Question 1

Question

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)

Bot GPT 4-o mini · Answer

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. --- ### 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:** $17x - 12$ --- Let me know if you have more questions!