91Ó°ÊÓ

Sketch the graph of the function. $$y=3 \sqrt{x+1}$$

Choose a method to solve the quadratic equation. What method did you use? Explain your choice. $$x^{2}+2 x-14=0$$

Find the missing length of the right triangle if a and b are the lengths of the legs and c is the length of the hypotenuse. $$a=14, c=21$$

A student proposes the following conjecture. The sum of the first n odd integers is \(n^{2} .\) She gives four examples: \(1=1^{2}\) \(1+3=4=2^{2}, 1+3+5=9=3^{2},\) and \(1+3+5+7=16=4^{2} .\) Do the examples prove her conjecture? Explain. Do you think the conjecture is true?

Solve the equation. Check for extraneous solutions. $$\sqrt{x}-10=0$$

For a fire hose with a nozzle that has a diameter of 2 inches, the flow rate \(f\) (in gallons per minute) can be modeled by \(f=120 \sqrt{p}\) where \(p\) is the nozzle pressure in pounds per square inch. Sketch a graph of the model.

Simplify the expression. $$5 \sqrt{7}+2 \sqrt{7}$$

Find the distance between the two points. Round the result to the nearest hundredth if necessary. 18\. $$(-3,1),(2,6)$$

For a fire hose with a nozzle that has a diameter of 2 inches, the flow rate \(f\) (in gallons per minute) can be modeled by \(f=120 \sqrt{p}\) where \(p\) is the nozzle pressure in pounds per square inch. If the flow rate is 1200 gallons per minute, what is the nozzle pressure?

Find a counterexample to show that the statement is not true. If \(a\) and \(b\) are real numbers, then \((a+b)^{2}=a^{2}+b^{2}\)