Answer :
Sure! Let's simplify and evaluate each expression step-by-step.
### Simplify the Expressions
1. (1) [tex]\(4 \cdot 9 + 1\)[/tex]:
[tex]\[
4 \cdot 9 = 36
\][/tex]
[tex]\[
36 + 1 = 37
\][/tex]
Answer: [tex]\(37\)[/tex]
2. (T) [tex]\(6 + 7 \cdot 10\)[/tex]:
[tex]\[
7 \cdot 10 = 70
\][/tex]
[tex]\[
6 + 70 = 76
\][/tex]
Answer: [tex]\(76\)[/tex]
3. (U) [tex]\(42 - 2 \cdot 7\)[/tex]:
[tex]\[
2 \cdot 7 = 14
\][/tex]
[tex]\[
42 - 14 = 28
\][/tex]
Answer: [tex]\(28\)[/tex]
4. (O) [tex]\(8 + 50 \div 2\)[/tex]:
[tex]\[
50 \div 2 = 25
\][/tex]
[tex]\[
8 + 25 = 33
\][/tex]
Answer: [tex]\(33\)[/tex]
5. (E) [tex]\((10)(3) - 4\)[/tex]:
[tex]\[
10 \cdot 3 = 30
\][/tex]
[tex]\[
30 - 4 = 26
\][/tex]
Answer: [tex]\(26\)[/tex]
6. (G) [tex]\(2 \cdot 8 + 3 \cdot 5\)[/tex]:
[tex]\[
2 \cdot 8 = 16
\][/tex]
[tex]\[
3 \cdot 5 = 15
\][/tex]
[tex]\[
16 + 15 = 31
\][/tex]
Answer: [tex]\(31\)[/tex]
7. (A) [tex]\(\frac{60}{3} - (2)(4)\)[/tex]:
[tex]\[
60 \div 3 = 20
\][/tex]
[tex]\[
2 \cdot 4 = 8
\][/tex]
[tex]\[
20 - 8 = 12
\][/tex]
Answer: [tex]\(12\)[/tex]
8. (T) [tex]\(5 \cdot 12 + \frac{32}{16}\)[/tex]:
[tex]\[
5 \cdot 12 = 60
\][/tex]
[tex]\[
32 \div 16 = 2
\][/tex]
[tex]\[
60 + 2 = 62
\][/tex]
Answer: [tex]\(62\)[/tex]
9. (Y) [tex]\(3 + 2 \cdot 5 \cdot 8\)[/tex]:
[tex]\[
2 \cdot 5 = 10
\][/tex]
[tex]\[
10 \cdot 8 = 80
\][/tex]
[tex]\[
3 + 80 = 83
\][/tex]
Answer: [tex]\(83\)[/tex]
10. (1) [tex]\((4)(6)(3) - 20 + 1\)[/tex]:
[tex]\[
4 \cdot 6 = 24
\][/tex]
[tex]\[
24 \cdot 3 = 72
\][/tex]
[tex]\[
72 - 20 = 52
\][/tex]
[tex]\[
52 + 1 = 53
\][/tex]
Answer: [tex]\(53\)[/tex]
11. (O) [tex]\(18 \div 2 \cdot 3\)[/tex]:
[tex]\[
18 \div 2 = 9
\][/tex]
[tex]\[
9 \cdot 3 = 27
\][/tex]
Answer: [tex]\(27\)[/tex]
12. (R) [tex]\(3 \cdot 3 + 4 \cdot 4 - 5 \cdot 5\)[/tex]:
[tex]\[
3 \cdot 3 = 9
\][/tex]
[tex]\[
4 \cdot 4 = 16
\][/tex]
[tex]\[
5 \cdot 5 = 25
\][/tex]
[tex]\[
9 + 16 = 25
\][/tex]
[tex]\[
25 - 25 = 0
\][/tex]
Answer: [tex]\(0\)[/tex]
### Evaluate Expressions with [tex]\( a = 2 \)[/tex], [tex]\( b = 3 \)[/tex], [tex]\( x = 5 \)[/tex], [tex]\( y = 8 \)[/tex], [tex]\( w = 20 \)[/tex]
1. (I) [tex]\(4x + 7\)[/tex]:
[tex]\[
4 \cdot 5 = 20
\][/tex]
[tex]\[
20 + 7 = 27
\][/tex]
Answer: [tex]\(27\)[/tex]
2. (C) [tex]\(1 + 6y\)[/tex]:
[tex]\[
6 \cdot 8 = 48
\][/tex]
[tex]\[
1 + 48 = 49
\][/tex]
Answer: [tex]\(49\)[/tex]
3. (H) [tex]\(9 - 2b\)[/tex]:
[tex]\[
2 \cdot 3 = 6
\][/tex]
[tex]\[
9 - 6 = 3
\][/tex]
Answer: [tex]\(3\)[/tex]
4. (O) [tex]\(8x + 3y\)[/tex]:
[tex]\[
8 \cdot 5 = 40
\][/tex]
[tex]\[
3 \cdot 8 = 24
\][/tex]
[tex]\[
40 + 24 = 64
\][/tex]
Answer: [tex]\(64\)[/tex]
5. (M) [tex]\(a + bw\)[/tex]:
