Chapter 9

Which quadratic equation is written in standard form? A. \(8 x+5 x^{2}-9=0\) B. \(5 x^{2}+8 x=9\) C. \(5 x^{2}+8 x-9=0\) D. \(9-8 x-5 x^{2}=0\)

Simplify the radical expression. $$ \sqrt{40} $$

Write the radical expression in simplest form. $$ \sqrt{\frac{48}{81}} $$

Evaluate the radical expression when a = 2 and b = 4. $$ \sqrt{b^{2}-8 a} $$

Consider the equation \(3 x^{2}-44=x^{2}+84\) Which statement is correct? A. The equation has exactly one solution. B. The equation has two solutions. C. The equation has no real solution. D. The number of solutions cannot be determined.

Simplify the radical expression. $$ \sqrt{24} $$

Write the radical expression in simplest form. $$ \sqrt{\frac{21}{35}} $$

Evaluate the expression when \(x=-2\) (Lessons \(1.3,2.3,2.5)\). $$ 2 x^{3}+2 x+2 $$

Simplify the radical expression. $$ \sqrt{60} $$

Evaluate the expression when \(x=-2\) (Lessons \(1.3,2.3,2.5)\). $$ 4 x^{2}+3 x+5 $$

Write the radical expression in simplest form. $$ -4 \sqrt{\frac{1}{10}} $$

Evaluate the radical expression when a = 2 and b = 4. $$ \frac{\sqrt{b^{2}+42 a}}{a} $$

Simplify the radical expression. $$ \sqrt{200} $$

A falcon dives toward a pigeon on the ground. When the falcon is at a height of 100 feet, the pigeon sees the falcon, which is diving at 220 feet per second. Estimate the time the pigeon has to escape. Round your solution to the nearest tenth of a second.

Evaluate the expression when \(x=-2\) (Lessons \(1.3,2.3,2.5)\). $$ 3 x^{2}+4 x+8 $$

Write the radical expression in simplest form. $$ 6 \sqrt{\frac{5}{9}} $$

Evaluate the radical expression when a = 2 and b = 4. $$ \frac{10+2 \sqrt{b}}{a} $$

Simplify the radical expression. $$ \frac{1}{2} \sqrt{80} $$

A hawk dives toward a snake. When the hawk is at a height of 200 feet, the snake sees the hawk, which is diving at 105 feet per second. Estimate the time the snake has to escape. Round your solution to the nearest tenth of a second.

Evaluate the expression when \(x=-2\) (Lessons \(1.3,2.3,2.5)\). $$ x^{2}+7 x+9 $$

Write the radical expression in simplest form. $$ 2 \sqrt{\frac{6}{18}} $$

Evaluate the radical expression when a = 2 and b = 4. $$ \frac{36-\sqrt{8 a}}{b} $$

Simplify the radical expression. $$ \frac{1}{3} \sqrt{27} $$

Use a vertical motion model to find how long it will take for the object to reach the ground. Round your solution to the nearest tenth. You drop your keys from a window 30 feet above ground to your friend below. Your friend does not catch them.

Find the slope and \(y\) -intercept of the graph of the equation. (Lesson 4.7) $$ y=5 x+6 $$

Use the following information. A tsunami is a destructive, fast-moving ocean wave that is caused by an undersea earthquake, landslide, or volcano. Scientists can predict arrival times of tsunamis by using water depth to calculate the speed of a tsunami. A model for the speed \(s\) (in meters per second) at which a tsunami moves is \(s=\sqrt{g d}\) where \(d\) is the depth (in meters) and \(g\) is 9.8 meters per second per second. Find the speed of a tsunami in a region of the ocean that is 1000 meters deep. Write your solution in simplest form.

Use a calculator to evaluate the expression. Round the results to the nearest hundredth. $$ 8 \pm \sqrt{5} $$

Simplify the radical expression. $$ \frac{1}{8} \sqrt{32} $$

Use a vertical motion model to find how long it will take for the object to reach the ground. Round your solution to the nearest tenth. An acorn falls 45 feet from the top of a tree.

