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3 years ago

How to find a measure of angle A?

1 answer:

4 0

To find the measure of the smallest angle of the triangle, we multiply 4 times 10. So, 4 x 10 = 40. Remember, the sum of the angles of a triangle is 180 degrees. Just take what you are given in a problem and try to determine what will make the final angle add up to 180 degrees. Hope this helps even though it probably won’t :D

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Put the following equation of a line into slope-intercept form, simplifying all

muminat

Answer:

y = 3/4 + 7

Step-by-step explanation:

you must put the equation into the form of y = mx + b

add 6x to both sides and put it in front of the 56

8y = 6x + 56

y must be by itself by x does not so we divide everything by 8

y = 6/8x + 7

we must simplify the fraction 6/8

y = 3/4x + 7

7 0

2 years ago

Please help!!! I'll mark you as brainliest!!!!

podryga [215]

0.504854369 as a percentage would be 50.4854369%

easiest way to remember: a percentage is a decimal rounded 2 decimal places to the right

rounded to the nearest tenth, the percentage will be 50.5%

if u need more help tell me

4 0

3 years ago

The graph represents function 1, and the equation represents funtion 2:

horsena [70]

Answer:

Step-by-step explanation:

we know that

The rate of change of a linear equation is a constant that is the same that the slope

step 1

we have

The equation of the graph (function 1) is equal to

y=4

Is a horizontal line

The slope is equal to zero

The rate of change of function 1 is zero

step 2

The equation of the function 2 is

$y=8x+12$

This is a linear equation in slope intercept form

where

the slope is equal to m=8

The rate of change of function 2 is 8

therefore

The rate of change of function 2 is 8 more than the rate of change of function 1

5 0

3 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

The equation of the line of best fit relating age (in years, x) and the median height (in cm, y) of boys is given.

lbvjy [14]

Answer:

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Backpack

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Wings of dawn back pack

8 0

2 years ago