180 degrees of the triage
Answer:
First, we write the augmented matrix.
⎡
⎢
⎣
1
−
1
1
2
3
−
1
3
−
2
−
9
|
8
−
2
9
⎤
⎥
⎦
Next, we perform row operations to obtain row-echelon form.
−
2
R
1
+
R
2
=
R
2
→
⎡
⎢
⎣
1
−
1
1
0
5
−
3
3
−
2
−
9
|
8
−
18
9
⎤
⎥
⎦
−
3
R
1
+
R
3
=
R
3
→
⎡
⎢
⎣
1
−
1
1
0
5
−
3
0
1
−
12
|
8
−
18
−
15
⎤
⎥
⎦
The easiest way to obtain a 1 in row 2 of column 1 is to interchange \displaystyle {R}_{2}R
2
and \displaystyle {R}_{3}R
3
.
Interchange
R
2
and
R
3
→
⎡
⎢
⎣
1
−
1
1
8
0
1
−
12
−
15
0
5
−
3
−
18
⎤
⎥
⎦
Then
−
5
R
2
+
R
3
=
R
3
→
⎡
⎢
⎣
1
−
1
1
0
1
−
12
0
0
57
|
8
−
15
57
⎤
⎥
⎦
−
1
57
R
3
=
R
3
→
⎡
⎢
⎣
1
−
1
1
0
1
−
12
0
0
1
|
8
−
15
1
⎤
⎥
⎦
The last matrix represents the equivalent system.
x
−
y
+
z
=
8
y
−
12
z
=
−
15
z
=
1
Using back-substitution, we obtain the solution as \displaystyle \left(4,-3,1\right)(4,−3,1).First, we write the augmented matrix.
⎡
⎢
⎣
1
−
1
1
2
3
−
1
3
−
2
−
9
|
8
−
2
9
⎤
⎥
⎦
Next, we perform row operations to obtain row-echelon form.
−
2
R
1
+
R
2
=
R
2
→
⎡
⎢
⎣
1
−
1
1
0
5
−
3
3
−
2
−
9
|
8
−
18
9
⎤
⎥
⎦
−
3
R
1
+
R
3
=
R
3
→
⎡
⎢
⎣
1
−
1
1
0
5
−
3
0
1
−
12
|
8
−
18
−
15
⎤
⎥
⎦
The easiest way to obtain a 1 in row 2 of column 1 is to interchange \displaystyle {R}_{2}R
2
and \displaystyle {R}_{3}R
3
.
Interchange
R
2
and
R
3
→
⎡
⎢
⎣
1
−
1
1
8
0
1
−
12
−
15
0
5
−
3
−
18
⎤
⎥
⎦
Then
−
5
R
2
+
R
3
=
R
3
→
⎡
⎢
⎣
1
−
1
1
0
1
−
12
0
0
57
|
8
−
15
57
⎤
⎥
⎦
−
1
57
R
3
=
R
3
→
⎡
⎢
⎣
1
−
1
1
0
1
−
12
0
0
1
|
8
−
15
1
⎤
⎥
⎦
The last matrix represents the equivalent system.
x
−
y
+
z
=
8
y
−
12
z
=
−
15
z=1
Using back-substitution, we obtain the solution as \displaystyle \left(4,-3,1\right)(4,−3,1).
A parallelogram in which adjacent sides are perpendicular to each other is called a rectangle. The value of x or the length of TU is 22.5.
<h3>What is a rectangle?</h3>
That parallelogram in which adjacent sides are perpendicular to each other is called a rectangle. A rectangle is always a parallelogram and a quadrilateral but the reverse statement may or may not be true.
Since all the rectangles are similar, therefore, the corresponding sides of the rectangle will be in ratio. Therefore,
Similarly, the breadth will be,
Hence, the value of x or the length of TU is 22.5.
Learn more about Rectangle:
brainly.com/question/15019502
#SPJ1
Answer:
84
Step-by-step explanation:
Total students he surveyed: 27
Amount that found it something OTHER than easy: 14 (11 moderate + 3 difficult)
This means that 
found it something other than easy
Multiply that by 162 to find the proportion for the larger population:
162 * (14/27), and we get 84.
The perimeter of a rectangle is <u>length + length + width + width</u>.
We know that the length of a rectangle is 3cm more than its width, which gives us the equation: (l for length and w for width)
l = 3 + w
We also know that the perimeter of the rectangle is 98cm, which gives us the equation:
98 = 2l + 2w (equation for perimeter of a rectangle as noted above)
We can divide both sides of this equation by 2 to get:
49 = l + w
Now we'll stick l = 3 + w into the above equation, which gives us:
49 = 3 + w + w
which simplifies to 49 = 3 + 2w.
Now we'll subtract 3 from both sides:
49 - 3 = 46
3 + 2w - 3 = 2w
which gives us 46 = 2w.
Dividing both sides by 2 gives us 23 = w.
Substituting w = 23 into the equation l = 3 + w gives us:
l = 3 + 23
l = 26cm.
Let's check our answer. 26cm is 3cm more than 23cm. 26cm + 26cm + 23cm + 23cm gives us 98cm. The length is 26cm and the width is 23cm.
