7.) write a verbal expression for the algebraic expression $\frac{r^4}{9}$.\
$\bigcirc$ r to the fourth power multiplied by nine.\
$\bigcirc$ r to the fourth power divided by nine.\
$\bigcirc$ the quotient of nine and r to the fourth power.\
$\bigcirc$ four times r divided by nine.\
write a verbal expression for the algebraic expression $2a + 6$.\
$\bigcirc$ two times a decreased by six.\
$\bigcirc$ two times the sum of a and six.\
$\bigcirc$ the sum of two and a plus six.\
$\bigcirc$ two times a plus six.\
9.) write a verbal expression for the algebraic expression $(c - 2)d$.\
$\bigcirc$ c minus 2 times d.\
$\bigcirc$ the sum of c and 2 times d.\
$\bigcirc$ the difference of c and 2 times d.\
$\bigcirc$ the difference of c and 2 increased by d.\
10.) which algebraic expression represents the given verbal expression?\
the quotient of seven and the sum of twice a number and three square\
$\bigcirc$ $7 \cdot 2x + 3^2$\
$\bigcirc$ $7 \cdot (2x + 3^2)$\
$\bigcirc$ $7 \div (2x + 3^2)$\
$\bigcirc$ $7 \div 2x + 3^2$\
11.) write an algebraic expression for the given verbal expression:\
a number, n, increased by sixteen\
12.) which equation represents the given sentence?\
the sum of 5 times a number m and 12 is equal to 27.\
$\bigcirc$ $5m + 12 = 27$\
$\bigcirc$ $5(m + 12) = 27$\
$\bigcirc$ $5 + 12m = 27$\
$\bigcirc$ $5(12m) = 27$

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Accepted Answer

### Question 7
# Brief Explanations:
The algebraic expression is $\frac{r^4}{9}$. "r to the fourth power" is $r^4$, and dividing by 9 gives "r to the fourth power divided by nine". The other options are incorrect: first multiplies by 9, third is 9 divided by $r^4$, fourth is $4r/9$.
# Answer: B. r to the fourth power divided by nine. (Assuming the second option is B, as per typical multiple - choice numbering; if the original options were labeled, use the correct label. Here, the second option text is "r to the fourth power divided by nine".)

### Question (Algebraic expression $2a + 6$)
# Brief Explanations:
The expression $2a+6$ means 2 multiplied by $a$ (two times $a$) and then added to 6 (plus six). "Two times a decreased by six" would be $2a - 6$, "Two times the sum of $a$ and six" would be $2(a + 6)$, "The sum of two and $a$ plus six" is $(2 + a)+6$ which is not the same as $2a+6$.
# Answer: D. Two times a plus six. (Assuming the fourth option is D; use the correct label based on original numbering. The fourth option text is "Two times a plus six".)

### Question 9
# Brief Explanations:
The expression $(c - 2)d$ can be thought of as (the difference of $c$ and 2) multiplied by $d$, which is equivalent to "the difference of $c$ and 2 increased by $d$" (in terms of verbal expression interpretation, as multiplication can be expressed as "increased by" in some verbal - algebraic translations). "c minus 2 times $d$" is $c-2d$, "The sum of $c$ and 2 times $d$" is $c + 2d$, "The difference of $c$ and 2 times $d$" is $c-2d$.
# Answer: D. The difference of c and 2 increased by d. (Assuming the fourth option is D; use the correct label based on original numbering. The fourth option text is "The difference of c and 2 increased by d".)

### Question 10
# Brief Explanations:
"The quotient of seven and the sum of twice a number and three squared" means 7 divided by (the sum of $2x$ and $3^2$). So the algebraic expression is $7\div(2x + 3^2)$. $7\cdot2x + 3^2$ is 7 times $2x$ plus $3^2$, $7\cdot(2x + 3^2)$ is 7 times the sum, $7\div2x+3^2$ is 7 divided by $2x$ plus $3^2$, which is not the same as the quotient of 7 and the sum.
# Answer: C. $7\div(2x + 3^2)$ (Assuming the third option is C; use the correct label based on original numbering. The third option text is $7\div(2x + 3^2)$.)

### Question 11
# Brief Explanations:
"A number, $n$, increased by sixteen" means we add 16 to $n$. The algebraic expression for this is $n + 16$.
# Answer: $n + 16$

### Question 12
# Brief Explanations:
"5 times a number $m$" is $5m$, "the sum of 5 times $m$ and 12" is $5m+12$, and "is equal to 27" gives the equation $5m + 12=27$. $5(m + 12)=27$ is 5 times the sum of $m$ and 12, $5 + 12m=27$ is 5 plus 12 times $m$, $5(12m)=27$ is 5 times 12 times $m$.
# Answer: A. $5m + 12 = 27$ (Assuming the first option is A; use the correct label based on original numbering. The first option text is $5m + 12 = 27$.)

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Question (Algebraic expression \(2a + 6\))