Can you help me solve the following equation and show the work? I’m trying to help my middle school daughter with her homework and I’m rusty! -2x+4(1-3x) =6x-20. I come up with x=1.2, but the homework has all answers equal to whole numbers.
Initial equation: [math]-2x + 4(1 - 3x) = 6x - 20[/math]Adding [math]2x[/math] to both sides of the equation: [math]4(1 - 3x) = 8x - 20 = 4(2x - 5)[/math]Dividing both sides of the equation by 4: [math]1 - 3x = 2x - 5[/math]Adding [math]3x[/math] to both sides of the equation: [math]1 = 5x - 5[/math]Adding 5 to both sides of the equation: [math]6 = 5x[/math]Dividing both sides of the equation by 5: [math]1.2 = x[/math]So, you’re not rusty, x = 1.2 is the only solution.[math]\\[/math]If the answer is supposed to be an integer solution (i.e. a whole number), this suggests that you have written the equation down incorrectly.But, you have mentioned that the solutions are all integers! Perhaps you’re referring to all the questions in the exercise? If not, the only way we’re going to have more than one solution to a question is if we are dealing with powers of x, such as [math]x^2[/math] (i.e. x squared).
Can you help me set up an equation?
It's a word problem I've been working on for nearly half an hour now. The question is:Aya rode her bicycle from her house to a friend’s house, averaging 16 kilometers per hour. It turned dark before she was ready to return home, so her friend drove her home at a rate of 80 kilometers per hour. If Aya’s total traveling time was three hours, how far away did her friend live? The only equation I have been able to come up with is 2d=3(16+80) but when solved that means that d=144 and when I put 16 into a ratio (1/16 = x/144) it told me that it would take 9 hours to go 144 km at 16 km/h so I don't think thats right lol. I'm lost.
Can you help me come up with the second and third equation?
You spend 4 times as many hours collecting toys as picking up trash: c = 4p 2 hours less serving the soup kitchen than picking up trash: p = s - 2
Quadratics help. Can you come up with an equation for this question? no need to solve?
(5 + 0.5*x) is the increase of price with 0.5 "pieces" AND (300 - 20*x) is the corresponding decrease of the attendance. 0.5*x added to the original price means 20*x fewer people. --------------------------------------... (5 + 0.5*x) * (300 - 20*x) = 1562.5. . . .---> this is the equation! And I made it --------------------------------------... . . . . according to the problem 0.5 * (10 + x) * 20 * (15 - x) = 1562.5 10 * (10 + x) * (15 - x) = 1562.5. . . . . .|:10 (10 + x) * (15 - x) = 156.25 150 - 10x + 15x - x^2 = 156.25 x^2 - 5x - 150 + 156.25 = 0 x^2 - 5x + 6.25 = 0 x^2 - 2*x(*2.5) + (2.5)^2 = 0 (x - 2.5)^2 = 0 ==> x - 2.5 = 0 ==> x = 2.5 So the price is 5 + 0.5*2.5 = 5 + 1.25 = 6.25 $ Hope it'll be of use!
Can you help me solve this college algebra equation?
There is only ONE substitution. You can't say that u=3k-9 and then say that u²=(1/3k-9)² because these aren't consistent. Let's say u=1/(3k-9). Then u²=1/(3k-9)² and the equation is: 2u² + 5u + 2 = 0 (2u+1)(u+2) = 0 2u+1=0 or u+2=0 u=-½ or u=-2 Now the part that I think you are referring to as 'unsubstitution'. 1/(3k-9)=-½ 3k-9=-2 Add 9 to each side. 3k=7 k=7/3 1/(3k-9)=-2 3k-9=-½ Add 9 to each side. 3k=8½ Divide by 3. k=17/6 Answer: k=17/6 or k=7/3. I hope this helps.
Can you help me solve this system of equations, I check my answer and it says it's wrong...?
2x + 3y = 6 4x² + 4y² = 36 => (2x)² + (2y)² = 36 Plugging in 2x = 6 - 3y from the first equation, => (6 - 3y)² +(2y)² = 36 => 13y² - 36y = 0 => y(13y - 36) = 0 => y = 0 or y = 36/13 y = 0 => 2x = 6 => x = 3 => (3, 0) is one solution. y = 36/13 => 2x = 6 - 108/13 => x = -15/13 => (-15/13, 36/13) is the second solution. Answer: (3, 0) and (-15/13, 36/13).
Math Question-please help me come up with an equation...?
Let x be the amount (in grams) of the 25% copper alloy, and let y be the amount of the 50% copper alloy. Then, .25x + .50y = .45(1000) and x + y = 1000. So, y = 1000-x then .25x + .50y = .45(1000) .25x + .50(1000-x)=450 .25x + 500 - .50x = 450 (.25-.50)x +500 = 450 -.25x = -50 (multiply both sides by -1) .25x = 50 (multiply both sides by 4) x=200, then substitute x in to the x + y = 1000 equation 200 + y = 1000 so y = 800. and make sure to label each grams of the appropriate % copper alloy.
I need help coming up with the equations for this problem.?
Greetings, x + y = 10 x*x = ysqrt10 x^2 = ysqrt10 x^2 = (10 - x)sqrt10 x^2 + sqrt10 x - 10sqrt10 = 0 x = [-sqrt10 +/- sqrt(10 + 40sqrt10)]/2 = 4.26033... y = 10 - 4.26033... y = 5.739668... Regards
Can you help me solve this reverse quadratic equation?
If x = 5 and x = 8 would make the equation equal to 0, then you know that (x-5) and (x-8) must be factors of the equation. The equation will take the form k(x-5)(x-8) = 0 where k = any real number. k(x² - 13x + 40) = 0 kx² - 13kx + 40k = 0 Pick any number you want for k and you will have met the requirements of the problem. Some examples: x² - 13x + 40 = 0 (A = 1, B = -13, C = 40) 2x² - 26x + 80 = 0 (A = 2, B = -26, C = 80) 100x² - 1300x + 4000 = 0 (A = 100, B = -1300, C = 4000) -6x² + 78x - 240 = 0 (A = -6, B = 78, C = -240) All of these have x = 5 and x = 8 as solutions.
I need help coming up with a sci-fi physics equation. It must look plausible—speculative but plausible. Can anyone help me?
I may be able to help you, if you can tell me something about what you are planning to use the equation for. Different equations have to be constructed for different physical properties, e.g. a field equation is different from an energy equation is different from a resistance equation.Bearing that in mind, you will also need to know which symbols to use and which symbols not to use. Constants like epsilon nought, pi, phi, elementary charge etc. are fair game, but established symbols denoting unit (V for Volts, gees for gravitational acceleration, N for force, etc.) must be either avoided or specifically defined to mean something else.This sounds intriguing, and I hope that this helps.