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3 years ago

Each set of ordered pairs represents a function. Write a rule that represents the function

Mathematics

1 answer:

Sonbull [250]3 years ago

5 0

Answer:

y=3x+1

Step-by-step explanation:

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A woman is looking for a bigger square office. She finds an office twice the area of her current office. If the perimeter of her

Sauron [17]

88×2=176this is the answer

4 0

3 years ago

Read 2 more answers

Consider the matrix A =(1 1 1 3 4 3 3 3 4) Find the determinant |A| and the inverse matrix A^-1.

solong [7]

Answer:

$A)\,\,det(A)=1$

$B)\,\,A^{-1}=\left[\begin{array}{ccc}7&-1&-1\\-3&1&0\\-3&0&1\end{array}\right]$

Step-by-step explanation:

$det(A) = \left\Bigg|\begin{array}{ccc}1&1&1\\3&4&3\\3&3&4\end{array}\right\Bigg|$

Expanding with first row

$det(A) = \left\Bigg|\begin{array}{ccc}1&1&1\\3&4&3\\3&3&4\end{array}\right\Bigg|\\\\\\det(A)= (1)\left\Big|\begin{array}{cc}4&3\\3&4\end{array}\right\Big|-(1)\left\Big|\begin{array}{cc}3&3\\3&4\end{array}\right\Big|+(1)\left\Big|\begin{array}{cc}3&4\\3&3\end{array}\right\Big|\\\\det(A)=1[16-9]-1[12-9]+1[9-12]\\\\det(A)=7-3-3\\\\det(A)=1$

To find inverse we first find cofactor matrix

$C_{1,1}=(-1)^{1+1}\left\Big|\begin{array}{cc}4&3\\3&4\end{array}\right\Big|=7\\\\C_{1,2}=(-1)^{1+2}\left\Big|\begin{array}{cc}3&3\\3&4\end{array}\right\Big|=-3\\\\C_{1,3}=(-1)^{1+3}\left\Big|\begin{array}{cc}3&4\\3&3\end{array}\right\Big|=-3\\\\C_{2,1}=(-1)^{2+1}\left\Big|\begin{array}{cc}1&1\\3&4\end{array}\right\Big|=-1\\\\C_{2,2}=(-1)^{2+2}\left\Big|\begin{array}{cc}1&1\\3&4\end{array}\right\Big|=1\\\\C_{2,3}=(-1)^{2+3}\left\Big|\begin{array}{cc}1&1\\3&3\end{array}\right\Big|=0\\\\$

$C_{3,1}=(-1)^{3+1}\left\Big|\begin{array}{cc}1&1\\4&3\end{array}\right\Big|=-1\\\\C_{3,2}=(-1)^{3+2}\left\Big|\begin{array}{cc}1&1\\3&3\end{array}\right\Big|=0\\\\\\C_{3,3}=(-1)^{3+3}\left\Big|\begin{array}{cc}1&1\\3&4\end{array}\right\Big|=1\\\\$

Cofactor matrix is

$C=\left[\begin{array}{ccc}7&-3&3\\-1&1&0\\-1&0&1\end{array}\right] \\\\Adj(A)=C^{T}\\\\Adj(A)=\left[\begin{array}{ccc}7&-1&-1\\-3&1&0\\-3&0&1\end{array}\right] \\\\\\A^{-1}=\frac{adj(A)}{det(A)}\\\\A^{-1}=\frac{\left[\begin{array}{ccc}7&-1&-1\\-3&1&0\\-3&0&1\end{array}\right] }{1}\\\\A^{-1}=\left[\begin{array}{ccc}7&-1&-1\\-3&1&0\\-3&0&1\end{array}\right]$

4 0

3 years ago

What is the slope of the line through the points (-2,-1) and (8,-3)?

RSB [31]

Answer:

- 1/5

Step-by-step explanation:

Slope of a line passing through two points can be calculated as:

$\text{slope}=\frac{\text{rise}}{\text{run}} \\\\ \text{slope}=\frac{\text{Difference of y coordinates}}{\text{Difference of x coordinates}}$

The given points are (-2, -1) and (8, -3). Using the values in above formula, we get:

$\text{slope}=\frac{-3-(-1)}{8-(-2)}\\\\ \text{slope}=\frac{-3+1}{8+2}\\\\ \text{slope}=\frac{-2}{10}\\\\ \text{slope}=\frac{-1}{5}$

Thus the slope of the line through the given points is -1/5. So 2nd option gives the correct answer

3 0

4 years ago

Read 2 more answers

If 2x=4(5-2x), then x=

NNADVOKAT [17]

x would equal 2 because:

4 times 5 is 20

4 times 2x is -8x

move over the 8x to the side with the 2x

then you have 10x=20

20/10 equals x=2

Hope this helps :)

3 0

3 years ago

In algebra, we use a(n) _____ to represent a variable.

elena-s [515]

Answer – A letter
In algebraic equations, a variable refers to an unknown or changeable number. Typically, all the letters in the alphabet are used to represent variables in algebra. Letters from the Greek alphabet are also used in some advanced algebra. Therefore, in algebra, we use a letter to represent a variable. <span>
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5 0

3 years ago

Read 2 more answers