60 algebra 2 questıons Solve 3x – y + 2z = 6

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QUESTION 1

Solve 3x – y + 2z = 6
-x + y = 2
x – 2z = –5
(-1, -3, -3)
(1, 3, 3)
(1, -3, -3)
(1, 3, -3)

2 points

QUESTION 2

Solve 2x + y + z = 5
4x – 2y – z = 0
3x – y + 2z = 6
(1, 1, 2)
(-1, -1, -2)
(5, 0, 6)
(1, 1, -2)

2 points

QUESTION 3

Solve 5x + 2y – 3z = 4
-2x – 4y + z = -8
x + y + z = 2
(2, 0, 0)
(0, 2, 0)
(2, -2, 0)
(0, -6, 9)

2 points

QUESTION 4

Solve 4x + y + z = 1
8x – 4y – 7z = 2
–5y – 9z = –33
(3, -33, 22)
(1, 2, 3)
(-3, 0.5, 2)
(0.5, 3, 2)

2 points

QUESTION 5

Solve 2x + y – z = 3
4x – y + 4z = 0
-3y + 2z = 6
(2, -4, -3)
(-2, 4, 3)
(4, 2, -7)
(-4, -2, 7)

2 points

QUESTION 6

Solve 4x + y – 2z = 0
2x – 3y + 3z = 9
-6x – 2y + z = 0
(0, 9, 0)
(0, -9, 0)

2 points

QUESTION 7

Solve x + 3y + 4z = 0
x – 2z = 8
y + z = 3

2 points

QUESTION 8

Twice the first number is eleven more than the sum of the other two numbers. The sum of twice the first number and three times the third number is one more than the second number. The second number is equal to the sum of the first number and the third number. Find the three numbers.
1^st number = -6, 2^nd number = 3.5, 3^rd number = 2.5
1^st number = 8, 2^nd number = 4, 3^rd number = 1
1^st number = -8, 2^nd number = -4, 3^rd number = -1
1^st number = 6, 2^nd number = 3.5, 3^rd number = -2.5

2 points

QUESTION 9

The sum of the length, width, and height of a rectangular box is 16 cm, the width is twice the height, and twice the length exceeds the sum of the width and height by 5. Find the length, width, and height of the box.
Length = 10 cm, Width = 4 cm, Height = 2 cm
Length = 7 cm, Width = 6 cm, Height = 3 cm
Length = 7 cm, Width = 3 cm, Height = 6 cm
Length = 10 cm, Width = 2 cm, Height = 4 cm

2 points

QUESTION 10

In a certain triangle, the angle of the greatest measure measures 75 degrees more than the angle of the least measure. If one-third the sum of the degree measures of the smallest and the largest angles is equal to the degree measure of the remaining angle, what is the degree measure of each angle of the triangle?

		Largest angle = 105, Middle angle = 45, Smallest angle = 30
		Largest angle = 100, Middle angle = 50, Smallest angle = 30
		Largest angle = 115, Middle angle = 45, Smallest angle = 40
		Largest angle = 120, Middle angle = 45, Smallest angle = 15

2 points

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QUESTION 1

If a parallelogram is a rhombus then the diagonals are congruent.
True
False

2 points

QUESTION 2

ABCD is a parallelogram. What is true about and

||

2 points

QUESTION 3

What property is true for a rectangle, a square and a rhombus?
All four angles are right angles
All four sides are congruent
Consecutive angles are supplementary
The diagonals are perpendicular

2 points

QUESTION 4

In a rectangle, the opposite sides are congruent.
True
False

2 points

QUESTION 5

The opposite sides of a parallelogram are _________.
adjacent
congruent
collinear
perpendicular

2 points

QUESTION 6

The following is a rhombus, therefore
True
False

2 points

QUESTION 7

If a parallelogram is a rectangle then the diagonals are congruent.
True
False

2 points

QUESTION 8

Figure ABCD is a square. Angle B measures . Find the value of x.
8
4
10
Not enough information

2 points

QUESTION 9

YWXZ is a rhombus with diagonals that intersect at point S. Side WX measures 4a + 12. Side XZ measures 6a. Find the value of a.
Not enough information is given.
16.8
-6
6

