The cost of renting a truck from Hamilton Auto Rental is $46.70 per day plus $0.10 per mile. The expression 46.70 + 0.10 represents the cost of renting a truck for one day and driving it m miles. Evaluate 46.70 + 0.10 for m = 130.
The cost of renting a truck for one day and driving it 130 miles is $
The cost of renting a truck for one day and driving it 130 miles is:
46.70 + 0.10 * 130 = 46.70 + 13 = $59.70
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Part 1
The Center for Science and Industry sells adult tickets for $18 and children's tickets for $5. The expression 18a+5c represents the total revenue from selling a adult tickets and c children's tickets. Evaluate the algebraic expression 18a+5c for a=133 and c=407.
The total revenue for and is $
The total revenue from selling 133 adult tickets and 407 children's tickets is:
18 * 133 + 5 * 407 = 2394 + 2035 = $4429
The width of a rectangle is w yards and the length of the rectangle is (5w-4) yards. The perimeter of the rectangle is given by the algebraic expression 2w+2(5w-4). Simplify the algebraic expression 2w+2(5w-4) and determine the perimeter of a rectangle whose width w is 2 yards.
simplify
To simplify the expression 2w + 2(5w - 4), we need to apply the distributive property.
First, distribute the 2 to the terms inside the parentheses:
2w + 2(5w - 4) = 2w + 10w - 8
Next, combine like terms:
2w + 10w - 8 = 12w - 8
Now, we can determine the perimeter of a rectangle with a width of 2 yards by substituting w = 2 into the simplified expression:
Perimeter = 12w - 8
Perimeter = 12(2) - 8
Perimeter = 24 - 8
Perimeter = 16 yards
Use the distributive property to remove the parentheses.
-3(7x-4y)
To remove the parentheses using the distributive property, you need to distribute the -3 to each term inside the parentheses.
-3(7x-4y) = -3 * 7x - 3 * (-4y)
This simplifies to:
-21x + 12y
Simplify each expression by combining like terms.
-5(n-4)+2(n+1)
To simplify the expression -5(n-4) + 2(n+1), distribute the -5 and the 2 to each term inside the parentheses:
-5(n-4) + 2(n+1) = -5n + 20 + 2n + 2
Next, combine like terms:
-5n + 20 + 2n + 2 = (-5n + 2n) + (20 + 2) = -3n + 22
Therefore, the simplified expression is -3n + 22.
Decide whether the statement is an example of the commutative, associative, identity, inverse, or distributive property.
-13+(8+6)=(8+6)+(-13)