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3 years ago

Use number properties to simplify the following expression.

Mathematics

2 answers:

eduard3 years ago

8 0

Answer:

Step-by-step explanation:

the answer is 3, because you always have to add the numbers in parantheses first. and 5+3= 8 (commutive of addition). u bring down the -5 and you have -5 + 8 = 3.

-5+(5+3)

-5+8

exis [7]3 years ago

4 0

The answer is
-5+8
=3

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8x – 2(x + 1) = 2(3x – 1)

Nina [5.8K]

8x - 2(x + 1) = 2(3x - 1)

First, expand to remove parenthesis. / Your problem should look like: $8x - 2x - 2 = 6x - 2$
Second, subtract 8x - 2x - 2 to get 6x - 2. / Your problem should look like: $6x - 2 = 6x - 2$
Third, both sides are equal, so there are infinite solutions. The equation is always true.

Answer: infinite solutions

8 0

3 years ago

Please help me out with this

Naily [24]

Answer:

y = -3x - 2

Step-by-step explanation:

Equation of a line passing through $(x_1,y_1)$ and slope m is,

$y-y_1=m(x-x_1)$

Slope of a line passing through $(x_1,y_1)$ and $(x_2,y_2)$ is,

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

Slope of the line passing through (0, -2) and (1, -5) will be,

Slope = $\frac{-2+5}{0-1}$

m = - 3

Therefore, equation of the line passing through (0, -2) and slope = -3 will be,

y + 2 = -3(x - 0)

y + 2 = -3x

y = -3x - 2

8 0

3 years ago

Solve the given initial-value problem. x' = 1 2 0 1 − 1 2 x, x(0) = 2 7

Ilia_Sergeevich [38]

I'll go out on a limb and guess the system is

$\mathbf x'=\begin{bmatrix}\frac12&0\\1&-\frac12\end{bmatrix}\mathbf x$

with initial condition $\mathbf x(0)=\begin{bmatrix}2&7\end{bmatrix}^\top$ . The coefficient matrix has eigenvalues $\lambda$ such that

$\begin{vmatrix}\frac12-\lambda&0\\1&-\frac12-\lambda\end{vmatrix}=\lambda^2-\dfrac14=0\implies\lambda=\pm\dfrac12$

The corresponding eigenvectors $\eta$ are such that

$\lambda=\dfrac12\implies\begin{bmatrix}\frac12-\frac12&0\\1&-\frac12-\frac12\end{bmatrix}\eta=\begin{bmatrix}0&0\\1&-1\end{bmatrix}\eta=\begin{bmatrix}0\\0\end{bmatrix}$
$\implies\eta=\begin{bmatrix}1\\1\end{bmatrix}$

$\lambda=-\dfrac12\implies\begin{bmatrix}\frac12+\frac12&0\\1&-\frac12+\frac12\end{bmatrix}\eta=\begin{bmatrix}1&0\\1&0\end{bmatrix}\eta=\begin{bmatrix}0\\0\end{bmatrix}$
$\implies\eta=\begin{bmatrix}0\\1\end{bmatrix}$

So the characteristic solution to the ODE system is

$\mathbf x(t)=C_1\begin{bmatrix}1\\1\end{bmatrix}e^{t/2}+C_2\begin{bmatrix}0\\1\end{bmatrix}e^{-t/2}$

When $t=0$ , we have

$\begin{bmatrix}2\\7\end{bmatrix}=C_1\begin{bmatrix}1\\1\end{bmatrix}+C_2\begin{bmatrix}0\\1\end{bmatrix}=\begin{bmatrix}C_1\\C_1+C_2\end{bmatrix}$

from which it follows that $C_1=2$ and $C_2=5$ , making the particular solution to the IVP

$\mathbf x(t)=2\begin{bmatrix}1\\1\end{bmatrix}e^{t/2}+5\begin{bmatrix}0\\1\end{bmatrix}e^{-t/2}$

$\mathbf x(t)=\begin{bmatrix}2e^{t/2}\\2e^{t/2}+5e^{-t/2}\end{bmatrix}$

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4 years ago

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4 years ago

If 9n + 2= (1/7) what is n?

neonofarm [45]

N=13/63
I dont really know how to explain it butbthats the answer

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4 years ago

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