2 points

QUESTION 10

KLMN is a kite. If angle MLK measures Angle MNK measures Find the value of x.
1.6
10.3
3.2
10

2 points

QUESTION 11

QRST is a parallelogram. Find x and y.
x = -1, y = -3
x = 1, y = 3
x = -1, y = 2
x = 2, y = 3

2 points

QUESTION 12

Figure ABCD is a square. Side AB measures 10x – 7. Side BC measures 2x + 52. Find the value of x.
5.625
7.375
4.917
3.75

2 points

QUESTION 13

Figure ABCD is a kite with diagonals which cross at point P. The angle APB measures . Find the value of x.
7.6
10.4
66
Not enough information

2 points

QUESTION 14

Triangle ABC is congruent to triangle DFE. Find x.
23
16
49.5
51

2 points

QUESTION 15

Triangle ABC is congruent to triangle XYZ. Angle A measures , angle B measures and angle X measures . Find the value of x.
20.5
13.67
16
10.5

2 points

QUESTION 16

Triangle RSV is congruent to triangle TVS. Find x.
23.5
20
18.5
21.5

2 points

QUESTION 17

Triangle DEF is congruent to triangle GHI. Side DE measures 52. Side GH measures 10x – 13. Side HI measures 12x – 16. Find the value of x.
7.14
1.5
5.67
6.5

2 points

QUESTION 18

Triangle DEF is congruent to triangle GHI. Side EF measures 52. Side GH measures 10x – 13. Side HI measures 12x – 16. Find the value of x.
7.14
1.5
5.67
6.5

2 points

QUESTION 19

Triangle PQR is congruent to triangle STU. Side PQ measures 3x + 15. Side QR measures 5x – 5. Side TU measures 60. Find the value of x.
15
13
13.75
10

2 points

QUESTION 20

Triangles QVS and RTS are similar. Find side VS.
70
60
50
40

2 points

QUESTION 21

Triangle DEF is similar to triangle PQR. Side DE measures 3, side EF measures 7 and side FD measures 9. Side PQ measures 5x – 25 and side RP measures 10x – 5. Find the value of x.
11
12
3
14

2 points

QUESTION 22

Triangle ABC is similar to triangle XYZ. Side AB measures 2, side BC measures x + 5, side CA measures x + 7, side XY measures 4 and side YZ measures 5x – 5. Find the value of x.
6.33
7.2
5
8

2 points

QUESTION 23

Triangle ABC is similar to triangle XYZ. Side AB measures 2, side BC measures x + 5, side CA measures x + 7, side XY measures 4 and side ZX measures 4x – 2. Find the value of x.
6.33
7.2
5
8

2 points

QUESTION 24

Triangles QVS and RTS are similar. Find side VS.
72.8
54.8
78.2
88.7

2 points

QUESTION 25

Triangles MOP and MNQ are similar. Find x.
6.25
7
5.5
6.75

2 points

QUESTION 26

Find x.
12
20
24
32

2 points

QUESTION 27

Point C is the center of the circle. Angle ACB measures . What is the measure of arc ADB?

2 points

QUESTION 28

Find the measure of angle X.

2 points

QUESTION 29

Point C is the center of the circle. Arc AB measures 5x + 2. Angle ACB measures 3x + 14. Find the value of x.
2
8
6
20

2 points

QUESTION 30

Point C is the center of the circle. Angle ACB measures . What is the measure of arc AB?

2 points

QUESTION 31

Angle ACB is an inscribed angle of circle P. What is the measure of ACB if the measure of is .

2 points

QUESTION 32

Point C is the center of the circle. What is if is equal to ?

2 points

QUESTION 33

Angle C is an inscribed angle of circle P. Angle C measures (3x + 5)° and arc AB measures (16x)°. Find x.
1
5
3
9

2 points

QUESTION 34

Angle C is an inscribed angle of circle P. Angle C measures (20x – 5)° and arc AB measures (30x + 30)°. Find the measure of arc AB.

100 degrees
50 degrees
75 degrees
150 degrees

2 points

QUESTION 35

Angle C is an inscribed angle of circle P. Angle C measures and arc AB measures . Find x.

2 points

QUESTION 36

Point C is the center of the circle. If angle ACB measures and AB measures , find x.