[tex]\[
b \cdot w = 3 \cdot 20 = 60
\][/tex]
[tex]\[
2 + 60 = 62
\][/tex]
Answer: [tex]\(62\)[/tex]
6. (V) [tex]\(aw - by\)[/tex]:
[tex]\[
a \cdot w = 2 \cdot 20 = 40
\][/tex]
[tex]\[
b \cdot y = 3 \cdot 8 = 24
\][/tex]
[tex]\[
40 - 24 = 16
\][/tex]
Answer: [tex]\(16\)[/tex]
7. (P) [tex]\(b + \frac{w}{x}\)[/tex]:
[tex]\[
\frac{w}{x} = \frac{20}{5} = 4
\][/tex]
[tex]\[
3 + 4 = 7
\][/tex]
Answer: [tex]\(7\)[/tex]
8. (G) [tex]\(\frac{bw}{x} - a + 7\)[/tex]:
[tex]\[
bw = 3 \cdot 20 = 60
\][/tex]
[tex]\[
\frac{60}{5} = 12
\][/tex]
[tex]\[
12 - 2 + 7 = 17
\][/tex]
Answer: [tex]\(17\)[/tex]
9. (K) [tex]\(abxy - 5w\)[/tex]:
[tex]\[
abxy = 2 \cdot 3 \cdot 5 \cdot 8 = 240
\][/tex]
[tex]\[
5w = 5 \cdot 20 = 100
\][/tex]
[tex]\[
240 - 100 = 140
\][/tex]
Answer: [tex]\(140\)[/tex]
10. (H) [tex]\(36 - 4ab\)[/tex]:
[tex]\[
4ab = 4 \cdot 2 \cdot 3 = 24
\][/tex]
[tex]\[
36 - 24 = 12
\][/tex]
Answer: [tex]\(12\)[/tex]
11. (P) [tex]\(5 + 3x - \frac{w}{a}\)[/tex]:
[tex]\[
3x = 3 \cdot 5 = 15
\][/tex]
[tex]\[
\frac{w}{a} = \frac{20}{2} = 10
\][/tex]
[tex]\[
5 + 15 - 10 = 10
\][/tex]
Answer: [tex]\(10\)[/tex]
Now, let's match the answers found above to the given list and assign the corresponding letters to their boxes:
- (17) = T
- (2) = T
- (14) = U
- (18) = R
- (11) = E
- (5) = G
- (15) = A
- (9) = Y
- (12) = R
- (10) = 1
- (4) = I
- (16) = K
- (3) = P
### Simplify the Expressions
1. (1) [tex]\(4 \cdot 9 + 1\)[/tex]:
[tex]\[
4 \cdot 9 = 36
\][/tex]
[tex]\[
36 + 1 = 37
\][/tex]
Answer: [tex]\(37\)[/tex]
2. (T) [tex]\(6 + 7 \cdot 10\)[/tex]:
[tex]\[
7 \cdot 10 = 70
\][/tex]
[tex]\[
6 + 70 = 76
\][/tex]
Answer: [tex]\(76\)[/tex]
3. (U) [tex]\(42 - 2 \cdot 7\)[/tex]:
[tex]\[
2 \cdot 7 = 14
\][/tex]
[tex]\[
42 - 14 = 28
\][/tex]
Answer: [tex]\(28\)[/tex]
4. (O) [tex]\(8 + 50 \div 2\)[/tex]:
[tex]\[
50 \div 2 = 25
\][/tex]
[tex]\[
8 + 25 = 33
\][/tex]
Answer: [tex]\(33\)[/tex]
5. (E) [tex]\((10)(3) - 4\)[/tex]:
[tex]\[
10 \cdot 3 = 30
\][/tex]
[tex]\[
30 - 4 = 26
\][/tex]
Answer: [tex]\(26\)[/tex]
6. (G) [tex]\(2 \cdot 8 + 3 \cdot 5\)[/tex]:
[tex]\[
2 \cdot 8 = 16
\][/tex]
[tex]\[
3 \cdot 5 = 15
\][/tex]
[tex]\[
16 + 15 = 31
\][/tex]
Answer: [tex]\(31\)[/tex]
7. (A) [tex]\(\frac{60}{3} - (2)(4)\)[/tex]:
[tex]\[
60 \div 3 = 20
\][/tex]
[tex]\[
2 \cdot 4 = 8
\][/tex]
[tex]\[
20 - 8 = 12
\][/tex]
Answer: [tex]\(12\)[/tex]
8. (T) [tex]\(5 \cdot 12 + \frac{32}{16}\)[/tex]:
[tex]\[
5 \cdot 12 = 60
\][/tex]
[tex]\[
32 \div 16 = 2
\][/tex]
[tex]\[
60 + 2 = 62
\][/tex]
Answer: [tex]\(62\)[/tex]
9. (Y) [tex]\(3 + 2 \cdot 5 \cdot 8\)[/tex]:
[tex]\[
2 \cdot 5 = 10
\][/tex]
[tex]\[
10 \cdot 8 = 80
\][/tex]
[tex]\[
3 + 80 = 83
