Resources

Resources

Prime factorization

a. Factor the expression

4 n^{2}-12 n-160

. Simplify your answer as much as possible, but do not combine like factors.

1

. Select all the choices which describes a positive association:

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x

y

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x

y

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E) There is no relationship between

x

y

1

. Write the algebraic definition for the piecewise function graph.

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f(x)=\left\{\begin{array}{l} \Rightarrow \\ \Rightarrow \\ \Rightarrow \end{array}\right.

1

. Let it be known that

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\begin{array}{l} \lim _{x \rightarrow 1} f(x)=2, \lim _{x \rightarrow 10} f(x)=1, f(1)=5 ; \\ \lim _{x \rightarrow 1} g(x)=1, \lim _{x \rightarrow 10} g(x)=\frac{1}{10}, g(1)=1 . \end{array}

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Find the limits of the functions if possible. If the boundary cannot be determined, explain why.

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1

\lim _{x \rightarrow 1} \frac{2 f(x)+g(x)}{f^{2}(x)}

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2

\lim _{x \rightarrow 1} g\left(\frac{f(x)}{2}\right)

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3

\lim _{x \rightarrow 1} f(2 g(x))

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4

\lim _{x \rightarrow 10} \lg (g(x))

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5

\lim _{x \rightarrow 10} 5^{f(x)}

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2

\lim _{x \rightarrow 3} f(x)

6 x-9 \leq f(x) \leq x^{2}

. Explain the answer.

1

. Let it be known that

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\begin{array}{l} \lim _{x \rightarrow 1} f(x)=2, \lim _{x \rightarrow 10} f(x)=1, f(1)=5 ; \\ \lim _{x \rightarrow 1} g(x)=1, \lim _{x \rightarrow 10} g(x)=\frac{1}{10}, g(1)=1 . \end{array}

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Find the limits of the functions if possible. If the boundary cannot be determined, explain why.

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1

\lim _{x \rightarrow 1} \frac{2 f(x)+g(x)}{f^{2}(x)}

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2

\lim g())

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3

\lim _{x \rightarrow 1} f(2 g(x))

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4

\lim _{x \rightarrow 10} \lg (g(x))

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5

\lim _{x \rightarrow 10} 5^{f(x)}

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2

\lim _{x \rightarrow 3} f(x)

6 x-9 \leq f(x) \leq x^{2}

. Explain the answer.

1

. Let it be known that

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\begin{array}{l} \lim _{x \rightarrow 1} f(x)=2, \lim _{x \rightarrow 10} f(x)=1, f(1)=5 ; \\ \lim _{x \rightarrow 1} g(x)=1, \lim _{x \rightarrow 10} g(x)=\frac{1}{10}, g(1)=1 . \end{array}

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Find the limits of the functions if possible. If the boundary cannot be determined, explain why.

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1

\lim _{x \rightarrow 1} \frac{2 f(x)+g(x)}{f^{2}(x)}

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2

\lim _{x \rightarrow 1} g\left(\frac{f(x)}{2}\right)

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3

\lim _{x \rightarrow 1} f(2 g(x))

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4

\lim _{x \rightarrow 10} \lg (g(x))

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5

\lim _{x \rightarrow 10} 5^{f(x)}

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2

\lim _{x 3} f(x)

6 x-9 \leq f(x) \leq x^{2}

. Explain the answer.

4

For the universal set \{whole numbers from

1

20

\}

draw separate Venn diagrams to show each of these subsets:

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3

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4

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5

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20

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Which of these four subsets has the fewest members?

For the following function, find (a) the critical numbers, (b) the open intervals where the function is increasing, and (c) the open intervals where it is decreasing.

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f(x)=x^{4}+12 x^{3}+28 x^{2}+4

5

. Examine this pattern to determine the next equation:

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\begin{array}{l} 37 \times 3=111 \\ 37 \times 6=222 \\ 37 \times 9=333 \\ 37 \times 12=444 \end{array}

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- Is your conjecture correct? Explain how you know?

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- This pattern eventually breaks down. Determine when the breakdown occurs.

On the number line, intervals are equally spaced, and point

x

lies in the interval

AB

. What are the lower and upper limits of all possible values of

x

Find the greatest common factor of these three expressions

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3 w^{4}, 10 w^{2} \text {, and } 6

Steven found that between

2012

2020

, as a country's per capita chicken egg consumption increased, the country's divorce rate decreased. Based on this information, which of the following conclusions is valid?

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1

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(A) Eating chicken eggs prevents divorces.

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(B) Divorces lead to a decrease in per capita chicken egg consumption.

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(C) There is a positive association between per capita chicken egg consumption and divorce rate.

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(D) There is a negative association between per capita chicken egg consumption and divorce rate.