SAT Question 5355c0ef: Equivalent Expressions answer and explanation with Desmos solution

09$.I{t}^{\prime }sgiventhattheexpression＄0.36x^2+0.63x+1.17$ can be rewritten as $a\left(4x^2+7x+13\right)$. Applying the distributive property to the expression $a\left(4x^2+7x+13\right)$ yields $4a{x}^2+7ax+13a$. Therefore, ＄0.36 x^{2} + 0.63 x + 1.17$canberewrittenas＄4a{x}^2+7ax+13a$. It follows that in the expressions ＄0.36 x^{2} + 0.63 x + 1.17$and$4 a x^{2} + 7 a x + 13 a$,thecoefficientsof$x^{2}$areequivalent,thecoefficientsof$x$areequivalent,andtheconstanttermsareequivalent.Therefore,＄0.36=4a$, $0.63=7a$, and ＄1.17 = 13 a$.Solvinganyoftheseequationsfor$a$yieldsthevalueof$a$.Dividingbothsidesoftheequation＄0.36=4a$ by $4$ yields $0.09=a$. Therefore, the value of $a$ is $0.09$. Note that 9/100, .09, .090, and 0.09 are examples of ways to enter a correct answer.