Mini Exam 23 — Timed Mini Exams

Questions in this quiz (9)

1. In right triangle $$DEF$$, angle $$E$$ is the right angle. If $$\tan(D)=\frac{5}{12}$$ and the length of side $$DE$$ is $$60$$, what is the length of side $$EF$$?

   • $$20$$
   • $$25$$
   • $$30$$
   • $$50$$

2. In the $$xy$$-plane, line $$M$$ is perpendicular to the line represented by the equation $$y=-4x+7$$. If line $$M$$ passes through the point $$(2,5)$$, which of the following is an equation of line $$M$$?

   • $$y=\frac{1}{4}x+\frac{9}{2}$$
   • $$y=-4x+13$$
   • $$y=\frac{1}{4}x+5$$
   • $$y=-\frac{1}{4}x+\frac{11}{2}$$

3. A workshop produces two types of custom tables: Type X and Type Y. The cost to produce a single Type Y table is a fixed amount. The cost to produce a single Type Y table is $$25\%$$ higher than the cost to produce a single Type X table. Each production day also has a fixed setup cost of $$800$$ dollars. On one day, the workshop produced $$160$$ tables, and the number of Type X tables produced was $$3$$ times the number of Type Y tables produced. The total production cost for the day, including setup, was $$11200$$ dollars. What is the production cost, in dollars, of a single Type X table?

   • $$40$$
   • $$\frac{91}{2}$$
   • $$50$$
   • $$\frac{1040}{17}$$

4. For $$x\ne-4$$, $$x\ne-3$$, $$x\ne3$$, consider the expression: $$\frac{x^2-9}{x^2+7x+12}\div\frac{x-3}{x+4}$$ Which of the following is equivalent to the given expression?

   • $$1$$
   • $$\frac{x+3}{x-3}$$
   • $$\frac{x-3}{x+4}$$
   • $$\frac{(x+3)^2}{(x+4)^2}$$

5. $$y=\sqrt{x+4}$$ $$y=x-2$$ How many distinct real solutions $$(x,y)$$ does the given system of equations have?

   • $$0$$
   • $$1$$
   • $$2$$
   • Infinitely many

6. In $$\triangle XYZ$$, $$XY=XZ$$. The measure of $$\angle YXZ$$ is $$100^\circ$$. Point $$W$$ is on $$YZ$$ such that $$YW=XY$$. What is the measure of $$\angle XWY$$?

   • $$40^\circ$$
   • $$50^\circ$$
   • $$70^\circ$$
   • $$110^\circ$$

7. A cylindrical tank with an internal radius of $$5$$ inches contains water. When a solid metal sphere is completely submerged in the tank, the water level rises by $$4$$ inches. What is the radius of the sphere, in inches?

   • $$\sqrt[3]{75}$$
   • $$5$$
   • $$2\sqrt[3]{6}$$
   • $$\sqrt[3]{150}$$

8. In a circle with center $$P$$, chord $$CD$$ has a length of $$16$$ units. The radius of the circle is $$10$$ units. What is the shortest distance, in units, from center $$P$$ to chord $$CD$$?

   • $$4$$
   • $$6$$
   • $$8$$
   • $$10$$

9. A radioactive isotope decays such that the amount remaining, in grams, after $$t$$ days is given by the function $$B(t)=120\left(\frac{1}{2}\right)^{t/20}$$. What is the half-life of the isotope, in days?

   • $$10$$
   • $$20$$
   • $$60$$
   • $$120$$