All categories

3 years ago

In the triangle below,∠1= 35° and ∠6 = 70°. WHat is the measurement of ∠4? ∠4= ?°

Mathematics

1 answer:

julia-pushkina [17]3 years ago

8 0

Answer:

145°

Step-by-step explanation:

< 6 + <2 = 180° {being linear pair }

70° + < 2 = 180°

< 2 = 180° - 70°

< 2 = 110°

Now

< 4 = < 1 + < 2 (exterior angle of a triangle is equal to the sum of two opposite interior angles)

<4 = 35° + 110°

= 145°

Hope it will help :)

You might be interested in

What is 5.129×103 answer the question

Rufina [12.5K]

Answer:

528.287

Step-by-step explanation:

If you use multiplication your answer comes to 528.287

7 0

4 years ago

What do we call the statement that determines if the null hypothesis is rejected?

geniusboy [140]

Answer:

c) alternate hypothesis

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers

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

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