Step: 1

900 is also included in the solution because the dorm can accommodate at most 900 students.

Step: 2

The inequality for the situation is S ≤ 900.

Correct Answer is : S ≤ 900

Step: 1

In order to continue the account in the bank, the amount should be greater than or equal to 500.

Step: 2

Among the choices, the inequality M ≥ 500 satisfies the statement.

Correct Answer is : M ≥ 500

Step: 1

The statement says that Dr. Mike needs at least 250 beds for his new hospital. So, 250 is also included in the solution.

Step: 2

The inequality for the statement is H ≥ 250.

Correct Answer is : H ≥ 250

Step: 1

The statement says the American soccer team needs to score no less than 2 goals against Germany to win the match. So, 2 is also included in the solution.

Step: 2

The inequality for the statement is G ≥ 2.

Correct Answer is : G ≥ 2

Step: 1

A parking lot can accommodate no more than 250 cars and 250 is included in the solution.

[Given statement.]

Step: 2

Among the choices, the inequality N ≤ 250 satisfies the statement.

Correct Answer is : N ≤ 250

Step: 1

The area of a rectangle = length × width.

Step: 2

The area of the rectangular fountain = (a ) × (a + 16) square meters.

Step: 3

192 = (a ) × (a + 16)

[Original equation.]

Step: 4

192 = a ^{2} + 16a

[Use distributive property.]

Step: 5

192 + 8^{2} = a ^{2} + 16a + 8^{2}

[Add (16 2 )^{2} = 8^{2} = 64 to each side.]

Step: 6

256 = (a + 8)^{2}

[Write the right hand side as a perfect square and simplify.]

Step: 7

± 16 = a + 8

[Evaluate square roots on both sides.]

Step: 8

± 16 - 8 = a + 8 - 8

[Subtract 8 from each side.]

Step: 9

[Simplify.]

Step: 10

Width = a = 8 meters

[The dimensions cannot be negative.]

Step: 11

Length = (a + 16) = (16 + 8) = 24 meters.

[Substitute 8 for a and add.]

Step: 12

The dimensions of the fountain are 8 meters wide and 24 meters long.

Correct Answer is : 8, 24

Step: 1

The area of a rectangle = length × width.

Step: 2

The front view area of the monitor = (a ) × (a + 24) square in.

Step: 3

112 = (a ) × (a + 24)

[Original equation.]

Step: 4

112 = a ^{2} + 24a

[Use distributive property.]

Step: 5

112 + 12^{2} = a ^{2} + 24a + 12^{2}

[Add (24 2 )^{2} = 12^{2} = 144 to each side.]

Step: 6

256 = (a + 12)^{2}

[Write the right hand side as a perfect square and simplify.]

Step: 7

±16 = (a + 12)

[Evaluate square roots on both sides.]

Step: 8

±16 - 12 = a + 12 - 12

[Subtract 12 from each side.]

Step: 9

[Simplify.]

Step: 10

Width = a = 4 in.

[Dimensions cannot be negative.]

Step: 11

Length = (a + 24) = (4 + 24) = 28 in.

[Substitute 4 for a and add.]

Step: 12

The dimensions of the front view of the monitor are 4 in. wide and 28 in. long.

Correct Answer is : 4 in. and 28 in.

Step: 1

The area of a rectangle = length × width.

Step: 2

The area of the rectangular book = (a ) × (a + 12) square centimeters.

Step: 3

364 = (a ) × (a + 12)

[Original equation.]

Step: 4

364 = a ^{2} + 12a

[Use distributive property.]

Step: 5

364 + 6^{2} = a ^{2} + 12a + 6^{2}

[Add (12 2 )^{2} = 6^{2} = 36 to each side.]

Step: 6

400 = (a + 6)^{2}

[Write the right hand side as a perfect square and simplify.]

Step: 7

± 20 = (a + 6)

[Evaluate square roots on both sides.]

Step: 8

± 20 - 6 = a + 6 - 6

[Subtract 6 from each side.]

Step: 9

[Simplify.]

Step: 10

Width = a = 14 centimeters

[Dimensions cannot be negative.]

Step: 11

Length = (a + 12) = (14 + 12) = 26 centimeters

[Substitute 14 for a and add.]

Step: 12

The book is 14 centimeters wide and 26 centimeters long.

