Question

algebra 1 eoc assessment sample questions

1. charlie needs to simplify the expression below before he substitutes values for x and y.

\\(\frac{x^{18}y^{12}+x^9y^8}{x^3y^4}\\)
if \\(x\
eq0\\) and \\(y\
eq0\\), which of the following is a simplified version of the expression above?
a \\(x^9y^5\\)
b \\(x^{24}y^{16}\\)
c \\(x^6y^3+x^3y^2\\)
d \\(x^{15}y^8+x^6y^4\\)

1. what is the slope of the line defined by the equation \\(8x + 2y = 5\\)?

Explanation:

(Question 4):

Step1: Split the fraction

$\frac{x^{18}y^{12} + x^9y^6}{x^3y^4} = \frac{x^{18}y^{12}}{x^3y^4} + \frac{x^9y^6}{x^3y^4}$

Step2: Apply exponent rules ($x^a/x^b=x^{a-b}$)

$\frac{x^{18}y^{12}}{x^3y^4} = x^{18-3}y^{12-4}=x^{15}y^8$
$\frac{x^9y^6}{x^3y^4} = x^{9-3}y^{6-4}=x^6y^2$

Step3: Combine the terms

$x^{15}y^8 + x^6y^2$

(Question 5):

Step1: Isolate $y$ (slope-intercept form)

$8x + 2y = 5 \implies 2y = -8x + 5$

Step2: Solve for $y$

$y = \frac{-8x + 5}{2} = -4x + \frac{5}{2}$

Step3: Identify slope (coefficient of $x$)

Slope = $-4$

Answer:

Question 4: D. $x^{15}y^{8} + x^{6}y^{4}$
Question 5: $-4$