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Exam 12: What Is Algebra

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Question 21

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Make a drawing of a balance for the equation $4 x + 5 = 5 x + 3$ . Solve the equation by showing actions with the balance, one step at a time.

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Question 22

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Give the first four numbers of each of the following sequences. A) An arithmetic sequence with first term 19 and difference 20 B) A geometric sequence with first term 1.2 and ratio 3

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Question 23

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Use $a ^ { m } \cdot a ^ { n } = a ^ { m + n }$ to justify defining $a ^ { \frac { 1 } { 2 } }$ = $\sqrt{a}$

Find a likely function rule for each of the following. Show your work. A) $\begin{array} { | l | l | } \hline x & f ( x ) \\\hline 2 & 15 \\\hline 3 & 19 \\\hline 4 & 23 \\\hline 5 & 27 \\\hline \ldots & \ldots \\\hline\end{array}$ f(x)= B) $\begin{array} { | l | l | } \hline x & y \\\hline 1 & 14 \\\hline 2 & 11 \\\hline 3 & 8 \\\hline 4 & 5 \\\hline \ldots & \ldots \\\hline\end{array}$ y= C) $\begin{array} { | l | l | } \hline x & g ( x ) \\\hline 4 & 29 \\\hline 3 & 21 \\\hline 1 & 5 \\\hline 2 & 13 \\\hline \ldots & \ldots \\\hline\end{array}$ g(x)= D) $\begin{array} { | l | l | } \hline x & y \\\hline 0 & 5 \\\hline 1 & 6 \\\hline 2 & 9 \\\hline 3 & 14 \\\hline 4 & 21 \\\hline \ldots & \ldots \\\hline\end{array}$ y=

Two students have been looking for a function rule for the data below. n | f(n) 1 3 2 5 3 8 4 12 Akeena: "I got f(n) = $\frac { 1 } { 2 }$ n(n +1) + 2." Bea: "Yes, but my mom worked a long time on it and said f(n) = $\frac { 1 } { 2 }$ n(n + 1) + 2 + (n - 1)(n - 2)(n - 3)(n - 4). Let's ask the teacher." How would you respond to the two students?

Calculate the sum and product of the pairs of polynomials. A) $4 x ^ { 2 } + {}^{-} 7 x + 3 \text { and } 3 x + 5$ B) $5 x + {}^{-} 6 \text { and } {}^{-} 3 x + 7$

For each situation, write an equation using a variable. Then solve the equation to answer the question. A) Krista has 4 more T-shirts than Leeann has, and Marika has 2 fewer T-shirts than Leeann has. The three students have 20 T-shirts in all. How many T-shirts does each have? B) The entry fee at the fair is $5, and ride tickets cost 75¢ each. Pat spent $19.25 in all, for entry and ride tickets. How many ride tickets did Pat buy?

What is the difference between an arithmetic sequence and a geometric sequence?