Question
Question 1(Multiple Choice Worth 6 points)
(01.03 MC)
Solve for all possible values of x.
square root of the quantity x minus 8 end quantity minus 3 equals 1
x = −4
x = 8
x = 12
x = 24
Question 2(Multiple Choice Worth 6 points)
(01.01 MC)
Which of the following represents fourth root of x cubed in exponential form?
x to the three fourths power
x to the four thirds power
4x3
3x4
Question 3(Multiple Choice Worth 6 points)
(01.07 MC)
Simplify the expression. Write your answer as a complex number.
3 times the square root of 16 plus the square root of negative 9
7 − 3i
7 + 3i
12 + 3i
12 − 3i
Question 4(Multiple Choice Worth 6 points)
(01.08 MC)
Multiply (x − 4)(x2 − 5x + 3).
x3 + 3x2 + 11x − 12
x3 − 5x2 + 13x − 12
x3 − 9x2 + 23x − 12
x3 − x2 + 17x − 12
Question 5(Multiple Choice Worth 6 points)
(01.07 MC)
Simplify the expression (8 + 6i)(8 − 6i).
28
100
64 − 48i
64 + 48i
Question 6(Multiple Choice Worth 6 points)
(01.07 MC)
Multiply (4 + i)(1 − 5i).
9 − 19i
−1 − 19i
4 − 5i2
4 − 19i − 5i2
Question 7(Multiple Choice Worth 6 points)
(01.02 MC)
Simplify open parentheses x to the 4 fifths power close parentheses to the 3 sevenths power.
x to the 7 twelfths power
x to the 12 over 35 power
x to the 13 over 35 power
x to the 43 over 35 power
Question 8(Multiple Choice Worth 6 points)
(01.08 MC)
Simplify (8j3 − 5j2 − 5) − (6j3 − 12j2 + 8j − 7).
2j3 − 17j2 + 8j − 12
2j3 + 7j2 + 8j − 12
2j3 − 17j2 − 8j + 2
2j3 + 7j2 − 8j + 2
Question 9(Multiple Choice Worth 6 points)
(01.08 MC)
Simplify the expression 4(x − 5)(x2 + x + 2).
4x3 − 4x2 − 3x − 10
4x3 − 16x2 − 12x − 40
4x3 + 12x2 − 40x − 40
4x3 − 40x2 + 12x − 40
Question 10(Multiple Choice Worth 6 points)
(01.08 HC)
Find the volume of a rectangular prism if the length is 4x, the width is 2x, and the height is x3 + 3x + 6. Use the formula V = l ⋅ w ⋅ h, where l is length, w is width, and h is height, to find the volume.
6x5 + 18x3 + 36x2
6x6 + 18x3 + 36x2
8x5 + 24x3 + 48x2
8x6 + 24x3 + 48x2
(01.03 MC)
Solve for all possible values of x.
square root of the quantity x minus 8 end quantity minus 3 equals 1
x = −4
x = 8
x = 12
x = 24
Question 2(Multiple Choice Worth 6 points)
(01.01 MC)
Which of the following represents fourth root of x cubed in exponential form?
x to the three fourths power
x to the four thirds power
4x3
3x4
Question 3(Multiple Choice Worth 6 points)
(01.07 MC)
Simplify the expression. Write your answer as a complex number.
3 times the square root of 16 plus the square root of negative 9
7 − 3i
7 + 3i
12 + 3i
12 − 3i
Question 4(Multiple Choice Worth 6 points)
(01.08 MC)
Multiply (x − 4)(x2 − 5x + 3).
x3 + 3x2 + 11x − 12
x3 − 5x2 + 13x − 12
x3 − 9x2 + 23x − 12
x3 − x2 + 17x − 12
Question 5(Multiple Choice Worth 6 points)
(01.07 MC)
Simplify the expression (8 + 6i)(8 − 6i).
28
100
64 − 48i
64 + 48i
Question 6(Multiple Choice Worth 6 points)
(01.07 MC)
Multiply (4 + i)(1 − 5i).
