The Center for Science and Industry sells adult tickets for $13 and children's tickets for $9. The expression 13a +9c represents the total revenue from selling a adult tickets and c children's tickets. Evaluate the algebraic expression 13a + 9c for a = 165 and c = 467.
The total revenue for a = 165 and c = 467 is what? simplify the result
To evaluate the algebraic expression 13a + 9c for a = 165 and c = 467, we substitute the given values into the expression:
13(165) + 9(467)
Multiplying:
2145 + 4203
Adding:
6348
Therefore, the total revenue for a = 165 and c = 467 is $6348.
The width of a rectangle is w yards and the length of the rectangle is (6w - 7) yards. The perimeter of the rectangle is given by the algebraic expression 2w + 2(6w - 7). Simplify the algebraic expression 2w+ 2( 6w - 7) and determine the perimeter of a rectangle whose width w is 2 yards.
Simplify the algebraic expression 2w+ 2( 6w - 7)
2w+ 2( 6w - 7) = [ ]
To simplify the algebraic expression 2w + 2(6w - 7), we follow the order of operations, which states that we should perform operations within parentheses first:
2w + 2(6w - 7) = 2w + 12w - 14
Next, we can combine like terms:
= (2w + 12w) - 14
= 14w - 14
Therefore, the simplified algebraic expression 2w + 2(6w - 7) is 14w - 14.
To determine the perimeter of a rectangle whose width w is 2 yards, we substitute the value into the expression:
Perimeter = 14w - 14
Perimeter = 14(2) - 14
Perimeter = 28 - 14
Perimeter = 14
Therefore, the perimeter of the rectangle with a width of 2 yards is 14 yards.
2w + 2 (6w - 7 ) =
To simplify the expression 2w + 2(6w - 7), we need to use the distributive property:
2w + 2(6w - 7) = 2w + 2 * 6w - 2 * 7
Now, we can simplify by performing the multiplication:
= 2w + 12w - 14
Next, we can combine like terms:
= 14w - 14
Therefore, the simplified expression for 2w + 2(6w - 7) is 14w - 14.
What is the perimeter of the rectangle whose width w is 2 yards?
[ ] yards
To find the perimeter of the rectangle when the width w is 2 yards, we substitute w = 2 into the expression we simplified earlier:
Perimeter = 14w - 14
Plugging in w = 2:
Perimeter = 14(2) - 14
Perimeter = 28 - 14
Perimeter = 14 yards
Therefore, the perimeter of the rectangle when the width is 2 yards is 14 yards.
Use the distributive property to remove the parentheses.
- (8x - 8y)
- (8x - 8y) = [ ]
To use the distributive property to remove the parentheses in - (8x - 8y), we need to distribute the negative sign to each term inside the parentheses:
- (8x - 8y) = -8x + 8y
Therefore, when we remove the parentheses using the distributive property, - (8x - 8y) simplifies to -8x + 8y.
Simplify each expression by combining like terms.
-8(n - 4) + 2 ( n + 1)
-8(n - 4) + 2 ( n + 1) = [ ]
To simplify the expression -8(n - 4) + 2(n + 1), we use the distributive property and then combine like terms:
-8(n - 4) + 2(n + 1) = -8n + 32 + 2n + 2
Now we can combine like terms:
= (-8n + 2n) + (32 + 2)
Simplifying further:
= -6n + 34
Therefore, -8(n - 4) + 2(n + 1) simplifies to -6n + 34.
Decide whether the statement is an example of the commutative, associative, identity, inverse, or distributive property.
- 15 + (7 + 6) = ( -15 + 7) + 6
The statement is an example of which of the following properties?
Identity
Associative
Inverse
Communtative
Distributive