Jacqueline has two part-time jobs. She earns $15 per hour, l , working as a lab assistant, and $12 per hour, s , working as a cashier. This is modeled by 15l+12s . Evaluate for l=5 and s=7 to find how much money Jacqueline will earn at her two jobs this week. (1 point) $$
To evaluate the expression, substitute l=5 and s=7 into the expression 15l+12s:
15l+12s = 15(5) + 12(7) = 75 + 84 = $159
Therefore, Jacqueline will earn $159 at her two jobs this week.
are u sure
Yes, I am sure. When we substitute l=5 and s=7 into the expression 15l+12s, we get 15(5) + 12(7) = 75 + 84 = 159.
Simplify 5a − 8c + b + 3c −9a + 6b
To simplify the expression 5a - 8c + b + 3c - 9a + 6b, we can combine like terms:
Combining like terms with the same variable:
5a - 9a = -4a (5 minus 9 is -4)
b + 6b = 7b (1 plus 6 is 7)
-8c + 3c = -5c ( -8 plus 3 is -5)
Putting it all together:
-4a - 5c + 7b
Therefore, the simplified expression is -4a - 5c + 7b.
8(3Expandp + 2) .(1 point)
To expand the expression 8(3p + 2), we distribute the 8 to both terms inside the parentheses:
8(3p + 2) = 8(3p) + 8(2) = 24p + 16
Therefore, the expanded form of 8(3p + 2) is 24p + 16.
Expand −4(6a − 5) .
To expand the expression -4(6a - 5), we distribute the -4 to both terms inside the parentheses:
-4(6a - 5) = -4(6a) - 4(-5) = -24a + 20
Therefore, the expanded form of -4(6a - 5) is -24a + 20.
Expand 74(8h+3) .
To expand the expression 74(8h + 3), we distribute the 74 to both terms inside the parentheses:
74(8h + 3) = 74(8h) + 74(3) = 592h + 222
Therefore, the expanded form of 74(8h + 3) is 592h + 222.
Expand 7/4(8h+3) .
To expand the expression (7/4)(8h + 3), we need to distribute the 7/4 to both terms inside the parentheses:
(7/4)(8h + 3) = (7/4)(8h) + (7/4)(3) = (7*8h)/4 + (7*3)/4 = (56h + 21)/4
Therefore, the expanded form of (7/4)(8h + 3) is (56h + 21)/4.
Find the GCF of 20x − 4
To find the greatest common factor (GCF) of 20x - 4, we need to factorize both terms completely.
First, let's factorize 20x. The prime factorization of 20x is 2 * 2 * 5 * x, which can also be written as 2^2 * 5 * x.
Next, let's factorize 4. The prime factorization of 4 is 2 * 2, which can also be written as 2^2.
Now, let's find the common factors between 2^2 * 5 * x and 2^2.
The highest power of each common prime factor is 2^2.
Therefore, the GCF of 20x - 4 is 2^2.
Note: If there were any additional terms and variables, we would need to consider the common prime factors among all terms. In this case, there is only one term and one variable.
Find the GCF of 30m + 12n
To find the greatest common factor (GCF) of 30m + 12n, we need to factorize both terms completely.
First, let's factorize 30m. The prime factorization of 30m is 2 * 3 * 5 * m.
Next, let's factorize 12n. The prime factorization of 12n is 2 * 2 * 3 * n.
Now, let's find the common factors between 2 * 3 * 5 * m and 2 * 2 * 3 * n.
The common prime factors are 2 and 3.
The highest power of each common prime factor is 2 * 3 = 6.
Therefore, the GCF of 30m + 12n is 6.
Factor 8a − 28 using the GCF
To factor 8a - 28 using the greatest common factor (GCF), we first need to identify the GCF between the two terms.
The GCF of 8a and 28 is 4.
Next, we divide each term by the GCF, 4:
(8a)/4 = 2a
(-28)/4 = -7
Therefore, factoring out the GCF, we can rewrite 8a - 28 as:
4(2a - 7)
So, the factored form of 8a - 28 is 4(2a - 7).
Factor 12y + 6 using the GCF.
To factor 12y + 6 using the greatest common factor (GCF), we first need to identify the GCF between the two terms.
The GCF of 12y and 6 is 6.
Next, we divide each term by the GCF, 6:
(12y)/6 = 2y
(6)/6 = 1
Therefore, factoring out the GCF, we can rewrite 12y + 6 as:
6(2y + 1)
So, the factored form of 12y + 6 is 6(2y + 1).
Subtract: (3b−2c)−(6c+2b)−(b+c)
To subtract the expression (3b - 2c) - (6c + 2b) - (b + c), we need to distribute the negative sign to each term inside the parentheses:
(3b - 2c) - (6c + 2b) - (b + c) = 3b - 2c - 6c - 2b - b - c = (3b - 2b - b) + (-2c - 6c - c)
Simplifying further:
= 0b - 9c
= -9c
Therefore, the expression (3b - 2c) - (6c + 2b) - (b + c) simplifies to -9c.