Choose the letter of the correct answer Write the chosen letter on a separate sheet of 1. The measure of the volume of a rectangular solid is a'b - 63b27a-9ab? Find the dimensions of the
solid
A.(a + 3b). (a - 3b), and (ab + 7)
C. (a + 3b). (3a - 3b), and (ab + )
B.(3a+ 3b). (a - 3b), and (ab + 7)
D. (a + 3b). (a-35), and (ab + 3)
2. The floor plan for a rectangular building states that the length of the building is to be 8 meters more than
times its width. If the floor area is to be 256 square meters, what must be the length and width of the building?
A.6 meters long and 16 meters wide C. 8 meters long and 32 meters wide
B.30 meters long and 10 meters wide D. 32 meters long and 8 meters wide
3. The area of the dining room is 130 square units. If the width is 3 meter less than its length what is the weidin
of the room?
A. 10 units
B. 11 units
C 12 units
D. 13 units
D. 2b + 10
4. One of the factors of 2b2 + 15b-50 is b +10. What is the other factor?
A.2b - 10
B. 2-5
0. 2b +5
5. The area of the nachos is 15x - 10x square centimeters. If the base is 5x centimeters, which is the length of
the height?
A. 3x - 2 cm.
B. 3x + 2 cm
C. 6x-4 cm
D. 6x + 4 cm
pose

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Complete Question

Choose the letter of the correct answer Write the chosen letter on a separate sheet of

1. The measure of the volume of a rectangular solid is a²b - 63b²-9ab³? Find the dimensions of the

solid

A.(a + 3b). (a - 3b), and (ab + 7)

C. (a + 3b). (3a - 3b), and (ab + 3 )

B.(3a+ 3b). (a - 3b), and (ab + 7)

D. (a + 3b). (a-3b), and (ab + 3)

2. The floor plan for a rectangular building states that the length of the building is to be 8 meters more than

times its width. If the floor area is to be 256 square meters, what must be the length and width of the building?

A.6 meters long and 16 meters wide C. 8 meters long and 32 meters wide

B.30 meters long and 10 meters wide D. 32 meters long and 8 meters wide

3. The area of the dining room is 130 square units. If the width is 3 meter less than its length what is the weidin

of the room?

A. 10 units

B. 11 units

C 12 units

D. 13 units

4. One of the factors of 2b2 + 15b-50 is b +10. What is the other factor?

A.2b - 10

B. 2-5

C. 2b +5

D. 2b + 10

5. The area of the nachos is 15x² - 10x square centimeters. If the base is 5x centimeters, which is the length of

the height?

A. 3x - 2 cm.

B. 3x + 2 cm

C. 6x-4 cm

D. 6x + 4 cm

1 A.(a + 3b). (a - 3b), and (ab + 7)

2 D. 32 meters long and 8 meters wide

3 A. 10 units

4 B. 2b -5

5. C. 6x - 4 cm

Step-by-step explanation:

Choose the letter of the correct answer Write the chosen letter on a separate sheet of

1. The measure of the volume of a rectangular solid is a²b - 63b²-9ab³? Find the dimensions of the

solid

We pick the options one after the other

A.(a + 3b). (a - 3b), and (ab + 7)

(a² -3ab + 3ab -9b²)(ab + 7)

(a² - 9b²) (ab + 7)

a²b - 9ab³ - 63b²

C. (a + 3b). (3a - 3b), and (ab + 7 )

(3a² - 3ab + 3ab -9b³)(ab + 3)

(3a² - 9b³)(ab + 3)

3a³b + 21ab² - 9b⁴a - 27b³

B.(3a+ 3b). (a - 3b), and (ab + 7)

(3a² - 9ab + 3ab - 9b²)(ab + 7)

(3a² - 6ab - 9b²)(ab + 7)

3a³b +21a² - 6a²b² + 42ab - 9ab³ - 63

D. (a + 3b). (a-3b), and (ab + 3)

(a² -3ab + 3ab - 9b²)(ab + 3)

(a² - 9b²) (ab + 3)

a³b + 3a² - 9ab³ - 27b²

Therefore, option A.(a + 3b). (a - 3b), and (ab + 7) is the correct option

2. The floor plan for a rectangular building states that the length of the building is to be 8 meters more than 3 times its width . If the floor area is to be 256 square meters, what must be the length and width of the building?

Area of a rectangle = Length × Width

Length of the building is to be 8 meters more than times its width.

= Length = 3W + 8

Area = 256m²

Hence:

256 =( 3W + 8 )× W

256 = 3W² + 8W

= 3W² + 8W - 256

Factorise

= 3W(W - 8) + 32(W - 8)

= (3W + 32) ( W - 8)

W - 8 = 0

W = Width = 8m

Length = 3W + 8

Length = 3(8) + 8

= 24 + 8

= 32m.

D. 32 meters long and 8 meters wide

3. The area of the dining room is 130 square units. If the width is 3 meter less than its length what is the width

of the room?

A. 10 units

B. 11 units

C 12 units

D. 13 units

Area = Length × Width

The width is 3 meter less than its length

W = L - 3

Area = 130 square units

Hence:

130 = L (L - 3)

130 = L² - 3L

L² - 3L - 130

= L² + 10L - 13L - 130

= L(L + 10) - 13(L + 10)

= (L - 13) (L + 10)

L - 13 = 0

L = Length = 13 units

L + 10 = 0

L = -10 units.

W = L - 3

L = 13 units

W = 13 - 3

W = 10 units

Therefore, the width of the room is 10 units

A. 10 units

4. One of the factors of 2b² + 15b-50 is b + 10. What is the other factor?

A.2b - 10

B. 2b -5

C. 2b +5

D. 2b + 10

2b² + 15b -50

One of the factors is b +10.

We factorise

2b² + 15b - 50

= 2b² + 20b - 5b - 50

= 2b(b + 10) - 5(b + 10)

= (2b - 5) (b + 10)

The other factor is 2b - 5

B. 2b -5

5. The area of the nachos is 15x² - 10x square centimeters. If the base is 5x centimeters, which is the length of

the height?

A. 3x - 2 cm.

B. 3x + 2 cm

C. 6x-4 cm

D. 6x + 4 cm

Nachos are triangular in shape

Area of a triangle = 1/2 × Base × height

A = 1/2 bh

A = bh/2

2A = bh

h = 2A/b

The area of the nachos is 15x - 10x square centimeters. If the base is 5x centimeters,

h = 2(15x² - 10x)/5x

h = 30x² - 20x/5x

h = 30x²/5x - 20x/5x

= 6x - 4 cm

the length of the height is:

C. 6x - 4 cm