directions: evaluate each expression if ( w = 2 ), ( x = 7 ), ( y = 24 ) and ( z = 5 ).
1. ( 7w )
2. ( x + 16 )
3. ( y div 3 )
4. ( z^2 + w )
5. ( \frac{y - 2z}{x} )
6. ( 16w + 3z )
7. ( x^2 - 2y )
8. ( 8(3 + w^2) )
9. ( y - 5w + 7x )
10. ( \frac{1}{2}w^3 )
11. ( \frac{3}{4}y + 10 )
12. ( 20 - \frac{1}{3}(x + 2) )
13. ( \frac{8}{9}x^2 - 2k ) (if ( k = 6 ))
14. ( 2a + b ) (if ( a = \frac{5}{12} ) and ( b = \frac{1}{8} ))
15. grant bought strawberries and bananas from the grocery store to make smoothies. the total amount he spent can be represented by the expression ( 1.8s + 0.65b ), where ( s ) is the number of pounds of strawberries and ( b ) is the number of pounds of bananas. if grant bought 2.7 pounds of strawberries and 1.4 pounds of bananas, how much did he spend?

Question

Accepted Answer

### Problem 1: $ 7w $
# Explanation:
## Step 1: Substitute $ w = 2 $
$ 7w = 7\times2 $
## Step 2: Calculate the product
$ 7\times2 = 14 $
# Answer: $ 14 $

### Problem 2: $ x + 16 $
# Explanation:
## Step 1: Substitute $ x = 7 $
$ x + 16 = 7 + 16 $
## Step 2: Calculate the sum
$ 7 + 16 = 23 $
# Answer: $ 23 $

### Problem 3: $ y \div 3 $
# Explanation:
## Step 1: Substitute $ y = 24 $
$ y \div 3 = 24 \div 3 $
## Step 2: Calculate the quotient
$ 24 \div 3 = 8 $
# Answer: $ 8 $

### Problem 4: $ z^2 + w $
# Explanation:
## Step 1: Substitute $ z = 5 $ and $ w = 2 $
$ z^2 + w = 5^2 + 2 $
## Step 2: Calculate $ 5^2 $
$ 5^2 = 25 $
## Step 3: Add $ 2 $ to the result
$ 25 + 2 = 27 $
# Answer: $ 27 $

### Problem 5: $ \frac{y - 2z}{x} $
# Explanation:
## Step 1: Substitute $ x = 7 $, $ y = 24 $, $ z = 5 $
$ \frac{y - 2z}{x} = \frac{24 - 2\times5}{7} $
## Step 2: Calculate the numerator
$ 24 - 2\times5 = 24 - 10 = 14 $
## Step 3: Divide the numerator by the denominator
$ \frac{14}{7} = 2 $
# Answer: $ 2 $

### Problem 6: $ 16w + 3z $
# Explanation:
## Step 1: Substitute $ w = 2 $, $ z = 5 $
$ 16w + 3z = 16\times2 + 3\times5 $
## Step 2: Calculate each term
$ 16\times2 = 32 $, $ 3\times5 = 15 $
## Step 3: Add the results
$ 32 + 15 = 47 $
# Answer: $ 47 $

### Problem 7: $ x^2 - 2y $
# Explanation:
## Step 1: Substitute $ x = 7 $, $ y = 24 $
$ x^2 - 2y = 7^2 - 2\times24 $
## Step 2: Calculate $ 7^2 $ and $ 2\times24 $
$ 7^2 = 49 $, $ 2\times24 = 48 $
## Step 3: Subtract the results
$ 49 - 48 = 1 $
# Answer: $ 1 $

### Problem 8: $ 8(3 + w^2) $
# Explanation:
## Step 1: Substitute $ w = 2 $
$ 8(3 + w^2) = 8(3 + 2^2) $
## Step 2: Calculate $ 2^2 $
$ 2^2 = 4 $
## Step 3: Calculate the sum inside the parentheses
$ 3 + 4 = 7 $
## Step 4: Multiply by 8
$ 8\times7 = 56 $
# Answer: $ 56 $

### Problem 9: $ y - 5w + 7x $
# Explanation:
## Step 1: Substitute $ w = 2 $, $ x = 7 $, $ y = 24 $
$ y - 5w + 7x = 24 - 5\times2 + 7\times7 $
## Step 2: Calculate each term
$ 5\times2 = 10 $, $ 7\times7 = 49 $
## Step 3: Perform the operations
$ 24 - 10 + 49 = 14 + 49 = 63 $
# Answer: $ 63 $

