1780013
Question 1
Question
Find the complex conjugate of \[7+\sqrt{-8}\]
Answer
-
\[7+4i\sqrt{2}\]
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\[7-4i\sqrt{2}\]
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\[7-2i\sqrt{2}\]
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\[7+2i\sqrt{2}\]
Question 2
Question
Find the domain of \[f(x)=\sqrt {\frac{x-2}{x^2 -4}}\]
Answer
-
{x | x ≠ 2}
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{x | x ≠ -2 and x ≠ 2}
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{x | x > -2 and x ≠ 2}
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{x | x > -2}
Question 3
Question
One of the roots of the following equation is 2+i. What is the other? \(x^2 -4x+5=0\)
Answer
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-2+i
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-2-i
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i-2
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2-i
Question 4
Question
What is the first step in simplifying \[\frac{6-4i}{-5+3i}\]
Answer
-
Multiply the fraction by \[\frac{6+4i}{-6+4i}\]
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Multiply the fraction by \[\frac{-5-3i}{-5-3i}\]
-
Multiply the fraction by \[6+4i\]
-
Multiply the fraction by \[-5-3i\]
Question 5
Question
Given: \[f(x)=\sqrt{x}-2x\] \[g(x)=\frac{x}{5-x}\] What is f(g(x))?
Answer
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\[\sqrt {\frac{x}{5-x}} -\frac{2x}{5-x}\]
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\[\frac {\sqrt x -2x}{5-\sqrt x +2x}\]
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\[\frac {\sqrt x -2x}{5-x}\]
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\[\frac {x\sqrt x-2x^2}{5-x}\]
Question 6
Question
Box A contains marbles: 12 red, 16 blue, 11 green, and 5 yellow. Box B contains chips: 8 red, 7 green, 11 blue, and 1 yellow. If you randomly pick one item from each box, what is the probability that both items will be blue?
Answer
-
\[\frac{1}{10}\]
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\[\frac{4}{27}\]
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\[\frac{19}{50}\]
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\[\frac{77}{100}\]
Question 7
Question
Ten students will participate in a spelling contest. How many outcomes for the first, second, and third place are possible?
Answer
-
30
-
90
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120
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720
Question 8
Question
A company assigns passwords to each of its 2000 employees. Each password consists of 3 distinct letters (no repeating letters) and 3 distinct digits. The company assigns a new password to each employee at the beginning of each month. To the nearest year, for how many years will the company be able to supply unique passwords?
Answer
-
468
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732
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5,616
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8,788
Question 9
Question
Which cubic polynomial has 3 and 3-i as zeroes?
Answer
-
\[x^3 -3x^2 -9x+27\]
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\[x^3 +3x^2 -10x+30\]
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\[x^3 -9x^2 +28x-30\]
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\[x^3 +9x^2 +28x+30\]
Question 10
Question
Julio throws an inflated ball up in the air. The following function models the ball's height in terms of time t, in seconds. \[h(t)=\frac{1}{20}t +\frac{1}{10}t +4\] After how many seconds will the ball hit the ground?
Answer
-
0
-
4
-
8
-
10
Question 11
Question
How many rational zeros does this polynomial function have? \(f(x)=(x^4 -16)(3x^2 -21)(4x^2 +1)\)
Answer
-
8
-
6
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4
-
2
Question 12
Question
Find x.
\(log_2 x=-3\)
Answer
-
\[\frac{1}{9}\]
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\[\frac{1}{8}\]
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\[8\]
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\[9\]
Question 13
Question
What is the complete factorization of the following if a, n, r, and q are integers?
\(16r^{3n} -54q^{6a}\)
Answer
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\(2(8r^{3n} -27q^{6a})\)
-
\((4r^{2n} +6q^a)(4r^n -9q^{5a})\)
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\(2(4r^{2n} +3q^a)(2r^n -9q^{5a})\)
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\(2(2r^n -3q^{2a})(4r^{2n} +6r^n q^{2a} +9q^{4a})\)
Question 14
Question
State the dimensions of Matricies A and B. Can these two matrices be multiplied?
Answer
-
Yes Matrix A: 2 X 4 Matrix B: 3 X 4
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Yes Matix A: 4 X 2 Matrix B: 4 X 3
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No Matrix A: 2 X 4 Matrix B: 3 X 4
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No Matix A: 4 X 2 Matrix B: 4 X 3
Question 15
Question
If A is a 3 X 2 matrix, B is a 3 X 3 matrix, and C is a 2 X 3 matrix, what are the dimensions of A X C X B?
Answer
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3 X 3
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2 X 2
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2 X 3
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18 X 18
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