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2 years ago

1.x-7=202.3x+6=12x-21

Mathematics

1 answer:

dusya [7]2 years ago

8 0

Answer:

1. x=27

2. x=3

Step-by-step explanation:

<h3>the first one </h3>

let's solve your equation step-by-step.

x−7=20

Step 1: Add 7 to both sides.

x−7+7=20+7

<h3>the second one </h3>

Let's solve your equation step-by-step.

3x+6=12x−21

Step 1: Subtract 12x from both sides.

3x+6−12x=12x−21−12x

−9x+6=−21

Step 2: Subtract 6 from both sides.

−9x+6−6=−21−6

−9x=−27

Step 3: Divide both sides by -9.

−9x/−9=−27/−9

<h3 />

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Solve the following system by any method -8x-8y=0 -8x+2y=-20

iVinArrow [24]

$\fbox{Solution by using Matrix}$

$\text{Linear Equation} = -8x-8y=0 , -8x+2y=-20$

$\text{Rewrite the linear equations above as a matrix}$

$\left[\begin{array}{ccc}8&-8&0\\-8&2&-20\\\end{array}\right]$

$\text{Apply to Row2 : Row2 + Row1}$

$\left[\begin{array}{ccc}8&-8&0\\-8&-6&-20\\\end{array}\right]$

$\text{ Simplify rows}$

$\left[\begin{array}{ccc}8&-8&0\\0&1&10/3\\\end{array}\right]$

$\text{Note: The matrix is now in echelon form.}$ $\text{The steps below are for back substitution.}$

$\text{Apply to Row1 : Row1 + 8 Row2}$

$\left[\begin{array}{ccc}8&0&80/30\\0&1&10/3\\\end{array}\right]$

$\text{ Simplify rows}$

$\left[\begin{array}{ccc}1&0&10/3\\0&1&10/3\\\end{array}\right]$

$\text{Therefore, the solution is}$

$x= \dfrac{10}{3} \ \text{and} \ \ y=\dfrac{10}{3}$

7 0

2 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 for x: 14-x= 5

tia_tia [17]

Answer:

x = 9

Step-by-step explanation:

We are going to isolate x

14 - x = 5

subtract 14 from 5

-x = -9

multiply both sides by -1 to make x positive

x = 9

6 0

3 years ago

Read 2 more answers

Look at the picture below and answer correctly so i can mark you as brainliest.

andreev551 [17]

Answer:

{14,13,6,0}

Step-by-step explanation:

It’s basically the y value :)

4 0

2 years ago

Read 2 more answers

A small business earns a profit of $6500 in January and $17,500 in May. What is the rate of change in profit for this time perio

MAXImum [283]

Rate of change of profit for this period is $2750 per month

<em><u>Solution:</u></em>

Given that,

Profit of $6500 in January and $17,500 in May

<em><u>To find: Rate of change</u></em>

Since,

January is the first month of the year (1) while May is the fifth month (5)

<em><u>Therefore, we get two points</u></em>

(1, 6500) and (5, 17500)

Using these points we can find the rate of change in profit for this time period

<em><u>The rate of change using the following formula:</u></em>

$m = \frac{y_2-y_1}{x_2-x_1}$

Here from the points,

$(x_1, y_1) = (1, 6500)\\\\(x_2, y_2) = (5, 17500)$

<em><u>Therefore, rate of change is given as:</u></em>

$m = \frac{17500-6500}{5-1}\\\\m = \frac{11000}{4}\\\\m = 2750$

Thus rate of change of profit for this period = $2750 per month

8 0

3 years ago

1.x-7=202.3x+6=12x-21​

1.x-7=202.3x+6=12x-21