Question

Question 1
A)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)
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Question 2
A)Simplify 5a−8c+b+3c−9a+6b.(1 point)
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Question 3
A) Simplify −34r + 3 − 56r − 6.(1 point)
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Question 4
A)Expand 8(3p+2).(1 point)
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Question 5
A)Expand −4(6a−5).(1 point)
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Question 6
A) Expand 74(8h+3).(1 point)
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Question 7
A)Expand −56(9b−12).(1 point)
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Question 8
A)Find the GCF of 20x − 4.(1 point)
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Question 9
A)Find the GCF of 30m + 12n.(1 point)
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Question 10
A)Factor 8a−28 using the GCF.(1 point)
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Question 11
A)Factor 12y+6 using the GCF.(1 point)
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Question 12
A)Add: 5(0.5k−1)+2(0.4−k). Answer should be in decimal form.(1 point)
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Question 13
A)Subtract 12(z+4)−3(14z+1). Use fractions in final form.(1 point)
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Question 14
A)Subtract: (3b−2c)−(6c+2b)−(b+c).(1 point)
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Question 15
A)What is the expression 4+8(3x−2)−7x when simplified? Apply the order of operations and the commutative and distributive properties. Show all your work.(4 points)

Math Short Answer Rubric (4 points)

Answer 1

Here are the answers to your questions:

### Question 1
**Evaluation of Jacqueline's earnings:**
Jacqueline's earnings from two jobs are represented by the expression \(15l + 12s\). We need to evaluate this for \(l = 5\) and \(s = 7\).

\[
15(5) + 12(7) = 75 + 84 = 159
\]

**Answer:** Jacqueline will earn $159 this week.

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### Question 2
**Simplification of the expression:**
\(5a - 8c + b + 3c - 9a + 6b\)

Combine like terms:
- For \(a\): \(5a - 9a = -4a\)
- For \(b\): \(b + 6b = 7b\)
- For \(c\): \(-8c + 3c = -5c\)

Putting it all together:
\[
-4a + 7b - 5c
\]

**Answer:** \(-4a + 7b - 5c\)

---

### Question 3
**Simplification of the expression:**
\(-34r + 3 - 56r - 6\)

Combine like terms:
- For \(r\): \(-34r - 56r = -90r\)
- For constants: \(3 - 6 = -3\)

Putting it all together:
\[
-90r - 3
\]

**Answer:** \(-90r - 3\)

---

### Question 4
**Expansion of the expression:**
\(8(3p + 2)\)

Using the distributive property:
\[
8 \times 3p + 8 \times 2 = 24p + 16
\]

**Answer:** \(24p + 16\)

---

### Question 5
**Expansion of the expression:**
\(-4(6a - 5)\)

Using the distributive property:
\[
-4 \times 6a + (-4) \times (-5) = -24a + 20
\]

**Answer:** \(-24a + 20\)

---

### Question 6
**Expansion of the expression:**
\(74(8h + 3)\)

Using the distributive property:
\[
74 \times 8h + 74 \times 3 = 592h + 222
\]

**Answer:** \(592h + 222\)

---

### Question 7
**Expansion of the expression:**
\(-56(9b - 12)\)

Using the distributive property:
\[
-56 \times 9b + (-56) \times (-12) = -504b + 672
\]

**Answer:** \(-504b + 672\)

---

### Question 8
**Finding the GCF:**
For \(20x - 4\), we can factor out the common factor:
The GCF is \(4\).

**Answer:** \(4\)

---

### Question 9
**Finding the GCF:**
For \(30m + 12n\), we can find the GCF:
The GCF is \(6\).

**Answer:** \(6\)

---

### Question 10
**Factoring \(8a - 28\) using GCF:**
The GCF is \(4\):
\[
8a - 28 = 4(2a - 7)
\]

**Answer:** \(4(2a - 7)\)

---

### Question 11
**Factoring \(12y + 6\) using GCF:**
The GCF is \(6\):
\[
12y + 6 = 6(2y + 1)
\]

**Answer:** \(6(2y + 1)\)

---

### Question 12
**Adding the expressions:**
\[
5(0.5k - 1) + 2(0.4 - k)
\]
Calculating each part:
\[
5(0.5k) - 5(1) + 2(0.4) - 2(k) = 2.5k - 5 + 0.8 - 2k
\]
Combining like terms:
\[
2.5k - 2k - 5 + 0.8 = 0.5k - 4.2
\]

**Answer:** \(0.5k - 4.2\)

---

### Question 13
**Subtracting the expressions:**
\[
12(z + 4) - 3(14z + 1)
\]
Expanding:
\[
12z + 48 - 42z - 3
\]
Combine like terms:
\[
12z - 42z + 48 - 3 = -30z + 45
\]

**Answer:** \(-30z + 45\)

---

### Question 14
**Subtracting the expressions:**
\[
(3b - 2c) - (6c + 2b) - (b + c)
\]
Distributing the negative:
\[
3b - 2c - 6c - 2b - b - c
\]
Combine like terms:
- For \(b\): \(3b - 2b - b = 0\)
- For \(c\): \(-2c - 6c - c = -9c\)

Final result:
\[
-9c
\]

**Answer:** \(-9c\)

---

### Question 15
**Simplifying the expression:**
\[
4 + 8(3x - 2) - 7x
\]
Expanding:
\[
4 + 24x - 16 - 7x
\]
Combine like terms:
\[
(24x - 7x) + (4 - 16) = 17x - 12
\]

**Final Result:** \(17x - 12\)

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Let me know if you have more questions!