Printer ink cartridges cost $19 each. The company that sells the ink cartridges charges a flat shipping rate of $7.50, no matter how many ink cartridges you buy.
Write an algebraic expression that describes the total cost for a single order of `x`, cartridges.
The algebraic expression that describes the total cost for a single order of x cartridges is:
19x + 7.50
To simplify 3(8 - 5x) + 2x, we need to distribute the 3 to each term inside the parentheses:
3 * 8 - 3 * 5x + 2x
This simplifies to:
24 - 15x + 2x
Combining like terms:
24 - 13x
So, the simplified expression is 24 - 13x.
Evaluate the expression `3b-ac` when `a\ =\ -2`, `b\ =3`, and `c=0.5`
To evaluate the expression 3b - ac with a = -2, b = 3, and c = 0.5, substitute the given values into the expression:
3b - ac
= 3(3) - (-2)(0.5)
= 9 - (-1)
= 9 + 1
= 10
Therefore, when a = -2, b = 3, and c = 0.5, the value of the expression 3b - ac is 10.
evaluate the expression 3b-ac when a = -2,b=3 and c=0.5
To evaluate the expression 3b - ac with a = -2, b = 3, and c = 0.5, substitute the given values into the expression:
3b - ac
= 3(3) - (-2)(0.5)
= 9 - (-1)
= 9 + 1
= 10
Therefore, when a = -2, b = 3, and c = 0.5, the value of the expression 3b - ac is 10.
Evaluate the expression 5x^2+2y when x=-3and y =0.25
To evaluate the expression 5x^2 + 2y with x = -3 and y = 0.25, substitute the given values into the expression:
5x^2 + 2y
= 5(-3)^2 + 2(0.25)
= 5(9) + 0.5
= 45 + 0.5
= 45.5
Therefore, when x = -3 and y = 0.25, the value of the expression 5x^2 + 2y is 45.5.
3mn/-2p when m = 1/3, n=-3 and p=3
To evaluate the expression (3mn) / (-2p) with m = 1/3, n = -3, and p = 3, substitute the given values into the expression:
(3mn) / (-2p)
= (3 * (1/3) * (-3)) / (-2 * 3)
= (-3) / (-6)
= 1/2
Therefore, when m = 1/3, n = -3, and p = 3, the value of the expression (3mn) / (-2p) is 1/2.
\left(3xy\ -\ 2xz\ +\ yz\right)\ +\ \left(2xy\ -\ 4xz\ -\ 5yz\right)
Simplifying the expression:
\((3xy - 2xz + yz) + (2xy - 4xz - 5yz)\)
Expanding the brackets:
\(3xy - 2xz + yz + 2xy - 4xz - 5yz\)
Combining like terms:
\(5xy - 6xz - 4yz\)
Therefore, the simplified expression is \(5xy - 6xz - 4yz\).
Which expression is equivalent to 3xy − 2xz + yz + 2xy − 4xz − 5yz?
To find the equivalent expression, we can combine like terms:
3xy + 2xy = 5xy
-2xz - 4xz = -6xz
yz - 5yz = -4yz
Putting it all together, the equivalent expression 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 need to combine like terms. Let's group the terms with x^2 and the terms without x^2:
(5x^2 - 2x^2) + (3x + 4x)
Simplifying each group:
3x^2 + 7x
Therefore, the equivalent expression is 3x^2 + 7x.
Which expression is equivalent to `-3\left(2x+5\right)\ +\ 7\ ?`
To simplify the expression -3(2x + 5) + 7, we can 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 simplified equivalent expression 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?
To describe the total cost for camping `n` nights, the algebraic expression would be:
Entrance Fee + (Price per Night * Number of Nights)
In this case, the entrance fee is not specified in the table, so let's represent it with the variable "E". The price per night of camping is $15, and the number of nights is "n". Therefore, the algebraic expression that describes the total cost for camping `n` nights is:
E + (15 * n)
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.
The algebraic expression that describes the total cost in terms of hours, x, that you rent the scooter is:
Cost of Scooter Rental = (7.50 * x) + 3
This expression takes into account the cost per hour of using the scooter, which is $7.50 multiplied by the number of hours, as well as the additional cost of $3 for renting a helmet.
simplify 12\left(x+4\right)
To simplify 12(x + 4), we need to distribute the 12 to each term inside the parentheses:
12 * x + 12 * 4
This simplifies to:
12x + 48
So, the simplified expression is 12x + 48.
simplify 12(x +4)
To simplify 12(x + 4), we need to distribute the 12 to each term inside the parentheses:
12 * x + 12 * 4
This simplifies to:
12x + 48
So, the simplified expression is 12x + 48.
simplify -2\left(2x-5\right)
To simplify -2(2x - 5), we need to distribute the -2 to each term inside the parentheses:
-2 * 2x - 2 * (-5)
This simplifies to:
-4x + 10
So, the simplified expression is -4x + 10.
\frac{1}{2}\left(6x+10\right)
To simplify 1/2(6x + 10), we need to distribute the 1/2 to each term inside the parentheses:
(1/2) * 6x + (1/2) * 10
This simplifies to:
3x + 5
So, the simplified expression is 3x + 5.
3\left(8-5x\right)\ +\ 2x
5x-4\left(2+3x\right)
To simplify 5x - 4(2 + 3x), we need to distribute the -4 to each term inside the parentheses:
5x - 4 * 2 - 4 * 3x
Simplifying:
5x - 8 - 12x
Now, combine like terms:
(5x - 12x) - 8
-7x - 8
So, the simplified expression is -7x - 8.