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#### 1-8) Angela has a rectangular piece of paper and cuts a rectangle out of a corner as shown at right

###### Math

1-8) Angela has a rectangular piece of paper and cuts a rectangle out of a corner as shown at right. What are the area and perimeter of the resulting shape?

6 cm

7 cm

16 cm

9 cm

21 cm

15 cm

1-16) Multiple Choice: Read the Math Notes box in this lesson and then examine the diagram at right. Which angle below is another name for ÐABC?

a. ÐABE

b. ÐGBD

c. ÐFBG

d. ÐEBC

c. none of these

1-17) If no sides of a triangle have the same Length, the triangle is called scalene (pronounced SKAY leen). And, as you might remember, if the triangle has at least two sides that are the same length, the triangle is called isosceles. Use the markings or description in each diagram below to decide if DABC is isosceles or scalene. Assume the diagrams are not drawn to scale.

1. ÐABC is a Isosceles triangle
2. ÐABC
3. ABDC is a square

1-18) Finding and using a pattern is an important problem-solving skill necessary for your study of mathematics. The patterns in Diamond Problems are used later in the course to solve other types of algebraic problems.

Look for a pattern in the first three diamonds below. For the fourth diamond, explain how to find the missing numbers (?) if you know the two numbers (#).

 10 2 5 7
 6 3 2 5

 4 -4 -1 -5

 ? # # ?

Copy the Diamond Problems below onto your paper, then use the pattern you discovered to complete each one.

a.

 5 3

b.

 -1 -2

c.

 8 6

d.

 1/2 8

e.

 12 -7

1-20) Copy the Venn diagram below on your paper. Then show where each person described below should be represented in the diagram. If a portion of the Venn diagram remains empty, describe the qualities a person would need to belong there.

#1: Studies a lot for class            #2: Has long hair

a. Carol: “I rarely study and enjoy braiding my long hair.”

b. Bob: “I never do homework and have a crew cut.”

c. Pedro: “I love joining after school study teams to prepare for tests, and I like being bald!”

d. Toby: “I really love playing in my heavy metal band, but now that I am enrolled at MIT, I have to study ail the time and don't have much time to play. My mom really wishes that I would cut my long, messy hair.”

1-26) Solve the equations below for x, if possible. Be sure to check your solution.

a. 3x – 1 /4 = -5/11

b. 6 – 5(2x – 3) = 4x + 7

c. 3x/4 + 2 = 4x – 1

1-38) Consider the equation y = ½ x — 4. 1-38 HW eTool (Desmos).

a. Without graphing, where is the x-intercept of y = ½ x — 4.

b. On graph paper, make a table and graph y = ½ x —4.

c. Using your graph from part (b), how can you find the x-intercept of y = ½ x — 4? How do you find it in the table? Explain.