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.

Question

The total revenue for a = 165 and c = 467 is ​what? simplify the result

Answer 1

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.

Answer 2

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) = [ ]

Answer 3

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.

Answer 4

2w + 2 (6w - 7 ) =

Answer 5

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.

Answer 6

What is the perimeter of the rectangle whose width w is 2 yards?

[ ] yards

Answer 7

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.

Answer 8

Use the distributive property to remove the parentheses.

- (8x - 8y)

- (8x - 8y) = [ ]

Answer 9

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.

Answer 10

Simplify each expression by combining like terms.

-8(n - 4) + 2 ( n + 1)

-8(n - 4) + 2 ( n + 1) = [ ]

Answer 11

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.

Answer 12

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

Answer 13

The statement is an example of the Associative property, specifically the Associative property of addition. This property states that changing the grouping of numbers being added does not affect the sum. In this case, both sides of the equation have the same sum (8) because the grouping has changed.