\][/tex]
Answer: [tex]\(83\)[/tex]
10. (1) [tex]\((4)(6)(3) - 20 + 1\)[/tex]:
[tex]\[
4 \cdot 6 = 24
\][/tex]
[tex]\[
24 \cdot 3 = 72
\][/tex]
[tex]\[
72 - 20 = 52
\][/tex]
[tex]\[
52 + 1 = 53
\][/tex]
Answer: [tex]\(53\)[/tex]
11. (O) [tex]\(18 \div 2 \cdot 3\)[/tex]:
[tex]\[
18 \div 2 = 9
\][/tex]
[tex]\[
9 \cdot 3 = 27
\][/tex]
Answer: [tex]\(27\)[/tex]
12. (R) [tex]\(3 \cdot 3 + 4 \cdot 4 - 5 \cdot 5\)[/tex]:
[tex]\[
3 \cdot 3 = 9
\][/tex]
[tex]\[
4 \cdot 4 = 16
\][/tex]
[tex]\[
5 \cdot 5 = 25
\][/tex]
[tex]\[
9 + 16 = 25
\][/tex]
[tex]\[
25 - 25 = 0
\][/tex]
Answer: [tex]\(0\)[/tex]
### Evaluate Expressions with [tex]\( a = 2 \)[/tex], [tex]\( b = 3 \)[/tex], [tex]\( x = 5 \)[/tex], [tex]\( y = 8 \)[/tex], [tex]\( w = 20 \)[/tex]
1. (I) [tex]\(4x + 7\)[/tex]:
[tex]\[
4 \cdot 5 = 20
\][/tex]
[tex]\[
20 + 7 = 27
\][/tex]
Answer: [tex]\(27\)[/tex]
2. (C) [tex]\(1 + 6y\)[/tex]:
[tex]\[
6 \cdot 8 = 48
\][/tex]
[tex]\[
1 + 48 = 49
\][/tex]
Answer: [tex]\(49\)[/tex]
3. (H) [tex]\(9 - 2b\)[/tex]:
[tex]\[
2 \cdot 3 = 6
\][/tex]
[tex]\[
9 - 6 = 3
\][/tex]
Answer: [tex]\(3\)[/tex]
4. (O) [tex]\(8x + 3y\)[/tex]:
[tex]\[
8 \cdot 5 = 40
\][/tex]
[tex]\[
3 \cdot 8 = 24
\][/tex]
[tex]\[
40 + 24 = 64
\][/tex]
Answer: [tex]\(64\)[/tex]
5. (M) [tex]\(a + bw\)[/tex]:
[tex]\[
b \cdot w = 3 \cdot 20 = 60
\][/tex]
[tex]\[
2 + 60 = 62
\][/tex]
Answer: [tex]\(62\)[/tex]
6. (V) [tex]\(aw - by\)[/tex]:
[tex]\[
a \cdot w = 2 \cdot 20 = 40
\][/tex]
[tex]\[
b \cdot y = 3 \cdot 8 = 24
\][/tex]
[tex]\[
40 - 24 = 16
\][/tex]
Answer: [tex]\(16\)[/tex]
7. (P) [tex]\(b + \frac{w}{x}\)[/tex]:
[tex]\[
\frac{w}{x} = \frac{20}{5} = 4
\][/tex]
[tex]\[
3 + 4 = 7
\][/tex]
Answer: [tex]\(7\)[/tex]
8. (G) [tex]\(\frac{bw}{x} - a + 7\)[/tex]:
[tex]\[
bw = 3 \cdot 20 = 60
\][/tex]
[tex]\[
\frac{60}{5} = 12
\][/tex]
[tex]\[
12 - 2 + 7 = 17
\][/tex]
Answer: [tex]\(17\)[/tex]
9. (K) [tex]\(abxy - 5w\)[/tex]:
[tex]\[
abxy = 2 \cdot 3 \cdot 5 \cdot 8 = 240
\][/tex]
[tex]\[
5w = 5 \cdot 20 = 100
\][/tex]
[tex]\[
240 - 100 = 140
\][/tex]
Answer: [tex]\(140\)[/tex]
10. (H) [tex]\(36 - 4ab\)[/tex]:
[tex]\[
4ab = 4 \cdot 2 \cdot 3 = 24
\][/tex]
[tex]\[
36 - 24 = 12
\][/tex]
Answer: [tex]\(12\)[/tex]
11. (P) [tex]\(5 + 3x - \frac{w}{a}\)[/tex]:
[tex]\[
3x = 3 \cdot 5 = 15
\][/tex]
[tex]\[
\frac{w}{a} = \frac{20}{2} = 10
\][/tex]
[tex]\[
5 + 15 - 10 = 10
\][/tex]
Answer: [tex]\(10\)[/tex]
Now, let's match the answers found above to the given list and assign the corresponding letters to their boxes:
- (17) = T
- (2) = T
- (14) = U
- (18) = R
- (11) = E
- (5) = G
- (15) = A
- (9) = Y
- (12) = R
- (10) = 1
- (4) = I
- (16) = K
- (3) = P