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3 years ago

Which pairs of figures are congruent? Which pairs are similar?

Mathematics

1 answer:

Wittaler [7]3 years ago

4 0

Answer:

1 is congruent, 2 is similar, 3 is similar, and 4 is congruent

Step-by-step explanation:

2 and 3 aren't the same size so they aren't congruent, but the other two are the same size and shape so they are congruent

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What is the row echelon form of this matrix?

USPshnik [31]

The row echelon form of the matrix is presented as follows;

$\begin{bmatrix}1 &-2 &-5 \\ 0& 1 & -7\\ 0&0 &1 \\\end{bmatrix}$

<h3>What is the row echelon form of a matrix?</h3>

The row echelon form of a matrix has the rows consisting entirely of zeros at the bottom, and the first entry of a row that is not entirely zero is a one.

The given matrix is presented as follows;

$\begin{bmatrix}-3 &6 &15 \\ 2& -6 & 4\\ 1&0 &-1 \\\end{bmatrix}$

The conditions of a matrix in the row echelon form are as follows;

There are row having nonzero entries above the zero rows.
The first nonzero entry in a nonzero row is a one.
The location of the leading one in a nonzero row is to the left of the leading one in the next lower rows.

Dividing Row 1 by -3 gives:

$\begin{bmatrix}1 &-2 &-5 \\ 2& -6 & 4\\ 1&0 &-1 \\\end{bmatrix}$

Multiplying Row 1 by 2 and subtracting the result from Row 2 gives;

$\begin{bmatrix}1 &-2 &-5 \\ 0& -2 & 14\\ 1&0 &-1 \\\end{bmatrix}$

Subtracting Row 1 from Row 3 gives;

$\begin{bmatrix}1 &-2 &-5 \\ 0& -2 & 14\\ 0&2 &4 \\\end{bmatrix}$

Adding Row 2 to Row 3 gives;

$\begin{bmatrix}1 &-2 &-5 \\ 0& -2 & 14\\ 0&0 &18 \\\end{bmatrix}$

Dividing Row 2 by -2, and Row 3 by 18 gives;

$\begin{bmatrix}1 &-2 &-5 \\ 0& 1 & -7\\ 0&0 &1 \\\end{bmatrix}$

The above matrix is in the row echelon form

Learn more about the row echelon form here:

brainly.com/question/14721322

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8 0

1 year ago

Help me please i don't understand this thanks

STALIN [3.7K]

Answer:

12.75

Step-by-step explanation:

12.75 rounded to the nearest tenth is 12.8, and 12.74 won't work because it will round to 12.7.

Therefore, 12.75 is the smallest possible number.

6 0

3 years ago

I need help with this one

Anika [276]

Answer:

Step-by-step explanation:

if you look closely, you can see that the side of it goes up 2, then 2, then 1.

7 0

3 years ago

Read 2 more answers

A contractor is building a fenced-in area at a daycare. The area will be rectangular with the length of its base equal to half t

AlladinOne [14]

Answer:

The length of fencing will be $300\ ft$

Step-by-step explanation:

Step 1

Find the dimensions of the rectangle

we know that

The area of a rectangle is equal to

$A=bh$

In this problem we have

$A=5,000\ ft^{2}$

$5,000=bh$ -----> equation A

$b=\frac{h}{2}$ -----> equation B

Substitute equation B in equation A

$5,000=(\frac{h}{2})h$

$10,000=h^{2}$

square root both sides

$h=100\ ft$

Find the value of b

$b=\frac{h}{2}$ -----> $b=\frac{100}{2}=50\ ft$

step 2

Find the length of fencing

The perimeter of a rectangle is equal to

$P=2(b+h)$

we have

$h=100\ ft$

$b=50\ ft$

substitute

$P=2(50+100)=300\ ft$

6 0

3 years ago

Caroline wants to give 8 equal size packets of flower seeds to her friends. she has half a pound of sunflower seeds. how much wi

777dan777 [17]

If she has half a pound of sunflower seeds and wants to split it into eight equal packets, each packet would be 1/16 of a pound. 1/16 of a pound is 1 ounce.

Therefore, each packet of seeds would weigh 1 ounce (1 oz.)

4 0

3 years ago

Read 2 more answers