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3 years ago

I am having trouble i need help.

Mathematics

2 answers:

lozanna [386]3 years ago

7 0

Answer:

A. y=2x-2

Step-by-step explanation:

zvonat [6]3 years ago

5 0

Answer:

the answer is A

Step-by-step explanation:

to find the slope intercept formula u need the slope, the y-intercept, and the X and Y

1st step: find the slope and to find the slope, pick any two points from the line

point 1: (2,2)

point 2: (3,4)

slope= y2-y1/x2-x1

4-2/3-2=2/1 or 2

the slope intercept form is y=mx+ b, so now substitute the variables for the known

y=2

x=2

m=2

2=2(2)+b

solve the equation

2=4+b

subtract 4 on both sides

b=-2

the slope intercept form is y=2x-2

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sweet [91]

Answer is “D” I took the test my self

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2 years ago

(1) (10 points) Find the characteristic polynomial of A (2) (5 points) Find all eigenvalues of A. You are allowed to use your ca

Yuri [45]

Answer:

Step-by-step explanation:

Since this question is lacking the matrix A, we will solve the question with the matrix

$\left[\begin{matrix}4 & -2 \\ 1 & 1 \end{matrix}\right]$

so we can illustrate how to solve the problem step by step.

a) The characteristic polynomial is defined by the equation $det(A-\lambdaI)=0$ where I is the identity matrix of appropiate size and lambda is a variable to be solved. In our case,

$\left|\left[\begin{matrix}4-\lamda & -2 \\ 1 & 1-\lambda \end{matrix}\right]\right|= 0 = (4-\lambda)(1-\lambda)+2 = \lambda^2-5\lambda+4+2 = \lambda^2-5\lambda+6$

So the characteristic polynomial is $\lambda^2-5\lambda+6=0$ .

b) The eigenvalues of the matrix are the roots of the characteristic polynomial. Note that

$\lambda^2-5\lambda+6=(\lambda-3)(\lambda-2) =0$

So $\lambda=3, \lambda=2$

c) To find the bases of each eigenspace, we replace the value of lambda and solve the homogeneus system(equalized to zero) of the resultant matrix. We will illustrate the process with one eigen value and the other one is left as an exercise.

If $\lambda=3$ we get the following matrix

$\left[\begin{matrix}1 & -2 \\ 1 & -2 \end{matrix}\right]$ .

Since both rows are equal, we have the equation

$x-2y=0$ . Thus x=2y. In this case, we get to choose y freely, so let's take y=1. Then x=2. So, the eigenvector that is a base for the eigenspace associated to the eigenvalue 3 is the vector (2,1)

For the case $\lambda=2$ , using the same process, we get the vector (1,1).

d) By definition, to diagonalize a matrix A is to find a diagonal matrix D and a matrix P such that $A=PDP^{-1}$ . We can construct matrix D and P by choosing the eigenvalues as the diagonal of matrix D. So, if we pick the eigen value 3 in the first column of D, we must put the correspondent eigenvector (2,1) in the first column of P. In this case, the matrices that we get are

$P=\left[\begin{matrix}2&1 \\ 1 & 1 \end{matrix}\right], D=\left[\begin{matrix}3&0 \\ 0 & 2 \end{matrix}\right]$

This matrices are not unique, since they depend on the order in which we arrange the eigenvalues in the matrix D. Another pair or matrices that diagonalize A is

$P=\left[\begin{matrix}1&2 \\ 1 & 1 \end{matrix}\right], D=\left[\begin{matrix}2&0 \\ 0 & 3 \end{matrix}\right]$

which is obtained by interchanging the eigenvalues on the diagonal and their respective eigenvectors

4 0

3 years ago

A wall is 20 feet long and requires 1,470 bricks to build. How high is the wall?

Arte-miy333 [17]

Answer: The height of wall is 10.5 feet.

Step-by-step explanation:

Since we have given that

Number of bricks to build = 1470

Length of wall = 20 feet

We need to find the height of wall.

As we know that

Bricklayer's formula is given by

$N=7LH\\\\1470=7\times 20\times H\\\\1470=140\times H\\\\\dfrac{1470}{140}=H\\\\10.5\ ft=H$

Hence, the height of wall is 10.5 feet.

3 0

3 years ago

Recursive formula for 26, 24, 22, 20

dexar [7]

Answer:

a_n = 28-2n

Step-by-step explanation:

Given sequence is:

26,24,22,20

We can see that the difference between consecutive terms is same so the sequence is an arithmetic sequence

The standard formula for arithmetic sequence is:

$a_n = a_1+(n-1)d$

Here,

a_n is the nth term

a_1 is the first term

and d is the common difference

So,

d = 24-26

= -2

a_1 = 26

Putting the values of d and a_1

$a_n = 26 + (n-1)(-2)\\a_n = 26-2n+2\\a_n = 28-2n$

Hence, the recursive formula for given sequence is: a_n = 28-2n ..

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2 years ago

I NEED HELP WITH THIS PLEASE !! I WILL GIVE BRAINLIEST!!I PROMISE!!:)

Shtirlitz [24]

Answer: The answer is A!!

Step-by-step explanation:

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2 years ago

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