Algebra 2 questions

photos of questions attached

Part A- Adding It All Up (possible 35 points)
Activity 1: Study the polygons below. You can cut each polygon into non-overlapping triangles by
connecting one vertex with each of the other nonadjacent vertices. In Geometry, this method is
called Triangulation.
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1. a. For each polygon, fill in the table as you work through each part of the activity. (9 pts)
Name of Polygon
Triangle
Quadrilateral
Pentagon
Hexagon
Heptagon
Octagon
Nonagon
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5
6
3
7
8
9
Number of Sides
1
2
3
Number of Triangles
4
1080
Sum of Interior Angles
180 360
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Activity 2: The diagrams show arrangements of tables and chairs. Each small table can seat 6
people. When you join tables, you lose space for some chairs. So, an arrangement of two tables has
10 chairs rather than 12 chairs.
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# of tables:
1
2
3
4
2. a. Make a table that lists the number of tables and the number of chairs in each arrangement
shown in the above diagram. (8 pts)
b. Find the number of chairs needed for arrangements of 5 tables and 6 tables. (2 pts)
MTHH 039
c. Write an expression for the number of chairs needed for n tables. (Hint: How many new chairs
are needed for each new table?) (3 pts)
3. You can arrange the tables and chairs differently. One possible pattern is shown below. Write an
expression for the number of chairs needed to make on large table out of k tables in this way. (3
pts)
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Part B – Guided Problem Solving (possible 20 points)
Geometry The sum of the lengths of any two sides of a triangle is greater than the length of the third
side. In AABC, BC = 4 and AC = 8 – AB. What can you conclude about AB? AABC has three sides,
so you can use the Triangle Inequality Theorem and write 3 conditions of the sides.
AC + BC > AB
1st Triangle Inequality condition
AB + BC> AC
2nd Triangle Inequality condition
AB + AC> BC
3rd Triangle Inequality condition
Given
BC= 4 and AC = 8 – AB
(8 – AB) + 4 > AB
Substitute 4 for BC and 8 – AB for AC in the 1st condition.
12 > 2AB
Solve and simplify.
12 > 2AB
Solve and simplify.
AB < 6 AB+ 4 > 8-AB
Substitute 4 for BC and 8 – AB for AC in the 2nd condition.
2AB >4
Solve and simplify.
AB > 2
AB + (8 – AB) >4
Substitute 4 for BC and 8 – AB for AC in the 3rd condition.
8>4
Simplify. True Statement.
2 AB
1st Triangle Inequality condition
AB + BC> AC
2nd Triangle Inequality condition
AB + AC> BC
3rd Triangle Inequality condition
Given
BC= 4 and AC = 8 – AB
(8 – AB) + 4 > AB
Substitute 4 for BC and 8 – AB for AC in the 1st condition.
12 > 2AB
Solve and simplify.
12 > 2AB
Solve and simplify.
AB < 6 AB+ 4 > 8-AB
Substitute 4 for BC and 8 – AB for AC in the 2nd condition.
2AB >4
Solve and simplify.
AB > 2
AB + (8 – AB) >4
Substitute 4 for BC and 8 – AB for AC in the 3rd condition.
8>4
Simplify. True Statement.
2