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3 years ago

What is the slope of the line that passes through 9,5 and 4,5

Mathematics

2 answers:

Leokris [45]3 years ago

8 0

Answer:

(5,0

Step-by-step explanation:

Vesnalui [34]3 years ago

6 0

Answer:

Step-by-step explanation:

slope m = (y₂ - y₁) / (x₂ - x₁)

= (5 - 5) / (4 - 9)

= 0 / -5

= 0

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7. En una reunió de nois i noies el nombre de noies és 25 vegades més que el de nois. Si surten de la reunió 10 nois i 10 noies,

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3 years ago

A = 4 0 0 1 3 0 −2 3 −1 Find the characteristic polynomial for the matrix A. (Write your answer in terms of λ.) Find the real ei

Illusion [34]

Answer:

Step-by-step explanation:

We are given the matrix

$A = \left[\begin{matrix}4&0&0 \\ 1&3&0 \\-2&3&-1 \end{matrix}\right]$

a) To find the characteristic polynomial we calculate $\text{det}(A-\lambda I)=0$ where I is the identity matrix of appropiate size. in this case the characteristic polynomial is

$\left|\begin{matrix}4-\lambda&0&0 \\ 1&3-\lambda&0 \\-2&3&-1-\lambda \end{matrix}\right|=0$

Since this matrix is upper triangular, its determinant is the multiplication of the diagonal entries, that is

$(4-\lambda)(3-\lambda)(-1-\lambda)=(\lambda-4)(\lambda-3)(\lambda+1)=0$

which is the characteristic polynomial of A.

b) To find the eigenvalues of A, we find the roots of the characteristic polynomials. In this case they are $\lambda=4,3,-1$

c) To find the base associated to the eigenvalue lambda, we replace the value of lambda in the expression $A-\lambda I$ and solve the system $(A-\lambda I)x =0$ by finding a base for its solution space. We will show this process for one value of lambda and give the solution for the other cases.

Consider $\lambda = 4$ . We get the matrix

$\left[\begin{matrix}0&0&0 \\ 1&-1&0 \\-2&3&-5 \end{matrix}\right]$

The second line gives us the equation x-y =0. Which implies that x=y. The third line gives us the equation -2x+3y-5z=0. Since x=y, it becomes y-5z =0. This implies that y = 5z. So, combining this equations, the solution of the homogeneus system is given by

$(x,y,z) = (5z,5z,z) = z(5,5,1)$

So, the base for this eigenspace is the vector (5,5,1).

If $\lambda = 3$ then the base is (0,4,3) and if $\lambda = -1$ then the base is (0,0,1)

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3 years ago

Elizabeth has half as many CDs as Jennifer. Which equation would represent the number of CDs that Jennifer has? (Let e = the num

Sergio [31]

Answer: C

Step-by-step explanation:

2j = 2 × j = e

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3 years ago

The sum of the measures of two complementary angles exceeds the difference of their measure by 86_. Find the measure of each ang

Bad White [126]

As the sum of two complementary angles = a + b = 90 degree -------(1)

Difference of two complementary angles = a – b

According to question;

The difference of two complementary angles exceed the sume (90) by 86.

a – b = 90 – 86 = 4 -------(2)

adding equation (1) and (2);

2a = 90 + 4 = 94

a = 94 / 2 = 47

putting a = 47 in equation (1);

47 + b = 90

b = 90 – 47 = 43

<span>So angle a = 47 and angle b = 43</span>

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4 years ago

36 pints of paint. They need divided into 11 small containers. If they are poured equally, how many pints of paint would b in ea

JulsSmile [24]

Answer:

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Step-by-step explanation:

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