9 − 19i
−1 − 19i
4 − 5i2
4 − 19i − 5i2
Question 7(Multiple Choice Worth 6 points)
(01.02 MC)
Simplify open parentheses x to the 4 fifths power close parentheses to the 3 sevenths power.
x to the 7 twelfths power
x to the 12 over 35 power
x to the 13 over 35 power
x to the 43 over 35 power
Question 8(Multiple Choice Worth 6 points)
(01.08 MC)
Simplify (8j3 − 5j2 − 5) − (6j3 − 12j2 + 8j − 7).
2j3 − 17j2 + 8j − 12
2j3 + 7j2 + 8j − 12
2j3 − 17j2 − 8j + 2
2j3 + 7j2 − 8j + 2
Question 9(Multiple Choice Worth 6 points)
(01.08 MC)
Simplify the expression 4(x − 5)(x2 + x + 2).
4x3 − 4x2 − 3x − 10
4x3 − 16x2 − 12x − 40
4x3 + 12x2 − 40x − 40
4x3 − 40x2 + 12x − 40
Question 10(Multiple Choice Worth 6 points)
(01.08 HC)
Find the volume of a rectangular prism if the length is 4x, the width is 2x, and the height is x3 + 3x + 6. Use the formula V = l ⋅ w ⋅ h, where l is length, w is width, and h is height, to find the volume.
6x5 + 18x3 + 36x2
6x6 + 18x3 + 36x2
8x5 + 24x3 + 48x2
8x6 + 24x3 + 48x2
Answers
GPT-4o mini
Here are the answers to each question:
**Question 1:**
Solve for all possible values of x in the equation \(\sqrt{x - 8} - 3 = 1\):
1. Add 3 to both sides: \(\sqrt{x - 8} = 4\)
2. Square both sides: \(x - 8 = 16\)
3. Add 8 to both sides: \(x = 24\)
**Answer:** x = 24
---
**Question 2:**
Which of the following represents the fourth root of \(x^3\) in exponential form?
- The fourth root can be expressed as \(x^{\frac{3}{4}}\).
**Answer:** \(x^{\frac{3}{4}}\)
---
**Question 3:**
Simplify the expression \(3\sqrt{16} + \sqrt{-9}\):
1. \(3\sqrt{16} = 3 \times 4 = 12\)
2. \(\sqrt{-9} = 3i\)
Combine them: \(12 + 3i\)
**Answer:** \(12 + 3i\)
---
**Question 4:**
Multiply \((x - 4)(x^2 - 5x + 3)\):
1. \(x^2(x) = x^3 - 5x^2 + 3x\)
2. \(-4(x^2 - 5x + 3) = -4x^2 + 20x - 12\)
3. Combine: \(x^3 - 9x^2 + 23x - 12\)
**Answer:** \(x^3 - 9x^2 + 23x - 12\)
---
**Question 5:**
Simplify \((8 + 6i)(8 - 6i)\):
- This is a difference of squares: \(8^2 - (6i)^2 = 64 - (-36) = 64 + 36 = 100\)
**Answer:** 100
---
**Question 6:**
Multiply \((4 + i)(1 - 5i)\):
1. \(4 \cdot 1 + 4 \cdot (-5i) + i \cdot 1 + i \cdot (-5i)\)
2. \(4 - 20i + i + 5 = 9 - 19i\)
**Answer:** \(9 - 19i\)
---
**Question 7:**
Simplify \((x^{\frac{4}{5}})^{\frac{3}{7}}\):
- Use the power of a power rule: \(x^{\frac{4}{5} \cdot \frac{3}{7}} = x^{\frac{12}{35}}\)
**Answer:** \(x^{\frac{12}{35}}\)
---
**Question 8:**
Simplify \((8j^3 - 5j^2 - 5) - (6j^3 - 12j^2 + 8j - 7)\):
Combine like terms:
- Combine \(j^3\): \(8j^3 - 6j^3 = 2j^3\)
- Combine \(j^2\): \(-5j^2 + 12j^2 = 7j^2\)
- Combine \(j\): \(-8j\)
- Combine constants: \(-5 + 7 = 2\)
Final answer: \(2j^3 + 7j^2 - 8j + 2\)
**Answer:** \(2j^3 + 7j^2 - 8j + 2\)
---
**Question 9:**
Simplify \(4(x - 5)(x^2 + x + 2)\):
1. Multiply: \(4((x)(x^2) + (x)(x) + (x)(2) - (5)(x^2) - (5)(x) - (5)(2))\)
2. This gives \(4(x^3 - 4x^2 - 10)\)
**Final Answer:** \(4x^3 - 16x^2 - 40\)
---
**Question 10:**
Find the volume of a rectangular prism:
\[
V = l \cdot w \cdot h = (4x) \cdot (2x) \cdot (x^3 + 3x + 6)
\]
1. Calculate:
- \(8x^2(x^3 + 3x + 6) = 8x^5 + 24x^3 + 48x^2\)
**Answer:** \(8x^5 + 24x^3 + 48x^2\)
---
I hope this helps!
