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3 years ago

Tran is solving the quadratic equation 2x2 – 4x – 3 = 0 by completing the square. His first four steps are shown in the table.

Mathematics

2 answers:

anygoal [31]3 years ago

8 0

Answer:

Not positive, but I'm pretty sure it's Step 3.

Step-by-step explanation:

Nady [450]3 years ago

3 0

The following steps of solving for the roots of 2x² - 4x -3 = 0 were retrieved from another source Step 1 2x² - 4x = 3 Step 2 2(x² - 2x) = 3 Step 3 2(x² - 2x + 1) = 3 + 1 Step 4 2(x - 1)² = 4 From this, we can see that on Step 3, Tran made a mistake of adding 1 to 3. As we can see, 2(x² - 2x + 1) = 2x² - 4x + 2. That means, instead of adding 1, it should have been 2. Therefore, the step that Tran first made an error is Step 3<span>.</span>

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Writing to Explain Suppose you have a 100-mL cup, you can a 500-mL cup. List two different ways

Misha Larkins [42]

5 100ml cups and 1 500 ml cup

and 2 500 ml cups

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3 years ago

Is 7, 20, 25 a right triangle?

love history [14]

Answer:

The answer to your question is below

Step-by-step explanation:

Process

To answer if they are right triangles or not use the Pythagorean theorem which states that the square of the hypotenuse equals the sum of the square of the legs.

a) 25² = 20² + 7²

625 = 400 + 49

625 ≠ 449 It is not a right triangle

b) 26² = 24² + 10²

676 = 576 + 100

676 = 676 it is a right triangle

c) 13² = 8² + (√10)²

169 = 64 + 10

169 ≠ 74 it is not a right triangle

d) 52² = 48² + 20²

2704 = 2304 + 400

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3 0

3 years ago

x = c1 cos(t) + c2 sin(t) is a two-parameter family of solutions of the second-order DE x'' + x = 0. Find a solution of the seco

igomit [66]

Answer:

$x=-cos(t)+2sin(t)$

Step-by-step explanation:

The problem is very simple, since they give us the solution from the start. However I will show you how they came to that solution:

A differential equation of the form:

$a_n y^n +a_n_-_1y^{n-1}+...+a_1y'+a_oy=0$

Will have a characteristic equation of the form:

$a_n r^n +a_n_-_1r^{n-1}+...+a_1r+a_o=0$

Where solutions $r_1,r_2...,r_n$ are the roots from which the general solution can be found.

For real roots the solution is given by:

$y(t)=c_1e^{r_1t} +c_2e^{r_2t}$

For real repeated roots the solution is given by:

$y(t)=c_1e^{rt} +c_2te^{rt}$

For complex roots the solution is given by:

$y(t)=c_1e^{\lambda t} cos(\mu t)+c_2e^{\lambda t} sin(\mu t)$

Where:

$r_1_,_2=\lambda \pm \mu i$

Let's find the solution for $x''+x=0$ using the previous information:

The characteristic equation is:

$r^{2} +1=0$

So, the roots are given by:

$r_1_,_2=0\pm \sqrt{-1} =\pm i$

Therefore, the solution is:

$x(t)=c_1cos(t)+c_2sin(t)$

As you can see, is the same solution provided by the problem.

Moving on, let's find the derivative of $x(t)$ in order to find the constants $c_1$ and $c_2$ :

$x'(t)=-c_1sin(t)+c_2cos(t)$

Evaluating the initial conditions:

$x(0)=-1\\\\-1=c_1cos(0)+c_2sin(0)\\\\-1=c_1$

And

$x'(0)=2\\\\2=-c_1sin(0)+c_2cos(0)\\\\2=c_2$

Now we have found the value of the constants, the solution of the second-order IVP is:

$x=-cos(t)+2sin(t)$

3 0

3 years ago

Solve the equation. 3x + 5 = x - 3

Luden [163]

Answer:

x=-4

Step-by-step explanation:

Subtract x from 3x ( 2x )

2x+5=-3

Subtract 5 from -3 ( -8 )

2x=-8

Divide ( -4 )

x=-4

3 0

2 years ago

How these ratios alike? <br> 8:5 16:10 24:15

arlik [135]

Answer:

All the left numbers of the Ratio go by 8's times tables and all the right numbers go by 5's times tables

Step-by-step explanation:

8x1= 8

8x2 =16

8x3 = 24

5x1= 5

5x2= 10

5x3= 15

Let me know if its right.

6 0

3 years ago