To fill in the blanks, we first need to analyze the given expressions.
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For the expression \( x^2 \): \[ x^2 = (x)(x) \] Therefore, the blanks would be filled with \( x \).
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For the expression \( 3x = ______ 9(x^2 - 2x + 3) \): Here, \( 3x = 9(x^2 - 2x + 3) \) can be simplified: \[ 3x = 9x^2 - 18x + 27 \] Factoring out \( 9 \) gives us: \[ 3x = 9(\frac{x}{3}) + 9(2) = 3 + 3 + 5 \] Which does not directly apply here, we seem to need a constant for the comparison. We will need to replace the "_______" with "1" or "3x/9." Thus matching assumptions leads to confusion; we will revisit calculations regarding expressions involving basic simplifications.
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For the equation \( 9x = () () + 5 \): This has several configurations depending on factoring behaviors akin to completing squares or distributing basic multiplication, hinting towards parameters allowing factorizations.
Since none of these require direct computation other than confirming layers of representation like quadratic forms, we utilize contained relationships between terms without further details.
Based on standard conclusions:
- For \( x^2 \) foreshadowing \( (x)(x) \).
- The value leading to \( 9x \).
We can surmise:
- \( \text{(first blank)} = 1 \)
- \( \text{(second blank)} = x^2 - 2x + 3 \) aligns structurally localized in behaviors suggesting composite coefficients or another \( \text{9x} \rightarrow (3x)(3) \).
Thus summarizing final completions in proportion to provided values:
Answers
- \( x^2 = (x)(x) \)
- \( 3x = 1 \cdot 9(x^2 - 2x + 3) \)
- \( 9x = (3)(3x) + 5 \)
An arrangement of final choices then rendering clarity leads us to: A) 1 across \( 3x \) context, followed by an addition of squared specifics aligns returned as 9 equations rooting from relations involving square terms relatable to each defined key structure.
In order of results the summaries from fill across each quote appear without further adjustments or nodes leading to peripheral confusion.
1 answer