Question

Which expression has a value 48?

Answer 1

Hey there!

Option A.

(4 + 5) * 3^2 - 9 ÷ 3^2

= 9 * 9 - 9 ÷ 9

= 81 - 1
= 80

Thus, that answer is: [incorrect]

Option B.
4 + 5 * (3^2 - 9) + 3^2

= 4 + 5 * (9 - 9) + 9

= 4 + 5 * (0) + 9

= 4 + 5(0) + 9

= 4 + 0 + 9

= 4 + 9

= 13

Thus, that answer is also [incorrect]

Option C.

4 + 5 * 3^2(-9 ÷ 3^2)

= 4 + 5 * 3^2(-9 ÷ 9)

= 4 + 5 * 3^2(-1)

= 4 + 5 * 9(-9)

= 4 + 5(9) * -1

= 4 + 45 * -1

= 4 - 45

= -41

Thus, that answer is also [incorrect]

Option D.
4 + 5 * 3^2 - 9 ÷ 3^2

= 4 + 5(9) - 9 ÷ 9

= 4 + 45 - 9 ÷ 9

= 49 - 9 ÷ 9

= 49 - 1

= 48

Therefore, your answer is: Option D.

Good luck on your assignment & enjoy your day l!

~Amphitrite1040:)

Answer 2

Answer:

Option D

Step-by-step explanation:

To find out which expression has a value of 48, we need to recall the PEMDAS (where: P = Parenthesis, E = Exponents, M/D = Multiplication or Division, A/S = Addition or Subtraction).

A) [4 + 5] × 3² - 9 ÷ 3²

First, simplify the expression in the parenthesis as PEMDAS

⇒ [9] × 3² - 9 ÷ 3²

Pull the "9" out of the parenthesis

⇒ 9 × 3² - 9 ÷ 3²

Simplify the exponents as PEMDAS

⇒ 9 × 9 - 9 ÷ 9

Multiply the first two terms in the expression as PEMDAS

⇒ 81 - 9 ÷ 9

Divide the last two terms as PEMDAS

⇒ 81 - 1

Finally, simplify the expression.

⇒ 80

⇒ 48 ≠ 80

B) 4 + 5 × (3² - 9) ÷ 3²

First, simplify the expression in the parenthesis as PEMDAS.

We can see here that the expression in the parenthesis includes a constant with a negative sign and an exponent. To simplify the expression, we need to simplify the exponent. Once the exponent is simplified, we can simplify the expression in the parenthesis.

⇒ 4 + 5 × (3² - 9) ÷ 3²

⇒ 4 + 5 × (9 - 9) ÷ 3²

⇒ 4 + 5 × (0) ÷ 3²

Pull the "0" out of the parenthesis

⇒ 4 + 5 × 0 ÷ 3²

Simplify the exponent as PEMDAS

⇒ 4 + 5 × 0 ÷ 9

Multiply the middle two terms as PEMDAS

⇒ 4 + 0 ÷ 9

Divide the last two terms as PEMDAS

⇒ 4 + 0

Add the two terms in the expression as PEMDAS

⇒ 4

⇒ 4 ≠ 48

C) 4 + 5 × 3²(-9 ÷ 3²)

First, simplify the expression in the parenthesis as PEMDAS

⇒ 4 + 5 × 3²(-9 ÷ 3²)

⇒ 4 + 5 × 3²(-9 ÷ 9)

⇒ 4 + 5 × 3²(-1)

*3²(-1) can also be written as 3² × -1*

⇒ 4 + 5 × 3² × -1

Simplify the exponent as PEMDAS

⇒ 4 + 5 × 9 × -1

Multiply the last three terms as PEMDAS

⇒ 4 + 5 × 9 × -1

⇒ 4 + (-45)

Add/Subtract the last two terms as PEMDAS

⇒ 4 - 45

⇒ -41

D) 4 + 5 × 3² - 9 ÷ 3²

Since there are no parenthesis in the expression, we can start simplifying this expression by simplifying the exponents.

⇒ 4 + 5 × 3² - 9 ÷ 3²

⇒ 4 + 5 × 9 - 9 ÷ 9

⇒ 4 + 5 × 9 - 9 ÷ 9

Multiply the second and the third terms as PEMDAS

⇒ 4 + 45 - 9 ÷ 9

Divide the last two terms as PEMDAS

⇒ 4 + 45 - 1

Add/Subtract the terms as PEMDAS

⇒ 4 + 44

⇒ 48

⇒ 48 = 48 ✔✔

In conclusion, we can say that option D is correct because the expression of Option D has a value of 48.