Answer: the first box is 1/5 since one of 5 squares are shaded.
The next box the answer is “there are 4 groups 1/5.
The next answer is 4/5
The last answer is 4/5
Step-by-step explanation:
Answer:
To solve the system of linear equations using Gaussian elimination, we'll write the augmented matrix and perform row operations to transform it into row echelon form.
The given system of equations:
-2x_1 + 3x_2 + x_3 = 2
-3x_1 + 4x_2 + 2x_3 = 2
x_1 - 5x_2 + 4x_3 = -9
-2x_1 + 4x_2 - 4x_3 = 8
Writing the augmented matrix:
[ -2 3 1 | 2 ]
[ -3 4 2 | 2 ]
[ 1 -5 4 | -9 ]
[ -2 4 -4 | 8 ]
1. Row 1 Ã (-3) + Row 2 â Row 2:
[ -2 3 1 | 2 ]
[ 9 -13 -5 | -6 ]
[ 1 -5 4 | -9 ]
[ -2 4 -4 | 8 ]
2. Row 1 Ã (1/2) + Row 3 â Row 3:
[ -2 3 1 | 2 ]
[ 9 -13 -5 | -6 ]
[ -1 (3/2) 2 | -5/2]
[ -2 4 -4 | 8 ]
3. Row 1 Ã (-1) + Row 4 â Row 4:
[ -2 3 1 | 2 ]
[ 9 -13 -5 | -6 ]
[ -1 (3/2) 2 | -5/2]
[ 0 7 -3 | 6 ]
4. Row 2 Ã (-9/7) + Row 3 â Row 3:
[ -2 3 1 | 2 ]
[ 9 -13 -5 | -6 ]
[ -1 0 (59/7) | -(23/7)]
[ 0 7 -3 | 6 ]
5. Row 2 Ã (2/3) + Row 4 â Row 4:
[ -2 3 1 | 2 ]
[ 9 -13 -5 | -6 ]
[ -1 0 (59/7) | -(23/7)]
[ 0 0 (-11/7) | 0 ]
6. Row 3 Ã (-14/11) + Row 4 â Row 4:
[ -2 3 1 | 2 ]
[ 9 -13 -5 | -6 ]
[ -1 0 (59/7) | -(23/7)]
[ 0 0 1 | 0 ]
7. Row 3 Ã (1/2) + Row 1 â Row 1:
[ -1 3/2 3/2 | (4/7) ]
[ 9 -13 -5 | -6 ]
[ -1 0 1 | 0 ]
[ 0 0 1 | 0 ]
8. Row 3 Ã (9/7) + Row 2 â Row 2:
[ -1 3/2 3/2 | (4/7) ]
[ 0 -26/7 -14/7 | -42/7 ]
[ -1 0 1 | 0 ]
[ 0 0 1 | 0 ]
9. Row 3 Ã (1/2) + Row 4 â Row 4:
[ -1 3/2 3/2 | (4/7) ]
[ 0 -26/7 -14/7 | -42/7 ]
[ -1 0 1 | 0 ]
[ 0 0 1 |
Answer:
1. "angle HGJ" or "angle JGH" (∠HGJ or ∠JGH)
2. "angle G" (∠G)
3. "angle 3" (∠3)
Step-by-step explanation:
Three ways the shaded angle can be named:
1. We can use capital letters to name the shaded angle. The middle letter indicates the vertex. Thus, we would name the shaded angle as: "angle HGJ" or "angle JGH". G is the middle letter, which indicates the vertex of the angle. Most often, the symbol "∠" is usually used to represent the word "angle". In short form, the shaded angle can be named as:
"∠ HGJ" or "∠ JGH"
2. The shaded angle can also be named according to the vertex. Thus, G is the vertex. The angle can be named "angle G" or "∠G"
3. Numbers can be placed at the vertex of the angle, and named accordingly. Thus, the shaded angle of which the vertex is labelled "3" can be named as "angle 3" or "∠3"
Answer:
positive 7
Step-by-step explanation:
-3x + y = 8
3y = 9x
y = -x
Answer:
-3x+y=8 and "3y=9x
Step-by-step explanation: