Name the property that is illustrated by the statement below: 2 + 7 + 3 = 2 + 7 + 3
The property illustrated by the statement is the commutative property of addition.
Evaluate the expression 3b−ac when a = −2, b =3, and c=0.5.
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
Evaluate the expression 5x2+2y when x = −3 and y =0.25.
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
Evaluate the expression 3mn −2p when m = 1 3, n =−3,and p=3.
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
Which expression is equivalent to 3xy − 2xz + yz + 2xy − 4xz − 5yz?
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.
Which expression is equivalent to `5x^{2}+3x-2x^{2}+4x?`
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`.
Which expression is equivalent to `-3\left(2x+5\right)\ +\ 7\ ?`
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`.
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?
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.
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
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.
12(x+4)
simplify the expression
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.
-2(2x-5)
simplify the expression
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.
1/2(6x+10
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.
3(8-5x)+2x
simplify the expression
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.
5x-4(2+3x)
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.