### Problem 10: $ \frac{1}{2}w^2 $
# Explanation:
## Step 1: Substitute $ w = 2 $
$ \frac{1}{2}w^2 = \frac{1}{2}\times2^2 $
## Step 2: Calculate $ 2^2 $
$ 2^2 = 4 $
## Step 3: Multiply by $ \frac{1}{2} $
$ \frac{1}{2}\times4 = 2 $
# Answer: $ 2 $

### Problem 11: $ \frac{3}{4}y + 10 $
# Explanation:
## Step 1: Substitute $ y = 24 $
$ \frac{3}{4}y + 10 = \frac{3}{4}\times24 + 10 $
## Step 2: Calculate $ \frac{3}{4}\times24 $
$ \frac{3}{4}\times24 = 18 $
## Step 3: Add 10
$ 18 + 10 = 28 $
# Answer: $ 28 $

### Problem 12: $ 20 - \frac{1}{3}(x + 2) $
# Explanation:
## Step 1: Substitute $ x = 7 $
$ 20 - \frac{1}{3}(x + 2) = 20 - \frac{1}{3}(7 + 2) $
## Step 2: Calculate the sum inside the parentheses
$ 7 + 2 = 9 $
## Step 3: Calculate $ \frac{1}{3}\times9 $
$ \frac{1}{3}\times9 = 3 $
## Step 4: Subtract the result from 20
$ 20 - 3 = 17 $
# Answer: $ 17 $

### Problem 13: $ \frac{8}{9}x^2 - 2k $ (if $ k = 6 $)
# Explanation:
## Step 1: Substitute $ x = 7 $, $ k = 6 $
$ \frac{8}{9}x^2 - 2k = \frac{8}{9}\times7^2 - 2\times6 $
## Step 2: Calculate $ 7^2 $
$ 7^2 = 49 $
## Step 3: Calculate $ \frac{8}{9}\times49 $ and $ 2\times6 $
$ \frac{8}{9}\times49 = \frac{392}{9} $, $ 2\times6 = 12 $
## Step 4: Subtract the results
$ \frac{392}{9} - 12 = \frac{392}{9} - \frac{108}{9} = \frac{284}{9} \approx 31.56 $ (or as an improper fraction $ \frac{284}{9} $)
# Answer: $ \frac{284}{9} $ (or approximately $ 31.56 $)

### Problem 14: $ 2a + b $ (if $ a = \frac{5}{12} $ and $ b = \frac{1}{8} $)
# Explanation:
## Step 1: Substitute $ a = \frac{5}{12} $, $ b = \frac{1}{8} $
$ 2a + b = 2\times\frac{5}{12} + \frac{1}{8} $
## Step 2: Simplify $ 2\times\frac{5}{12} $
$ 2\times\frac{5}{12} = \frac{10}{12} = \frac{5}{6} $
## Step 3: Find a common denominator for $ \frac{5}{6} $ and $ \frac{1}{8} $ (24)
$ \frac{5}{6} = \frac{20}{24} $, $ \frac{1}{8} = \frac{3}{24} $
## Step 4: Add the fractions
$ \frac{20}{24} + \frac{3}{24} = \frac{23}{24} $
# Answer: $ \frac{23}{24} $

### Problem 15: Total amount spent $ 1.8s + 0.65b $ ( $ s = 2.7 $, $ b = 1.4 $)
# Explanation:
## Step 1: Substitute $ s = 2.7 $, $ b = 1.4 $
$ 1.8s + 0.65b = 1.8\times2.7 + 0.65\times1.4 $
## Step 2: Calculate each term
$ 1.8\times2.7 = 4.86 $, $ 0.65\times1.4 = 0.91 $
## Step 3: Add the results
$ 4.86 + 0.91 = 5.77 $
# Answer: $ \$5.77 $

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Problem 1: \( 7w \)

Step 1: Substitute \( w = 2 \)

Step 2: Calculate the product

Step 1: Substitute \( x = 7 \)

Step 2: Calculate the sum

Step 1: Substitute \( y = 24 \)

Step 2: Calculate the quotient

Answer:

Problem 2: \( x + 16 \)