Splash Screen. Lesson Menu Five-Minute Check (over Lesson 6–6) CCSS Then/Now New Vocabulary Key...
-
Upload
gervais-french -
Category
Documents
-
view
214 -
download
0
Transcript of Splash Screen. Lesson Menu Five-Minute Check (over Lesson 6–6) CCSS Then/Now New Vocabulary Key...
Five-Minute Check (over Lesson 6–6)
CCSS
Then/Now
New Vocabulary
Key Concept: Solving Radical Equations
Example 1: Solve Radical Equations
Example 2: Solve a Cube Root Equation
Example 3: Standardized Test Example: Solve a Radical Equation
Key Concept: Solving Radical Inequalities
Example 4: Solve a Radical Inequality
Over Lesson 6–6
A.
B.
C.
D.
Over Lesson 6–6
A. 12
B. 8
C. 4
D. 2
Over Lesson 6–6
A.
B.
C.
D.
Over Lesson 6–6
A. 2w
2
B. 2w
C. w
2
D.
Over Lesson 6–6
A.
B.
C. 5
D. 10
Over Lesson 6–6
A. 82.6 kcal/day
B. 156.8 kcal/day
C. 826.5 kcal/day
D. 1568.1 kcal/day
The equation gives the approximate energy output y in kilocalories per day (kcal/day) for a reptile with a body mass m kilograms. The average mass of an alligator is 360 kilograms. Find the energy output of a reptile this size. Round your answer to the nearest tenth.
Content Standards
A.SSE.2 Use the structure of an expression to identify ways to rewrite it.
Mathematical Practices
4 Model with mathematics.
You solved polynomial equations.
• Solve equations containing radicals.
• Solve inequalities containing radicals.
• radical equation
• extraneous solution
• radical inequality
Solve Radical Equations
A. Solve .
Add 2 to each side.
Find the squares.
Square each side to eliminate the radical.
Add 1 to each side to isolate the radical.
Original equation
Solve Radical Equations
Original equation
Answer: The solution checks. The solution is 38.
Check
Simplify.
Replace y with 38.?
Solve Radical Equations
B. Solve .
Divide each side by –4.
Isolate the radical.
Find the squares.
Square each side.
Original equation
Solve Radical Equations
Square each side.
Evaluate the squares.
Replace x with 16.
Simplify.
Original equationCheck
Evaluate the square roots.
Answer: The solution does not check, so there is no real solution.
A. 19
B. 61
C. 67
D. no real solution
A. Solve .
B. Solve .
A. 2
B. 4
C. 9
D. no real solution
Solve a Cube Root Equation
Original equation
Subtract 5 from each side.
Cube each side.
Evaluate the cubes.
In order to remove the power, or cube root, you must
first isolate it and then raise each side of the equation to
the third power.
Solve a Cube Root Equation
Answer: The solution is –42.
Subtract 1 from each side.
Divide each side by 3.
Original equation
Replace y with –42.
Simplify.
The cube root of –125 is –5.Add.
Check
A. –14
B. 4
C. 13
D. 26
A m = –2
B m = 0
C m = 12
D m = 14
Solve a Radical Equation
Original equation
Add 4 to each side.
Divide each side by 7.
Raise each side to the sixth power.
Evaluate each side.
Subtract 4 from each side.
Answer: The answer is C.
Solve a Radical Equation
A. 221
B. 242
C. 266
D. 288
Solve a Radical Inequality
Since the radicand of a square root must be greater than or equal to zero, first solve 3x – 6 0 to identify the values of x for which the left side of the inequality is defined.
3x – 6 0
3x 6
x 2
Solve a Radical Inequality
Answer: The solution is 2 x 5.
Original inequality
Isolate the radical.
Eliminate the radical.
Add 6 to each side.
Divide each side by 3.
Solve a Radical Inequality
Check
Only the values in the interval 2 x 5 satisfy the inequality.
Test some x-values to confirm the solution. Let
Use three test values: one less than 2,
one between 2 and 5, and one greater than 5.
A.
B.
C.
D.