Epciucno
1. match each expression in the left column to its equivalent expre
column. use the table in the right to write the letters that corre
the numbers.
off column to its equivalent expression in the right
1. 7(12)
2. 3(15)
3. 3a +9
a. 5(1 + 3a)
b. 3(a + 3)
c. 3(x + y + 2)
4. 9a + 3
d. 7(8 + 4)
5. 5 + 15a
e. 3(x + 2y + 3x)
6. 10 + 5a
f. 5(2 + a)
7. 3x + 6y + 9z
g. 3(3a + 1)
8. 3x + 3y + 3z
h. (2 + 1)(15)

1 ⇒ D

2 ⇒ H

3 ⇒ B

4 ⇒ G

5 ⇒ A

6 ⇒ F

7 ⇒ E

8 ⇒ C

Step-by-step explanation:

* Lets explain how to solve the problem

- The left column has expressions and the right column has the

  equivalent expressions

- We must find the equivalent letter for each number

1.

# 7(12)

∵ 12 can be a sum of two numbers

∴ The equivalent expression to 7(12) is 7(8 + 4)

∴ 1 ⇒ D

2.

# 3(15)

∵ 3 can be a sum of two numbers

∴ The equivalent expression to 3(15) is (2 + 1)(15)

∴ 2 ⇒ H

3.

# 3a + 9

∵ 3 and 9 have a common factor 3

∵ 3a + 9 ⇒ divide them by 3

∵ 3a ÷ 3 = a and 9 ÷ 3 = 3

∴ 3a + 9 = 3(a + 3)

∴ The equivalent expression to 3a + 9 is 3(a + 3)

∴ 3 ⇒ B

4.

# 9a + 3

∵ 9 and 3 have a common factor 3

∵ 9a + 3 ⇒ divide them by 3

∵ 9a ÷ 3 = 3a and 3 ÷ 3 = 1

∴ 9a + 3 = 3(3a + 1)

∴ The equivalent expression to 9a + 3 is 3(3a + 1)

∴ 4 ⇒ G

5.

# 5 + 15a

∵ 5 and 15 have a common factor 5

∵ 5 + 15a ⇒ divide them by 5

∵ 5 ÷ 5 = 1 and 15a ÷ 5 = 3a

∴ 5 + 15a = 5(1 + 3a)

∴ The equivalent expression to 5 + 15a is 5(1 + 3a)

∴ 5 ⇒ A

6.

# 10 + 5a

∵ 10 and 5 have a common factor 5

∵ 10 + 5a ⇒ divide them by 5

∵ 10 ÷ 5 = 2 and 5a ÷ 5 = a

∴ 10 + 5a = 5(2 + aa)

∴ The equivalent expression to 10 + 5a is 5(2 + a)

∴ 6 ⇒ F

7.

# 3x + 6y + 9z

∵ The coefficient of x , y , z have a common factor 3

∵ 3x ÷ 3 = x

∵ 6y ÷ 3 = 2y

∵ 9z ÷ 3 = 3z

∴ 3x + 6y + 9z = 3(x + 2y + 3z)

∴ The equivalent expression to 3x + 6y + 9z is 3(x + 2y + 3z)

∴ 7 ⇒ E

8.

# 3x + 3y + 3z

∵ The coefficient of x , y , z have a common factor 3

∵ 3x ÷ 3 = x

∵ 3y ÷ 3 = y

∵ 3z ÷ 3 = z

∴ 3x + 3y + 3z = 3(x + y + z)

∴ The equivalent expression to 3x + 3y + 3z is 3(x + y + z)

∴ 8 ⇒ C

1 - D  

2 - H

3 - B

4 - G

5 - A

6 - F

7 - E

8 - C

Step-by-step explanation:

Step-by-step explanation:

From the picture attached,

Area of ΔECD =    

                       =

From ΔEFD,

sin(32°) =

sin(32°) =

EF = 14 × sin(32°)

    = 7.42 cm

By cosine rule,

EC² = DE² + CD² - 2(DE)(CD)cos(32°)

EC² = 14² + 27² - 2(14)(27)cos(32°)

EC² = 196 + 729 - 641.12

EC² = 283.88

EC = 16.85 cm

Area of ΔECD = Area of ΔAEB =

                                                   = 100.17

Area of ΔECD + Area of ΔAEB = 2(100.17)

                                                   = 200.34 cm²

Area of sector BEC =

Here, θ = central angle of the sector

Area of sector BEC =

                                =

                                = 260.16 cm²

Area of the logo = Area of triangles AEB + Area of triangle ECD + Area of sector BEC

= 200.34 + 260.16

= 460.50

≈ 460 cm²