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3 years ago

Pls help will mark brainliest!!!!!!

Mathematics

2 answers:

laiz [17]3 years ago

8 0

Answer:

They are congruent figures

Step-by-step explanation:

Marianna [84]3 years ago

7 0

Answer:

Figure ABCD is congruent to figure A’B’C’D’. So can say that Figure ABCD is similar to figure A’B’C’D’.

Step-by-step explanation:

It is given that Figure ABCD is reflected about the y-axis to obtain figure A’B’C’D’.

Reflection is a rigid transformation it means the size and shape of the figure remains same but reflected across a line of reflection.

In other words we can say that Figure ABCD is congruent to figure A’B’C’D’.

$ABCD\cong A'B'C'D'$

Corresponding parts of congruent figures are same.

$m\angle A=m\angle A'$

$m\angle B=m\angle B'$

$m\angle C=m\angle C'$

$m\angle D=m\angle D'$

Therefore, the correct statement is "Figure ABCD is similar to figure A’B’C’D’".

You might be interested in

Dale deposits $4000 into an account that pays simple interest at a rate of 6% per year. How much interest will he be paid in the

BartSMP [9]

Answer:

$1200

Step-by-step explanation:

$4000 x .06 = $240 x 5 years = $1200

7 0

3 years ago

PLEASE ANSWER THIS QUESTION TOO !! FOR 30 POINTS AND BRAINLIEST!!

s344n2d4d5 [400]

Answer:

3000 books

Step-by-step explanation:

We know the author receives a one time fee of $2500. On top of that, the author will receive $1.50 per book sold. This is a constant rate and is linear because of this. We can use y=mx+b. M is the slope or rate of change. M here is $1.50. B is the starting value which is $2500 here.

We write y=1.5x+2500.

This equation will give the amount of money the author earns for x number of books sold. If y=7000 for the author earning 7000. We will use inverse operations to isolate and find x.

7000=1.5x+2500

7000-2500=1.5x+2500-2500

4500=1.5x

4500/1.5=x

3000=x

8 0

3 years ago

Read 2 more answers

Which of the binomials below is a factor of this expression?<br> 16x2 + 40xy + 25y2

svet-max [94.6K]

(4x+5y)2 is the right answer

8 0

3 years ago

Read 2 more answers

(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

Ann [662]

1) The accumulated amount after six years and the total interest that Trevor will receive if the interest rate is 4.5% per annum simple interest after 6 years are <u>R25,400</u> and <u>R5,400</u> respectively.

2) The accumulated amount after six years and the total interest that Trevor will receive if the interest rate is 4.5% per annum compound interest after 6 years are<u> R26,045.20</u> and <u>R6,045.20</u> respectively.

<h3>Data and Calculations:</h3><h3>Simple Interest:</h3>

Principal = R20,000

Investment period = 6 years

Interest rate = 4.5%

Simple interest for 6 years = R5,400 ($20,000 x 6 x 4.5%)

Principal + Interest = R25,400 (R20,000 + R5,400)

<h3>Compound Interest:</h3>

Principal = R20,000

Investment period = 6 years

Interest rate = 4.5%

N (# of periods) = 6 years

I/Y (Interest per year) = 4.5%

PV (Present Value) = R20,000

PMT (Periodic Payment) = R0

<u>Results</u>:

FV = R26,045.20

Total Interest = R6,045.2

Learn more about simple and compound interests at brainly.com/question/3575751

#SPJ1

8 0

2 years ago