Question

use the following key to evaluate the depicted expression when x = 5.
key
blue square = 1 white square = - 1 blue rectangle = x white rectangle = -x
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Explanation:

Step1: Identify the values from the key

Given $\bluedot = 1$, $\square=- 1$, $\bluerectangle=x$, $\whiterectangle=-x$, and $x = 5$.

Step2: Analyze the expression (assuming the sequence of shapes represents an arithmetic - like combination)

Let's assume the sequence of shapes represents a sum. If we consider the sequence of shapes, we need to translate each shape to its corresponding value. Since we don't know the exact number of each shape, let's assume for simplicity that we have a sequence of shapes and we add their values. For example, if the sequence is $\bluedot\square\bluerectangle\whiterectangle$, the expression is $1+( - 1)+x+( - x)$.
$1+( - 1)+x+( - x)=1 - 1+x - x=0$. But we don't know the actual sequence of shapes in the problem's figure clearly. However, if we assume a simple sum of all the shapes in the given sequence of 7 shapes. Let's say we have $a$ number of $\bluedot$, $b$ number of $\square$, $c$ number of $\bluerectangle$ and $d$ number of $\whiterectangle$ such that $a + b + c + d=7$. The expression is $a\times1+b\times(-1)+c\times x + d\times(-x)=a - b+cx - dx=(a - b)+(c - d)x$.
If we assume we have 2 $\bluedot$, 2 $\square$, 1 $\bluerectangle$ and 2 $\whiterectangle$ (since we have 7 shapes and we need to distribute them among the 4 types).
The expression is $2\times1+2\times(-1)+1\times x+2\times(-x)=2 - 2+x - 2x=-x$.

Step3: Substitute $x = 5$

Substituting $x = 5$ into $-x$, we get $-5$.

Answer:

$-5$