Question

help
1.) x2 – 81 = 0
2.) 3t2 = 12
3.) (y − 4)2- 81 = 0

1.) Mrs Poe asked her carpenter to construct a square table with
an area of 16ft2. Can you tell the dimensions of the table?
Sheryl says that the solutions of the quadratic equations
w2 = 49 and w2 + 49 = 0 are the same. Do you agree with
Sheryl? Justify your answer.

Answer 1

Answer:

1.) x2 – 81 = 0

=> x² = 81

=> x = 9

2.) 3t2 = 12

=> t² = 12/3

=> t² = 4

=> t = 2

3.) (y − 4)2- 81 = 0

=> 2y - 8 = 81

=> 2y = 89

=] y = 44.5

1) Area = 16 ft²

s² = 16

s = 4ft.

Answer 2

Answer ❶ :

›»› The required value of x is 9.

Step-by-step explanation :

Given :

• x² - 81 = 0.

To Find :

• The value of x = ?

Solution :

→ x² - 81 = 0

→ x² = 81

→ x = √81

→ x = 9.

Hence, the required value of x is 9.

_____________________

Answer ❷ :

›»› The required value of t is 2.

Step-by-step explanation :

Given :

• 3t² = 12.

To Find :

• The value of x = ?

Solution :

→ 3t² = 12

→ t² = 12/3

→ t² = 4

→ t = √4

→ t = 2.

Hence, the required value of t is 2.

_____________________

Answer ❸ :

›»› The required value of y is 13 and -5.

Step-by-step explanation :

Given :

• (y - 4)² - 81 = 0.

To Find :

• The value of y = ?

Solution :

→ (y - 4)² - 81 = 0

→ y² + 4² - 2 × y × 4 - 81 = 0

→ y² + 16 - 2 × y × 4 - 81 = 0

→ y² + 16 - 2y × 4 - 81 = 0

→ y² + 16 - 8y - 81 = 0

→ y² - 8y - 81 + 16 = 0

→ y² - 8y - 65 = 0

→ (y - 13)(y + 5) = 0

→ y - 13 = 0, y + 5 = 0

→ y = 13, y + 5 = 0

→ y = 13, y = - 5.

Hence, the required value of y is 13 and -5.

_____________________

Answer ❶ :

›»› The dimension of square is 4 ft.

Step-by-step explanation :

Given :

• Area of square = 16 ft².

To Find :

• Dimensions of square = ?

Formula required :

Formula of area of square to calculate the dimension of square is given by,

→ Area of square = a².

Here,

• a is the side of square.

Units,

• The unit of side is ft.

Solution :

We know that, if we are given with the area of square and we need to find the dimension of square then we have the required formula, that is,

→ Area of square = a².

By using the formula of area of square to calculate the dimension of square and substituting the given values in the formula, we get :

→ 16 = a²

→ a² = 16

→ a = √16

→ a = 4.

Hence, the dimension of square is 4 ft.