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3 years ago

Write an expression that equals 40 include the Exponent

Mathematics

1 answer:

Leokris [45]3 years ago

4 0

Maybe let's just do the prime factorization.

40=2x2x2x5

answer:2^3x5

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WHAT TYPE OF NUMBER RESULTS FROM DIVIDING A NEGATIVE NUMBER BY A NEGATIVE NUMBER?

Jet001 [13]

Answer:

a positive

Step-by-step explanation:

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3 years ago

Find the eigenvectors and eigenvalues for the matrix.<br> A =<br> [3 1<br> 1 3]

Wittaler [7]

Answer:

Eigenvalues : 4 and 2

Eigenvectors : <1,1> and <-1,1>.

Step-by-step explanation:

The given matrix is

$A=\begin{bmatrix}3&1\\1&3\end{bmatrix}$

We need to find the eigenvectors and eigenvalues for the matrix.

$|A-\lambda I|=0$

λ represents the eigen values.

$\det \left(\begin{bmatrix}3&1\\1&3\end{bmatrix}-\lambda\begin{bmatrix}1&0\\ 0&1\end{bmatrix}\right)=0$

$\lambda^2-6\lambda+8=0$

$\lambda=4,2$

For $\lambda=4$

$(A-\lambda I)X=0$

$\left(\begin{bmatrix}3&1\\1&3\end{bmatrix}-4\begin{bmatrix}1&0\\ 0&1\end{bmatrix}\right)\begin{bmatrix}\text{x}\\ \text{y}\end{bmatrix}=\begin{bmatrix}0\\ 0\end{bmatrix}$

$\begin{bmatrix}-1&1\\ 1&-1\end{bmatrix}\begin{bmatrix}\text{x}\\ \text{y}\end{bmatrix}=\begin{bmatrix}0\\ 0\end{bmatrix}$

$R_2\rightarrow R_2-R_1$

$\begin{bmatrix}1&-1\\ 0&0\end{bmatrix}\begin{bmatrix}x\\ y\end{bmatrix}=\begin{bmatrix}0\\ 0\end{bmatrix}$

$x-y=0$

$x=y$

Eigenvector $=\begin{bmatrix}y\\ y\end{bmatrix}\space\space\:y\ne \:0$

Eigenvector $=\begin{bmatrix}1\\ 1\end{bmatrix}$

Similarly,

For $\lambda=2$

$(\begin{bmatrix}3&1\\ 1&3\end{bmatrix}-2\begin{bmatrix}1&0\\ 0&1\end{bmatrix})\begin{bmatrix}\text{x}\\ \text{y}\end{bmatrix}=\begin{bmatrix}0\\ 0\end$

$\begin{bmatrix}1&1\\ 1&1\end{bmatrix}\begin{bmatrix}\text{x}\\ \text{y}\end{bmatrix}=\begin{bmatrix}0\\ 0\end{bmatrix}$

$R_2\rightarrow R_2-R_1$

$\begin{bmatrix}1&1\\ 0&0\end{bmatrix}\begin{bmatrix}\text{x}\\ \text{y}\end{bmatrix}=\begin{bmatrix}0\\ 0\end{bmatrix}$

$x+y=0$

$x=-y$

Eigenvector $=\begin{bmatrix}-y\\ y\end{bmatrix}\space\space\:y\ne \:0$

Eigenvector $=\begin{bmatrix}-1\\ 1\end{bmatrix}$

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3 years ago

Help Please

Nina [5.8K]

if we change 2½ years to an improper fraction, that'd be 5/2 years.

$\bf ~~~~~~ \textit{Simple Interest Earned Amount}\\\\A=P(1+rt)\qquad \begin{cases}A=\textit{accumulated amount}\\P=\textit{original amount deposited}\to& \$850\\r=rate\to 2\%\to \frac{2}{100}\to &0.02\\t=years\to &\frac{5}{2}\end{cases}\\\\\\A=850\left( 1+0.02\cdot \cfrac{5}{2} \right)\implies A=850(1.05)\implies A=892.5$

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4 years ago

Which property is shown?

Mkey [24]

Not 100 percent sure but I believe the answer is D

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3 years ago

Please answer the question above

PilotLPTM [1.2K]

1) A cube has 6 sides & each side is a square. Is s is the side then the total area of te cube is = (6s²)

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4 years ago