practice b
1-6 order of operations
simplify each expression.
1. ( 18 - 12 + 4^2 )
2. ( 5 cdot 3 + 2(4) )
3. ( -27 + 6(3 - 5) )
4. ( -7 - (2^4 div 8) )
5. ( -6 cdot 3 + |-3(-4 + 2^3)| )
6. ( \frac{-16 + 4}{2(sqrt{13} - 4)} )

evaluate each expression for the given value of the variable.
7. ( 3 - y^2 + 7 ) for ( y = 5 )
8. ( -3(x + 12 cdot 2) ) for ( x = -8 )
9. ( (m + 6) div (2 - 5) ) for ( m = 9 )
10. ( -5t + 12 - \frac{1}{2}t ) for ( t = -10 )

translate each word phrase into a numerical or algebraic expression.
11. the product of 6 and the sum of 3 and 20
12. the absolute value of the difference of ( m ) and ( -15 )
13. the quotient of ( -18 ) and the sum of ( -2 ) and ( d )

degrees fahrenheit ( f ) can be converted to degrees celsius ( c ) using the expression ( \frac{5}{9}(f - 32) ). degrees celsius can be converted to degrees fahrenheit using the expression ( \frac{9}{5}c + 32 ).

14. the hottest recorded day in florida history was ( 109^circ f ), which occurred on june 29, 1931 in monticello. convert this temperature to degrees celsius. round your answer to the nearest tenth of a degree.

15. the coldest recorded day in florida history was about ( -18.9^circ c ), which occurred on february 13, 1899 in the city of tallahassee. convert this temperature to degrees fahrenheit. round your answer to the nearest tenth of a degree.

Question

practice b
1-6 order of operations
simplify each expression.
1. ( 18 - 12 + 4^2 )
2. ( 5 cdot 3 + 2(4) )
3. ( -27 + 6(3 - 5) )
4. ( -7 - (2^4 div 8) )
5. ( -6 cdot 3 + |-3(-4 + 2^3)| )
6. ( \frac{-16 + 4}{2(sqrt{13} - 4)} )

evaluate each expression for the given value of the variable.
7. ( 3 - y^2 + 7 ) for ( y = 5 )
8. ( -3(x + 12 cdot 2) ) for ( x = -8 )
9. ( (m + 6) div (2 - 5) ) for ( m = 9 )
10. ( -5t + 12 - \frac{1}{2}t ) for ( t = -10 )

translate each word phrase into a numerical or algebraic expression.
11. the product of 6 and the sum of 3 and 20
12. the absolute value of the difference of ( m ) and ( -15 )
13. the quotient of ( -18 ) and the sum of ( -2 ) and ( d )

degrees fahrenheit ( f ) can be converted to degrees celsius ( c ) using the expression ( \frac{5}{9}(f - 32) ). degrees celsius can be converted to degrees fahrenheit using the expression ( \frac{9}{5}c + 32 ).

14. the hottest recorded day in florida history was ( 109^circ f ), which occurred on june 29, 1931 in monticello. convert this temperature to degrees celsius. round your answer to the nearest tenth of a degree.

15. the coldest recorded day in florida history was about ( -18.9^circ c ), which occurred on february 13, 1899 in the city of tallahassee. convert this temperature to degrees fahrenheit. round your answer to the nearest tenth of a degree.

Accepted Answer

### Problem 1: $18 - 12 + 4^2$
# Explanation:
## Step 1: Calculate the exponent
First, we handle the exponentiation: $4^2 = 16$
## Step 2: Perform subtraction and addition from left to right
Now, substitute the result back into the expression: $18 - 12 + 16$
First, $18 - 12 = 6$
Then, $6 + 16 = 22$
# Answer: $22$

### Problem 2: $5 \cdot 3 + 2(4)$
# Explanation:
## Step 1: Perform multiplication operations
First, calculate $5 \cdot 3 = 15$ and $2(4)=8$
## Step 2: Perform addition
Now, add the results: $15 + 8 = 23$
# Answer: $23$

### Problem 3: $-2[7 + 6(3 - 5)]$
# Explanation:
## Step 1: Simplify the innermost parentheses
First, calculate $3 - 5=-2$
## Step 2: Perform the multiplication inside the brackets
Then, $6(-2)= - 12$
## Step 3: Perform the addition inside the brackets
Next, $7+( - 12)=7 - 12=-5$
## Step 4: Perform the final multiplication
Finally, $-2\times(-5) = 10$
# Answer: $10$

### Problem 4: $-7-(2^4\div8)$
# Explanation:
## Step 1: Calculate the exponent
First, $2^4 = 16$
## Step 2: Perform the division
Then, $16\div8 = 2$
## Step 3: Perform the subtraction
Finally, $-7 - 2=-9$
# Answer: $-9$

