Which expression is equivalent to the given polynomial expression?

Mathematics

1 answer:

ivolga24 [154]3 years ago

6 0

Answer:

C. -31m⁴n - 8m²

Step-by-step explanation:

Given:

(9mn - 19m⁴n) - (8m² + 12m⁴n + 9mn)

Required:

Determine an expression equivalent to it

Solution:

(9mn - 19m⁴n) - (8m² + 12m⁴n + 9mn)

Distribute the negative sign to open the parentheses

9mn - 19m⁴n - 8m² - 12m⁴n - 9mn

Combine like terms

9mn - 9mn - 19m⁴n - 12m⁴n - 8m²

-31m⁴n - 8m²

Therefore, -31m⁴n - 8m² is an equivalent expression of (9mn - 19m⁴n) - (8m² + 12m⁴n + 9mn)

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Brilliant_brown [7]

Answer:

1. 3,168 in³

2. $\frac{3}{4}$

Step-by-step explanation:

1. The total volume of the tank - as calculated by the formula for a rectangular prism - $V=LWH$ , where L is length, W is width, and H is height. 15 · 24 · 11 = 3,960 in³. Next, we divide 3,960 by five to get 792. If 792 in³ is the air at the top, we can then subtract that from 3,960 and get 3,168. So there are 3,168 in³ of water in the tank.

2. If we dump 3,168 in³ of water into a 12,672 in³ tank, then $\frac{3,168}{12,672}$ of the tank will be full. Simplified, that is $\frac{1}{4}$ . So that means $\frac{3}{4}$ of the tank will be empty.