28504)   on 2012-11-22 13:03:11 (Show Source): You can put this solution on YOUR website!25-x^2 >= 0 25 >= x^2 x^2 <= 25 sqrt(x^2) <= sqrt(25) |x| <= 5 -5 <= x <= 5 So the domain is -5 <= x <= 5 Domain in set-builder notation: $\large \left\{x|-5\le x\le 5, x\in\mathbb{R}\right\}$ Domain in interval notation: $\large \left[-5,5 \right ]$
 Travel_Word_Problems/683928: A turtle travels 20m in 8minutes. How long does it take for the turtle to travel 0.5m?1 solutions Answer 423810 by jim_thompson5910(28504)   on 2012-11-22 12:48:35 (Show Source): You can put this solution on YOUR website!20/8 = 0.5/x 20x = 8*0.5 20x = 4 x = 4/20 x = 1/5 x = 0.2 So it will take 0.2 minutes or 0.2*60 = 12 seconds. ========================================================================== Alternative way to do this d = rt 20 = r*8 20/8 = r 2.5 = r r = 2.5 ------------------------------ d = rt 0.5 = 2.5*t 0.5/2.5 = t 0.2 = t t = 0.2 So we get the same answer.
 Geometry_Word_Problems/683919: 1 solutions Answer 423809 by jim_thompson5910(28504)   on 2012-11-22 12:42:43 (Show Source): You can put this solution on YOUR website!Problem missing
 Functions/683926: Is the following relation a function? Explain your answer. (1,2), (2,3), (2,5), (2,7)1 solutions Answer 423808 by jim_thompson5910(28504)   on 2012-11-22 12:42:09 (Show Source): You can put this solution on YOUR website!The x value of 2 maps to y = 3, y = 5 and y = 7 at the same time. So it is NOT a function. It is only a function when every x value maps to EXACTLY ONE y value. Note: Let's say that this requirement wasn't part of the definition of a function. If we have (2,3) and (2,5), then what is f(2)? Is it 3? or is it 5? It can't be both at the same time since f(2) is a single number. This is why the definition above is put in place.
 Linear-systems/683910: can you please help me solve this: Solve the following system by substitution -2x=8y+18 -33=7y-4x1 solutions Answer 423807 by jim_thompson5910(28504)   on 2012-11-22 12:39:29 (Show Source): You can put this solution on YOUR website!-2x = 8y+18 x = (8y+18)/(-2) x = (8y)/(-2)+18/(-2) x = -4y - 9 ------------------------------------------------------- -33 = 7y-4x -33 = 7y-4(-4y-9) -33 = 7y+16y+36 -33 = 23y+36 I'll let you finish. Once you have found the value of y, use it to find the value of x.
 Matrices-and-determiminant/683916: Can you please help solve this: Write an augmented matrix for the following system of equations. x-4y+4z=-9 2x-9y+8z=1 6y-9z=-1 Thank you ;-)1 solutions Answer 423806 by jim_thompson5910(28504)   on 2012-11-22 12:33:03 (Show Source): You can put this solution on YOUR website!x-4y+4z=-9 2x-9y+8z=1 6y-9z=-1 1x-4y+4z=-9 2x-9y+8z=1 0x+6y-9z=-1 1x+(-4)y+4z=-9 2x+(-9)y+8z=1 0x+6y+(-9)z=-1 $\large \left[ \begin{array}{c c c | c} 1 & -4 & 4 & -9\\ 2 & -9 & 8 & 1\\ 0 & 6 & -9 & -1 \end{array}\right ]$ Feel free to ask me any questions you have. Thanks.
 Matrices-and-determiminant/683915: Please help me with this problem. Solve the system. If the system has infinitely many solutions,write the set with z arbitrary. 5x-3y+z=0 x+y=0 -15x+9y-3z=0 Thanks1 solutions Answer 423804 by jim_thompson5910(28504)   on 2012-11-22 12:23:59 (Show Source): You can put this solution on YOUR website!x+y=0 y=-x ----------------------- 5x-3y+z=0 5x-3(-x)+z=0 5x+3x+z=0 8x+z=0 ---------------------- -15x+9y-3z=0 -15x+9(-x)-3z=0 -15x-9x-3z=0 -24x-3z=0 --------------------- So we have the new system of equations 8x+z=0 -24x-3z=0 3(8x+z)=3*0 -24x-3z=0 24x+3z=0 -24x-3z=0 ---------- 0x+0y=0 0=0 Since that equation is ALWAYS true regardless of what x, y and z are, this means that there are an infinite number of solutions. Solve the first equation for x to get 8x+z = 0 8x = -z x = -z/8 Since y = -x, we know that y = -(-z/8) ----> y = z/8 So in the end, x = -z/8, y = z/8 and z is a free variable (ie it can be any number) Therefore, the final answer as an ordered triple is $\large \left(-\frac{z}{8},\frac{z}{8},z \right )$ ============================================================================ Note: what does $\large \left(-\frac{z}{8},\frac{z}{8},z \right )$ mean exactly? Well... *** If z = 8, then $\large \left(-\frac{z}{8},\frac{z}{8},z \right )$ becomes $\large \left(-\frac{8}{8},\frac{8}{8},8 \right )$ which turns into $\large \left(-1,1,8 \right )$ which is one of the infinitely many solutions. If you plug x = -1, y = 1 and z = 8 into the original system, you'll find that all 3 satisfy all 3 equations. *** If z = 16, then $\large \left(-\frac{z}{8},\frac{z}{8},z \right )$ becomes $\large \left(-\frac{16}{8},\frac{16}{8},16 \right )$ which turns into $\large \left(-2,2,16 \right )$ which is another solution of the infinitely many solutions. If you plug x = -2, y = 2 and z = 16 into the original system, you'll find that all 3 satisfy all 3 equations. You can plug in ANY real number for 'z' to get an ordered triple that is a solution to the original system of equations.
 Travel_Word_Problems/683920: If I am going 55 mph and another car is driving a mile behind me going the exact speed will they catch up to me?1 solutions Answer 423803 by jim_thompson5910(28504)   on 2012-11-22 12:18:06 (Show Source): You can put this solution on YOUR website!No they will not because you both will travel the same distance in the same amount of time. However, you will have traveled a bit more distance because you got the head start. Since the car behind you travels the same distance as you (minus that head start), the car will never catch up or pass you.
 Equations/683918: The density of an object is W/V. If the density of an object is 5.25x10^-7 oz/ft^3? and the volume is 2.2x10^3 ft^3, then find the weight? Honestly i get to an answer 2.39 x10^-10 but i guess it's nor right So i'm be happy if somebody can help me out?1 solutions Answer 423802 by jim_thompson5910(28504)   on 2012-11-22 12:15:58 (Show Source): You can put this solution on YOUR website!D = W/V 5.25x10^-7 = W/(2.2x10^3) (5.25x10^-7)*(2.2x10^3) = W (5.25*2.2)x(10^-7*10^3) = W (11.55)x(10^-4) = W (1.155 x 10^1)x(10^-4) = W 1.155 x (10^1*10^-4) = W 1.155 x 10^-3 = W W = 1.155 x 10^-3 So the weight is roughly 1.155 x 10^-3 ounces or 0.001155 ounces.