Correct Answer is : 14 cm, 26 cm

Step: 1

The area of a rectangle = Length × Width.

Step: 2

The area of the rectangular notice board = (a ) × (a - 6) square feet.

Step: 3

27 = (a ) × (a - 6)

[Original equation.]

Step: 4

27 = a ^{2} - 6a

[Use distributive property.]

Step: 5

27 + (- 3)^{2} = a ^{2} - 6a + (- 3)^{2}

[Add (- 6 2 )^{2} = (- 3)^{2} = 9 to each side.]

Step: 6

36 = (a - 3)^{2}

[Write the right side of the equation as a perfect square and simplify.]

Step: 7

± 6 = (a - 3)

[Evaluate square roots on both sides.]

Step: 8

± 6 + 3 = a - 3 + 3

[Subtract 3 from each side.]

Step: 9

[Simplify.]

Step: 10

Width of the rectangular notice board is a = 9 feet.

[Dimensions cannot be negative.]

Step: 11

Length of the rectangular notice board is (a - 6) = (9 - 6) = 3 feet.

[Repalce a with 9 and add.]

Step: 12

The rectangular notice board is 9 feet by 3 feet.

Correct Answer is : 9 feet by 3 feet

Step: 1

The area of a rectangle = Length × Width

Step: 2

The area of the rectangular carpet = (a ) × (a - 10) square feet

Step: 3

56 = (a ) × (a - 10)

[Original equation.]

Step: 4

56 = a ^{2} - 10a

[Use distributive property.]

Step: 5

56 + (- 5)^{2} = a ^{2} - 10a + (- 5)^{2}

[Add (- 10 2 )^{2} = (- 5)^{2} = 25 to each side.]

Step: 6

81 = (a - 5)^{2}

[Write the right side of the equation as a perfect square and simplify.]

Step: 7

± 9 = (a - 5)

[Evaluate square roots on both sides.]

Step: 8

± 9 + 5 = a - 5 + 5

[Add 5 on each side.]

Step: 9

[Simplify.]

Step: 10

Length of the rectangular carpet is a = 14 feet.

[Dimensions cannot be negative.]

Step: 11

Width of the rectangular carpet is (a - 10) = (14 - 10) = 4 feet.

[Repalce a with 14 and add.]

Step: 12

The dimensions of the carpet are 14 feet by 4 feet.

Correct Answer is : 14 feet by 4 feet

Step: 1

[Original equation.]

Step: 2

0 = - 16t ^{2} - 30t + 124

[Height = 0, when the pen is on the ground.]

Step: 3

Compare the original equation with the standard form to get the values of a , b and c .

Step: 4

[Substitute the values in the quadratic formula.]

Step: 5

[Evaluate power and multiply.]

Step: 6

= [ 3 0 ± 9 4 ] ( - 3 2 )

[Simplify the radical.]

Step: 7

= - 3.875, 2

[Simplify.]

Step: 8

The ball reaches the ground after 2 seconds.

[Consider positive value as t represents time.]

Correct Answer is : 2 seconds

Step: 1

[Original equation.]

Step: 2

0 = - 16t ^{2} + (- 24t ) + 16

[Replace h with 0, as the height is zero at the water level.]

Step: 3

[Substitute a = - 16, b = - 24 and c = 16 in the quadratic formula.]

Step: 4

[Simplify.]

Step: 5

[Simplify inside the radical.]

Step: 6

[Simplify the radical.]

Step: 7

[Since t represents time, consider the positive integer.]

Correct Answer is : 0.50

Step: 1

[Original equation.]

Step: 2

0 = - 16t ^{2} + vt + s

[h = 0 for ground level.]

Step: 3

0 = - 16t ^{2} - 25t + 73.5

[Replace v with - 25 and s = 73.5.]

Step: 4

[Substitute the values of a = - 16, b = - 25 and c = 73.5 in the quadratic formula.]

Step: 5

= [ 2 5 ± ( 6 2 5 + 4 7 0 4 ) ] - 3 2

[Evaluate the power and multiply.]

Step: 6

= 2 5 ± 5 3 2 9 - 3 2

[Add within the grouping symbols.]

Step: 7

= 2 5 ± 7 3 - 3 2

[Find the square root.]

Step: 8

[Simplify.]

Step: 9

The apple will reach the ground about 1.5 seconds after it was thrown.

Correct Answer is : 1.5 seconds

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