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Ipatiy [6.2K]
3 years ago
6

Latrell is packing boxes that can contain two types of items. Board games weigh 3 pounds and remote controlled cars weigh 1.5 po

unds. The box can hold no more than 25 pounds.
Let x represent the number of board games. Let y represent the number of remote controlled cars.


Enter an inequality that represents the situation.
Mathematics
2 answers:
iogann1982 [59]3 years ago
5 0
3x + 1.5 y < 25
hope this helps!
enot [183]3 years ago
4 0
3x+1.5y≤25 X represents board games and each board game weighs 3 lbs (3x). Y represents remote controlled cars which each weigh 1.5 lbs (1.5y). The inequality sign (less than or equal to, ≤) is used because in total the amount of board games and remote controlled cars CANNOT exceed 25 lbs. 
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Option C

When (2x - 3)^2 is subtracted from 5x^2 then the result is x^2 + 12x - 9

<h3><u>Solution:</u></h3>

Given that (2x - 3)^2 is subtracted from 5x^2

We have to find the result

Subtraction is a mathematical operation that tells us the difference between two numbers.

When "a" is subtracted from "b", we write in mathematical expression as "b - a"

So (2x - 3)^2 is subtracted from 5x^2 is written mathematically as:

\rightarrow 5x^2 - (2x - 3)^2

<em><u>Expanding the above expression using algebraic identity:</u></em>

(a-b)^2 = a^2 - 2ab + b^2

\rightarrow 5x^2 - ((2x)^2 -2(2x)(3) + (3)^2)\\\\\rightarrow 5x^2 - (4x^2 - 12x + 9)

Multiplying the nnegative sign with terms inside bracket

<em><u>There are two simple rules to remember: </u></em>

  • When you multiply a negative number by a positive number then the product is always negative.
  • When you multiply two negative numbers or two positive numbers then the product is always positive.

\rightarrow 5x^2 - (4x^2 - 12x + 9)\\\\\rightarrow 5x^2 - 4x^2 + 12x -9\\\\\rightarrow x^2 + 12x - 9

Hence the result is: x^2 + 12x - 9

3 0
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