Rational inequalities Quiz 1

Question 1

Solve the given equation for the possible range of solutions: $$\dfrac{{{{	ext{z}}^2} + 5{	ext{z}} - 6}}{{z - 3}} \geqslant 0$$

Accepted Answer

$$\left[ { - 6,1} \right] \cup \left( {3,\infty } \right)$$

Answer

$$R$$

Answer

$$\left[ {1,\infty } \right]$$

Answer

$$\emptyset $$

Question 2

Joseph enters a race where he has to cycle and run. He cycles a distance of $$20km$$, and then runs for $$15km$$. His average running speed is half of his average cycling speed. Joseph completes the race in less than $$2\dfrac{1}{2}$$ hours, what can we say about his average speeds?

Accepted Answer

10,20

Answer

21,21

Answer

20,60

Answer

60,30

Question 3

The Yellow Taxi Cab Co. charges a $${{\$$ 3.75}}$$ flat rate and $$ \$$ 0.75$$ for each additional mile. Emma has no more than $$\$$ 14$$ to spend on a ride. How many miles can Emma ride without exceeding her spending limit?

Accepted Answer

13

Answer

20

Answer

15

Answer

21

Question 4

The sum of three consecutive odd integers is no less than $${	ext{75}}$$. What is the middle integer?

Accepted Answer

25

Answer

31

Answer

37

Answer

41

Question 5

Lily has $$\$$ 500$$ to invest. If he invests $$\$$ 300$$ at $$9\% $$, at what rate must he invest the remaining $$\$$ 200$$ so that the total yearly interest from the two investments exceeds $$\$$ 47$$?

Accepted Answer

10%

Answer

0.1%

Answer

20%

Answer

50%