Heart of Algebra: Linear Equations (2 variables) — Quiz 3

Questions in this quiz (10)

1. How many liters of a $$30\%$$ saline solution must be added to $$4$$ liters of a $$10\%$$ saline solution to obtain a $$20\%$$ saline solution?

   • 4

2. The table shows three values of $$x$$ and their corresponding values of $$y$$, where $$k$$ is a constant. What is the slope of the line that represents this relationship in the $$xy$$-plane?

   • $$-15$$
   • $$-\frac{15}{2}$$
   • $$\frac{15}{2}$$
   • $$15$$

3. A chemist mixes two liquids to obtain a solution with a total volume of $$72$$ milliliters. If $$18$$ milliliters of the solution is alcohol, how many milliliters is water?

   • 54

4. A company is calculating the total cost of materials for a project. The equation $$0.05(200x)+0.10(150y)+2400=5400$$ represents the total cost, where $$x$$ and $$y$$ are quantities of two materials. What is the best interpretation of $$2400$$ in this context?

   • $$\text{The cost of the first material}$$
   • $$\text{The cost of the second material}$$
   • $$\text{A fixed cost independent of }x\text{ and }y$$
   • $$\text{The total cost of both materials}$$

5. A total of $$420$$ sticks were used to construct squares and pentagons. The equation $$4x+5y=420$$ represents this situation, where $$x$$ is the number of squares and $$y$$ is the number of pentagons. What does the ordered pair $$(30,60)$$ represent?

   • $$30\text{ squares and }60\text{ pentagons}$$
   • $$30\text{ pentagons and }60\text{ squares}$$
   • $$30\text{ sticks and }60\text{ shapes}$$
   • $$30\text{ shapes and }60\text{ sticks}$$

6. The line with equation $$\frac{3}{4}x+\frac{1}{2}y=6$$ is graphed in the $$xy$$-plane. What is the $$x$$-coordinate of the $$x$$-intercept?

   • 8

7. A company sells custom notebooks. The price $$P$$, in dollars, is a linear function of the number of pages $$n$$, as shown in the table below. Which of the following could define the relationship between $$n$$ and $$P$$?

   • $$P=3n+1$$
   • $$P=3n+5$$
   • $$P=\frac{8}{3}n+1$$
   • $$P=\frac{9}{3}n+5$$

8. What is the slope of the graph of $$y=\frac{1}{5}(20x+10)-2x$$ in the $$xy$$-plane?

   • 2

9. Line $$m$$ in the $$xy$$-plane is perpendicular to the line with equation $$y=4$$. What is the slope of line $$m$$?

   • $$0$$
   • $$4$$
   • $$-\frac{1}{4}$$
   • $$\text{Undefined}$$

10. Figure $$C$$ and figure $$D$$ are both regular polygons. The sum of their perimeters is $$72$$ inches. The equation $$4x+8y=72$$ represents this situation, where $$x$$ is the number of sides of figure $$C$$ and $$y$$ is the number of sides of figure $$D$$. Which statement best interprets the $$8$$ in this context?

    • $$\text{Each side of figure }D\text{ has a length of }8\text{ inches}$$
    • $$\text{Figure }D\text{ has }8\text{ sides}$$
    • $$\text{Each side of figure }C\text{ has a length of }8\text{ inches}$$
    • $$\text{Figure }C\text{ has }8\text{ sides}$$