20
15
12
10

2 points

QUESTION 37

Point C is the center of the circle. If angle ACB measures and arc AB measures (x - 10)°, find x.
7
8
9
10

2 points

QUESTION 38

Circles M and K are congruent, arc QR is congruent to arc LN and arc OP is congruent to arc VW. Find y.
4
-4
-1
1

2 points

QUESTION 39

Circles M and K are congruent, is congruent to and is congruent to Find x.

-2
3
4
2

2 points

QUESTION 40

Circles M and K are congruent, is congruent to and is congruent to Find x.
2
-1
3
4

2 points

QUESTION 41

Circles M and K are congruent, is congruent to
What is the length of
10
15
20
25

2 points

QUESTION 42

Circles M and K are congruent, arc QR is congruent to arc LN and arc OP is congruent to arc VW. Find x.
3
-3
5
-5

2 points

QUESTION 43

Circles M and K are congruent, is congruent to and is congruent to Find y.

2
1
-1
-3

2 points

QUESTION 44

Find the measure of Angle A if is equal to 31° and is equal to 67°.

2 points

QUESTION 45

Find x.

2 points

QUESTION 46

and are tangent to circle D. Find angle B if arc AEC measures 210°.
105°
30°
285°
Cannot be determined

2 points

QUESTION 47

Find x.

2 points

QUESTION 48

Find angle A if is equal to 66° and is equal to 20°.

2 points

QUESTION 49

and are tangent to circle D. Find x if = and =7. Find x.
10
6
8
12

2 points

QUESTION 50

Find angle A if is equal to 23° and is equal to 15°.

2 points

Tags: math algebra 2

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Explanation & Answer

Attached.

QUESTION 1
1. Solve 3x – y + 2z = 6
-x + y = 2
x – 2z = –5

Answer:
Add the first equation to the third equation we have
3x-y+2z+x-2z=6-5 combine like term then 4x-y=1
Add this equation to the second equation we have:
4x-y-x+y=1+2 then 3x=3 then x=1
Plug x=1 into the second equation we have:
-1+y=2 then y=3
Plug x=1 into the third equation we have
1-2z=-5 then z=3
Final we can say the solution is (x, y, z) = (1, 3, 3)

(x,y,z)

(-1, -3, -3)
(1, 3, 3)
(1, -3, -3)
(1, 3, -3)

2 points

QUESTION 2
1. Solve 2x + y + z = 5
4x – 2y – z = 0
3x – y + 2z = 6

Answer:
Add the first equation to the second equation we have
2x+y+z+4x-2y-z=5+0 combine like term then 6x-y=5 then y=6x-5
Multiply both side of the second equation by 2 and add to the third equation we have:
8x -4y-2z+3x-y+2z=0+6 then 11x-5y=6
Plug y = 6x-5 into the equation 11x-5y =6 we have:
11x-5(6x-5)=6 then 11x-30x+25=6 then x=1
Plug x=1 into the equation y = 6x-5 we have:

y=6*1-5 =1
Plug x=1 and y=1 into the first equation we have:
2*1+1+z=5 then z=2
Final we can say the solution is(x, y, z) = (1, 1, 2)
2.
(x,y,z)

(1, 1, 2)
(-1, -1, -2)
(5, 0, 6)
(1, 1, -2)

2 points

QUESTION 3
Solve 5x + 2y – 3z = 4
-2x – 4y + z = -8
x+y+z=2

Answer:
Subtract the second equation to the third equation we have
-2x-4y+z-x-y-z=-8-2 combine like term then -3x-5y= -10
Multiply both side of the third equation by 3 and add to the first equation we have:
3x+3y+3z+5x+2y-3z=6+4 then 8x+5y=10
Add the equation 3x-5y= -10 to the equation 8x+5y=10 we have
3x-5y+8x+5y=-10+10 then 11x=0 then x=0
Plug x=0 into the equation 8x +5y=10 we have:
8*0+5y=10 then y=2
Plug x=0 and y=2 into the third equation we have:
0+2+z=2 then z=0
Final we can say the solution is: (x, y ,z)=(0, 2, 0)

1.
(x,y,z)

2 points

(2, 0, 0)
(0, 2, 0)
(2, -2, 0)
(0, -6, 9)

