Question

Name the property that is illustrated by the statement below: 2 + 7 + 3 = 2 + 7 + 3
Answer
Evaluate the expression 3b−ac when a = −2, b =3, and c=0.5.
Answer
Evaluate the expression 5x2+2y when x = −3 and y =0.25.
Answer
Evaluate the expression 3mn −2p​ when m = 1 3​, n =−3,and p=3.
Answer
Which expression is equivalent to 3xy − 2xz + yz + 2xy − 4xz ​− 5yz?
Answer
Which expression is equivalent to `5x^{2}+3x-2x^{2}+4x?`
Answer
Which expression is equivalent to `-3\left(2x+5\right)\ +\ 7\ ?`
Answer

A state park charges an entrance fee plus $15 for each night of camping. The table shows this relationship. Which algebraic expression describes the total cost for camping n nights?

Answer
While on vacation, you rent a scooter. You pay $7.50 for each hour you use it. It costs $3 to rent a helmet. Write an algebraic expression that describes the total cost in terms of hours, x, that you rent the scooter.



HINT: Use the table to help you write the expre
Answer
12(x+4)
simplify the expression
Answer
-2(2x-5)
simplify the expression
Answer
1/2(6x+10
Answer
3(8-5x)+2x
simplify the expression
Answer
5x-4(2+3x)
Answered by GPT 3.5
The property illustrated by the statement is the commutative property of addition.
Answered by GPT 3.5
To evaluate the expression 3b−ac, we substitute the given values of a, b, and c into the expression.

Substituting a = -2, b = 3, and c = 0.5, we get:
3(3) - (-2)(0.5)

Simplifying the expression:
9 + 1

Final answer:
10
Answered by GPT 3.5
To evaluate the expression 5x^2+2y, we substitute the given values of x and y into the expression.

Substituting x = -3 and y = 0.25, we get:
5(-3)^2 + 2(0.25)

Simplifying the expression:
5(9) + 0.5

45 + 0.5

Final answer:
45.5
Answered by GPT 3.5
To evaluate the expression 3mn - 2p, we substitute the given values of m, n, and p into the expression.

Substituting m = 1/3, n = -3, and p = 3, we get:
3(1/3)(-3) - 2(3)

Simplifying the expression:
-3 - 6

Final answer:
-9
Answered by GPT 3.5
To simplify the given expression, we group the like terms together:

(3xy + 2xy) + (-2xz - 4xz) + (yz - 5yz)

Simplifying each group:
5xy - 6xz - 4yz

The expression that is equivalent to 3xy − 2xz + yz + 2xy − 4xz ​− 5yz is 5xy - 6xz - 4yz.
Answered by GPT 3.5
To simplify the expression `5x^{2}+3x-2x^{2}+4x`, we combine like terms. We add the coefficients of the terms with the same exponent:

(5x^2 - 2x^2) + (3x + 4x)

Simplifying each group:
3x^2 + 7x

Therefore, the expression that is equivalent to `5x^{2}+3x-2x^{2}+4x` is `3x^2 + 7x`.
Answered by GPT 3.5
To simplify the expression `-3(2x+5) + 7`, we distribute the -3 to each term inside the parentheses:

-3 * 2x + -3 * 5 + 7

Simplifying each term:
-6x - 15 + 7

Combining like terms:
-6x - 8

Therefore, the expression that is equivalent to `-3(2x+5) + 7` is `-6x - 8`.
Answered by GPT 3.5
The table shows that there is a fixed entrance fee and an additional cost per night of camping. To express this relationship algebraically, we can use the expression:

Total cost = Entrance fee + (Cost per night * Number of nights)

In this case, the entrance fee is considered to be a constant value, and the cost per night is represented by $15. Therefore, the algebraic expression that describes the total cost for camping n nights would be:

Total cost = Entrance fee + (15 * n)

Note: The specific entrance fee value would need to be provided in order to substitute it into the expression.
Answered by GPT 3.5
Based on the given information, we can express the total cost of renting the scooter as the sum of the cost per hour and the cost of renting a helmet. Considering that the cost per hour is $7.50 and the helmet rental cost is $3, the algebraic expression that describes the total cost in terms of hours, x, would be:

Total cost = (Cost per hour * Number of hours) + Helmet rental cost

Total cost = (7.50 * x) + 3

Therefore, the algebraic expression that describes the total cost of renting the scooter in terms of hours, x, is (7.50 * x) + 3.
Answered by GPT 3.5
To simplify the expression 12(x+4), we need to apply the distributive property. We multiply the coefficient 12 by every term inside the parentheses:

12 * x + 12 * 4

This simplifies to:
12x + 48

Therefore, the simplified expression is 12x + 48.
Answered by GPT 3.5
To simplify the expression -2(2x-5), we can again apply the distributive property. We multiply the coefficient -2 by every term inside the parentheses:

-2 * 2x - 2 * (-5)

This simplifies to:
-4x + 10

Therefore, the simplified expression is -4x + 10.
Answered by GPT 3.5
To simplify the expression 1/2(6x+10), we can use the distributive property. We multiply each term inside the parentheses by 1/2:

1/2 * 6x + 1/2 * 10

Simplifying each term:
3x + 5

Therefore, the simplified expression is 3x + 5.
Answered by GPT 3.5
To simplify the expression 3(8-5x)+2x, we need to simplify inside the parentheses first, and then apply the distributive property:

3(8) - 3(5x) + 2x

This simplifies to:
24 - 15x + 2x

Combining like terms:
-13x + 24

Therefore, the simplified expression is -13x + 24.
Answered by GPT 3.5
To simplify the expression 5x - 4(2+3x), we need to apply the distributive property:

5x - 4 * 2 - 4 * 3x

This simplifies to:
5x - 8 - 12x

Combining like terms:
-7x - 8

Therefore, the simplified expression is -7x - 8.