**Question 1:**
Solve for all possible values of x in the equation \(\sqrt{x - 8} - 3 = 1\):
1. Add 3 to both sides: \(\sqrt{x - 8} = 4\)
2. Square both sides: \(x - 8 = 16\)
3. Add 8 to both sides: \(x = 24\)
**Answer:** x = 24
---
**Question 2:**
Which of the following represents the fourth root of \(x^3\) in exponential form?
- The fourth root can be expressed as \(x^{\frac{3}{4}}\).
**Answer:** \(x^{\frac{3}{4}}\)
---
**Question 3:**
Simplify the expression \(3\sqrt{16} + \sqrt{-9}\):
1. \(3\sqrt{16} = 3 \times 4 = 12\)
2. \(\sqrt{-9} = 3i\)
Combine them: \(12 + 3i\)
**Answer:** \(12 + 3i\)
---
**Question 4:**
Multiply \((x - 4)(x^2 - 5x + 3)\):
1. \(x^2(x) = x^3 - 5x^2 + 3x\)
2. \(-4(x^2 - 5x + 3) = -4x^2 + 20x - 12\)
3. Combine: \(x^3 - 9x^2 + 23x - 12\)
**Answer:** \(x^3 - 9x^2 + 23x - 12\)
---
**Question 5:**
Simplify \((8 + 6i)(8 - 6i)\):
- This is a difference of squares: \(8^2 - (6i)^2 = 64 - (-36) = 64 + 36 = 100\)
**Answer:** 100
---
**Question 6:**
Multiply \((4 + i)(1 - 5i)\):
1. \(4 \cdot 1 + 4 \cdot (-5i) + i \cdot 1 + i \cdot (-5i)\)
2. \(4 - 20i + i + 5 = 9 - 19i\)
**Answer:** \(9 - 19i\)
---
**Question 7:**
Simplify \((x^{\frac{4}{5}})^{\frac{3}{7}}\):
- Use the power of a power rule: \(x^{\frac{4}{5} \cdot \frac{3}{7}} = x^{\frac{12}{35}}\)
**Answer:** \(x^{\frac{12}{35}}\)
---
**Question 8:**
Simplify \((8j^3 - 5j^2 - 5) - (6j^3 - 12j^2 + 8j - 7)\):
Combine like terms:
- Combine \(j^3\): \(8j^3 - 6j^3 = 2j^3\)
- Combine \(j^2\): \(-5j^2 + 12j^2 = 7j^2\)
- Combine \(j\): \(-8j\)
- Combine constants: \(-5 + 7 = 2\)
Final answer: \(2j^3 + 7j^2 - 8j + 2\)
**Answer:** \(2j^3 + 7j^2 - 8j + 2\)
---
**Question 9:**
Simplify \(4(x - 5)(x^2 + x + 2)\):
1. Multiply: \(4((x)(x^2) + (x)(x) + (x)(2) - (5)(x^2) - (5)(x) - (5)(2))\)
2. This gives \(4(x^3 - 4x^2 - 10)\)
**Final Answer:** \(4x^3 - 16x^2 - 40\)
---
**Question 10:**
Find the volume of a rectangular prism:
\[
V = l \cdot w \cdot h = (4x) \cdot (2x) \cdot (x^3 + 3x + 6)
\]
1. Calculate:
- \(8x^2(x^3 + 3x + 6) = 8x^5 + 24x^3 + 48x^2\)
**Answer:** \(8x^5 + 24x^3 + 48x^2\)
---
I hope this helps!