Central school is hosting a “central has talent” show. They will award various prizes for the best 3 acts in the show. First pla

Response:

The factored expression is .

Detailed explanation:

Provided:

Our goal is to express the given equation in a factored form.

Factoring pertains to rewriting an expression so that the product of its factors yields the original expression

Let’s consider the expression .

We recognize the algebraic identity

Thus, we have .

Matching with the above identity, we assign x= a, and b = 11, leading to

.

Consequently, the factored expression is .

2x + 4

To represent 2x + 4, the following is required:

2 positive x-tiles corresponding to 2x.

4 positive unit tiles for the value of 4.

3x + (-1)

To illustrate 3x + (-1), you will need:

3 positive x-tiles to depict 3x.

1 negative unit tile to signify (-1).

Answer:

$110.

Step-by-step explanation:

Let x represent the cost of the item that Carmen bought from the department store.

Carmen possesses $30 in store bucks along with a 25% discount coupon for a local department store. Our goal is to determine the maximum cost for Carmen's purchase such that after applying her store bucks and discount, her total remains at or below $60 before sales tax.

Since the $30 in store bucks is deducted prior to applying the 25% discount, we need to find x such that x - 30 minus 25% of (x - 30) must be less than or equal to 60. This can be set up as an equation:

Thus, Carmen's purchases should total no more than $110 before sales tax.