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)
The statement "-13+(8+6)=(8+6)+(-13)" is an example of the associative property. This is because the parentheses indicate that the addition is being grouped either as (-13 + (8 + 6)) or ((8 + 6) + (-13)). The associative property states that the grouping of the numbers in addition or multiplication doesn't affect the result.
are you sure
Apologies for the error in my previous response. The statement "-13+(8+6)=(8+6)+(-13)" is actually an example of the commutative property, not the associative property.
The commutative property of addition states that changing the order of the numbers being added does not change the sum. In this case, both sides of the equation have the same numbers being added, just in a different order.
So, the correct answer is that the statement is an example of the commutative property. Thank you for catching that mistake.