Find the slope and \(y\) -intercept of the graph of the equation. (Lesson 4.7) $$ y=-4 x+5 $$

Use the following information. A tsunami is a destructive, fast-moving ocean wave that is caused by an undersea earthquake, landslide, or volcano. Scientists can predict arrival times of tsunamis by using water depth to calculate the speed of a tsunami. A model for the speed \(s\) (in meters per second) at which a tsunami moves is \(s=\sqrt{g d}\) where \(d\) is the depth (in meters) and \(g\) is 9.8 meters per second per second. Find the speed of a tsunami in a region of the ocean that is 4000 meters deep. Write your solution in simplest form.

Use a calculator to evaluate the expression. Round the results to the nearest hundredth. $$ 2 \pm 5 \sqrt{3} $$

Simplify the radical expression. $$ \frac{2}{3} \sqrt{300} $$

Use a vertical motion model to find how long it will take for the object to reach the ground. Round your solution to the nearest tenth. A lacrosse player throws a ball upward from her playing stick from an initial height of 7 feet, with an initial velocity of 90 feet per second.

Find the slope and \(y\) -intercept of the graph of the equation. (Lesson 4.7) $$ y-8 x=2 $$

Use the following information. A tsunami is a destructive, fast-moving ocean wave that is caused by an undersea earthquake, landslide, or volcano. Scientists can predict arrival times of tsunamis by using water depth to calculate the speed of a tsunami. A model for the speed \(s\) (in meters per second) at which a tsunami moves is \(s=\sqrt{g d}\) where \(d\) is the depth (in meters) and \(g\) is 9.8 meters per second per second. CRITICAL THINKING Is the speed of a tsunami in water that is 4000 meters deep four times the speed of a tsunami in water that is 1000 meters? Explain why or why not.

Use a calculator to evaluate the expression. Round the results to the nearest hundredth. $$ -6 \pm 4 \sqrt{2} $$

Complete the statement using \(<,>,\) or \(=.\) (Skills Review pp. \(763,770,771\) ) $$\frac{8}{7} ? 1 \frac{1}{7}$$

Use a vertical motion model to find how long it will take for the object to reach the ground. Round your solution to the nearest tenth. You throw a ball downward with an initial velocity of -10 feet per second out of a window to a friend 20 feet below. Your friend does not catch the ball.

Find the slope and \(y\) -intercept of the graph of the equation. (Lesson 4.7) $$ 2 x+3 y=6 $$

Use a calculator to evaluate the expression. Round the results to the nearest hundredth. $$ \frac{1 \pm 6 \sqrt{8}}{6} $$

Complete the statement using \(<,>,\) or \(=.\) (Skills Review pp. \(763,770,771\) ) $$\frac{8}{3} ? 2 \frac{1}{3}$$

A batter hits a pitched baseball when it is 3 feet off the ground. After it is hit, the height h (in feet) of the ball is modeled by \(h=-16 t^{2}+80 t+3\) where t is the time (in seconds). How long will it take for the ball to hit the ground? Round to the nearest hundredth.

Solve the inequality. Then graph the solution. \((\text {Lesson } 6.1)\) $$ -9 \leq x-7 $$

Use a calculator to evaluate the expression. Round the results to the nearest hundredth. $$ \frac{7 \pm 3 \sqrt{2}}{-1} $$

Complete the statement using \(<,>,\) or \(=.\) (Skills Review pp. \(763,770,771\) ) $$\frac{17}{5} ? 3 \frac{4}{5}$$

An astronaut standing on the moon’s surface throws a rock upward with an initial velocity of 50 feet per second. The height of the rock can be modeled by \(m=-2.7 t^{2}+50 t+6,\) where m is the height of the rock (in feet) and t is the time (in seconds). If the astronaut throws the same rock upward with the same initial velocity on Earth, the height of the rock is modeled by \(e=-16 t^{2}+50 t+6.\) Would the rock hit the ground in less time on the moon or on Earth? Explain your answer.

Solve the inequality. Then graph the solution. \((\text {Lesson } 6.1)\) $$ -15>x-8 $$

Use a calculator to evaluate the expression. Round the results to the nearest hundredth. $$ \frac{4 \pm 7 \sqrt{3}}{2} $$

Find the length of a side \(s\) of a square that has the same area as a rectangle that is 12 centimeters wide and 33 centimeters long. Write your solution in simplest form.