TRUE
The system of equations can have zero solutions, one solution, two solutions, any finite number of solutions, or an infinite number of solutions. If it is a system of LINEAR equations, then the only possibilities are zero solutions, one solution, and an infinite number of solutions. With linear equations, think of each equation describing a straight line. The solution to the system of equations will be where these lines intersect (a point). If they do not intersect at all (or maybe two of the lines intersect, and the third one doesn't) then there is no solution. If the equations describe the same line, then there will be infinite solutions (every point on the line satisfies both equations). If the system of equations came from a real world problem (like solving for currents or voltages in different parts of a circuit) then there should be a solution, if the equations were chosen properly.
A proof in calculus is when it will make a statement, such as: If y=cos3x, then y'''=18sin3x. Then it will tell you to do a proof. This means you have to solve the equation step by step, coming to the solution, which should be the same as in the statement. If you do come to the same answer as in the statement, then you just correctly did a calculus proof.
3
Unrealized capital gains or losses should generally not be included in the calculation of return, as they represent potential future gains rather than actual realized profits. Return calculations typically focus on realized gains, which reflect the actual cash flow generated from investments. However, including unrealized gains can provide insights into the overall performance of an investment portfolio and its market value over time. Ultimately, the choice depends on the context and purpose of the analysis.
there is no problem with this quadratic equation it's 2x square - 3x -2 = 0 I need an answer. where it says square there should be a little 2 at the top corner of the 2x to make it 2x square thanks If you can't factor it easily then use the quadratic equation: The two solutions are: 2 & -.5
As long as time permits you defiantly should.
true
After deriving a solution to the equation, it's crucial to substitute your answer back into the original equation to verify its validity. This step ensures that the solution not only fits within the mathematical framework but also satisfies all conditions outlined by the equation. If the substituted answer holds true, it confirms that your solution is correct; otherwise, further investigation is needed. Always double-checking your work helps to ensure accuracy in problem-solving.
Using the original form of the equation to check your solution ensures that you verify the accuracy of your answer within the context of the problem. It helps confirm that the solution satisfies all conditions and constraints set by the equation. Additionally, checking against the original form can reveal any potential errors made during the solving process, ensuring the integrity of your solution. This practice reinforces understanding and builds confidence in your problem-solving skills.
A solution.
If you mean for a math problem, after coming up with a solution you should usually check the solution in the original equation, to be safe.
It means that whatever you have substituted is the solution of the given linear equation. Or you have substituted the equation in itself.
To show that a wave function is a solution to the time-independent Schrödinger equation for a simple harmonic oscillator, you substitute the wave function into the Schrödinger equation and simplify. This will involve applying the Hamiltonian operator to the wave function and confirming that it equals a constant times the wave function.
You document the attempted solution You return to the beginning of the troubleshooting process
1) Replace the inequality signs in the solution and in the original question with = signs. Substitute the solution inn the question: it should make it true. 2) (Back to the inequalities) Pick another number that satisfies the solution inequality - e.g. if x>2, pick 5. Substitute this into the original inequality: if it makes it true, then you are good to go!
Let x represent the gallons of 10% ammonia solution. The total volume of the mixture is x + 50 gallons. The equation for the mixture is: 0.10x + 0.30(50) = 0.15(x + 50). Solving this equation gives x = 50 gallons of the 10% ammonia solution needed.
You should be able to look at this equation, or use the discriminant and know that there are no real roots.