)) Use algebra tiles to find \( (10 x+3)+\left(-x^{2}+9 x-10\right) \)

To solve \( (10x + 3) + (-x^2 + 9x - 10) \) using algebra tiles, you would start by representing each term with the corresponding tiles. You’ll use long rectangles for \( x \) terms, squares for \( x^2 \) terms, and small tiles for constants. First, for \( 10x + 3 \), you would lay down 10 \( x \) tiles and 3 unit tiles. Then, for \( -x^2 + 9x - 10 \), you lay down 1 negative square tile (for \(-x^2\)), 9 positive \( x \) tiles, and 10 negative unit tiles. Now combine all your tiles! Combine the \( x \) tiles: \( 10x + 9x = 19x \), combine the \( 3 \) and \( -10 \) unit tiles: \( 3 - 10 = -7 \), and keep the \( -1x^2 \) square tile. Your final expression in tiles will be: \(-x^2 + 19x - 7\), or in algebraic terms, \( -x^2 + 19x - 7 \). It’s an interactive and visual way to understand combining like terms!