QUESTION 4
Solve 4x + y + z = 1
8x – 4y – 7z = 2
–5y – 9z = –33

Answer:
Multiply both side of the first equation by 2 and subtract to the second equation we have:
8x+2y+2z-8x+4y+7z=2-2 then 6y+9z=0
Add the equation 6y+9z=0 to the third equation we have:
6y+9z-5y-9z=0-33 then y=-33
Plug y=-33 into the equation 6y+9z=0 we have:
6*(-33)+9z=0 then z=22
Plug y=-33 and z=22 into the first equation we have:
4x-33+22=1 then x=3
Final we can say the solution is: (x, y, z) = (3, -33, 22)
1.
(x,y,z)=

(3, -33, 22)
(1, 2, 3)
(-3, 0.5, 2)
(0.5, 3, 2)

2 points

QUESTION 5
Solve 2x + y – z = 3
4x – y + 4z = 0
-3y + 2z = 6

Answer:
Multiply both side of the first equation by 2 and subtract to the second equation we have:
4x+2y-2z-4x+y-4z=6-0 then 3y-6z=6
Add the equation 3y-6z=6 to the third equation we have:
3y-6z-3y+2z=6+6 then -4z=12 then z=-3
Plug z=-3 into the equation 3y-6z=6 we have:
3y-6*(-3) = 6 then y=-4
Plug y=-4 and z=-3 into the first equation we have:
2x-4+3=3 then x=2

Final we can say the solution is: (x, y, z) = (2, -4, -3)
1.
(x,y,z)

(2, -4, -3)
(-2, 4, 3)
(4, 2, -7)
(-4, -2, 7)

2 points

QUESTION 6
Solve 4x + y – 2z = 0
2x – 3y + 3z = 9
-6x – 2y + z = 0

Answer:
Multiply both side of the third equation by 2 and add to the first equation we have:
-12x-4y+2z+4x+y-2z=0+0 then -8x-3y=0
Multiply both side of the third equation by 3 and subtract to the second equation we have:
-18x-6y+3z-2x+3y-3z=0-9 then -20x-3y=-9
Subtract the equation -8x-3y=0 to the equation-20x-3y=-9 we have:
-8x-3y+20x+3y=0+9 then 12x=9 then x=3/4
Plug x=3/4 into the equation -8x-3y=0 we have:
-8*(3/4)-3y=0 then y=-2
Plug x=3/4 and y=-2 into the first equation we have:
4*(3/4)-2-2z=0 then z=1/2
Final we can say the solution is: (x, y, z)=(3/4,-2,1/2)
1.
(0, 9, 0)

(0, -9, 0)
(x,y,z)

2 points
QUESTION 7
Solve x + 3y + 4z =0
x – 2z = 8
y+z=3

Answer:

Subtract the first equation to the second equation we have:
x+3y+4z-x+2z=0-8 then 3y+6z=-8 then y+2z=-8/3
Subtract the equation y+2z=-8/3 to the third equation we have:
y+2z-y-z=-8/3-3 then z=-17/3
Plug z=-17/3 into the equation x – 2z = 8we have:
x – 2*(-17/3) = 8 then x=-10/3
Plug z=-17/3 into the equation x+y=3 we have:
y-17/3=3 then y=26/3
Final the solution is: (x,y,z)=(-10/3, 26/3, -17/3)

(x,y,z)

2 points

QUESTION 8
1. Twice the first number is eleven more than the sum...

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		1^st number = -6, 2^nd number = 3.5, 3^rd number = 2.5
		1^st number = 8, 2^nd number = 4, 3^rd number = 1
		1^st number = -8, 2^nd number = -4, 3^rd number = -1
		1^st number = 6, 2^nd number = 3.5, 3^rd number = -2.5

		Length = 10 cm, Width = 4 cm, Height = 2 cm
		Length = 7 cm, Width = 6 cm, Height = 3 cm
		Length = 7 cm, Width = 3 cm, Height = 6 cm
		Length = 10 cm, Width = 2 cm, Height = 4 cm

		All four angles are right angles
		All four sides are congruent
		Consecutive angles are supplementary
		The diagonals are perpendicular

		True
		False

		True
		False

		adjacent
		congruent
		collinear
		perpendicular

		True
		False

60 algebra 2 questıons Solve 3x – y + 2z = 6

Description

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