### Problem 5: $-6\cdot3+\vert-3(-4 + 2^3)\vert$
# Explanation:
## Step 1: Calculate the exponent inside the absolute value
First, $2^3 = 8$
## Step 2: Simplify the expression inside the absolute value
Then, $-4 + 8 = 4$
## Step 3: Perform the multiplication inside the absolute value
Next, $-3\times4=-12$
## Step 4: Take the absolute value
Then, $\vert-12\vert = 12$
## Step 5: Perform the multiplication outside the absolute value
Next, $-6\times3=-18$
## Step 6: Perform the addition
Finally, $-18 + 12=-6$
# Answer: $-6$

### Problem 6: $\frac{-16 + 4}{2(\sqrt{13}-4)}$
# Explanation:
## Step 1: Simplify the numerator
First, $-16 + 4=-12$
## Step 2: Rationalize the denominator (multiply numerator and denominator by the conjugate of the denominator $\sqrt{13}+4$)
The denominator is $2(\sqrt{13}-4)$, so we multiply numerator and denominator by $\sqrt{13}+4$:
$$
\begin{align*}
\frac{-12}{2(\sqrt{13}-4)}\times\frac{\sqrt{13}+4}{\sqrt{13}+4}&=\frac{-12(\sqrt{13}+4)}{2((\sqrt{13})^2-4^2)}\
&=\frac{-12(\sqrt{13}+4)}{2(13 - 16)}\
&=\frac{-12(\sqrt{13}+4)}{2(-3)}\
&=\frac{-12(\sqrt{13}+4)}{-6}\
&= 2(\sqrt{13}+4)\
&=2\sqrt{13}+8
\end{align*}
$$
If we want a decimal approximation, $\sqrt{13}\approx3.6055$, so $2\times3.6055 + 8\approx7.211+8 = 15.211\approx15.2$ (but the exact form is $2\sqrt{13}+8$)
# Answer: $2\sqrt{13}+8$ (or approximately $15.2$)

### Problem 7: $3 - y^2+7$ for $y = 5$
# Explanation:
## Step 1: Substitute $y = 5$ into the expression
First, calculate $y^2$ when $y = 5$: $y^2=5^2 = 25$
## Step 2: Simplify the expression
Now, substitute back: $3-25 + 7$
First, $3-25=-22$
Then, $-22 + 7=-15$
# Answer: $-15$

### Problem 8: $-3(x + 12\cdot2)$ for $x=-8$
# Explanation:
## Step 1: Simplify the expression inside the parentheses
First, calculate $12\cdot2 = 24$
## Step 2: Substitute $x=-8$ into the expression inside the parentheses
Then, $x + 24=-8 + 24 = 16$
## Step 3: Perform the multiplication
Finally, $-3\times16=-48$
# Answer: $-48$

### Problem 9: $(m + 6)\div(2 - 5)$ for $m = 9$
# Explanation:
## Step 1: Substitute $m = 9$ into the numerator
First, $m + 6=9 + 6 = 15$
## Step 2: Simplify the denominator
Then, $2 - 5=-3$
## Step 3: Perform the division
Finally, $15\div(-3)=-5$
# Answer: $-5$

### Problem 10: $-5t+12-\frac{1}{2}t$ for $t=-10$
# Explanation:
## Step 1: Combine like terms
First, combine the $t$ terms: $-5t-\frac{1}{2}t=-\frac{10}{2}t-\frac{1}{2}t=-\frac{11}{2}t$
So the expression becomes $-\frac{11}{2}t + 12$
## Step 2: Substitute $t=-10$ into the expression
Then, $-\frac{11}{2}\times(-10)+12$
First, $-\frac{11}{2}\times(-10)=55$
Then, $55 + 12 = 67$
# Answer: $67$

### Problem 11: the product of 6 and the sum of 3 and 20
# Explanation:
First, find the sum of 3 and 20: $3 + 20 = 23$
Then, find the product of 6 and 23: $6\times23$
# Answer: $6(3 + 20)$ (or $138$ if we calculate the product)

### Problem 12: the absolute value of the difference of $m$ and $-15$
# Explanation:
The difference of $m$ and $-15$ is $m-(-15)=m + 15$
Then, take the absolute value of that difference: $\vert m-(-15)\vert=\vert m + 15\vert$
# Answer: $\vert m + 15\vert$

### Problem 13: the quotient of $-18$ and the sum of $-2$ and $d$
# Explanation:
First, find the sum of $-2$ and $d$: $-2 + d$
Then, find the quotient of $-18$ and that sum: $\frac{-18}{-2 + d}$
# Answer: $\frac{-18}{-2 + d}$

### Problem 14: Convert $109^{\circ}F$ to degrees Celsius using $C=\frac{5}{9}(F - 32)$
# Explanation:
## Step 1: Substitute $F = 109$ into the formula
First, $F-32=109 - 32 = 77$
## Step 2: Multiply by $\frac{5}{9}$
Then, $C=\frac{5}{9}\times77=\frac{385}{9}\approx42.8$ (rounded to the nearest tenth)
# Answer: Approximately $42.8^{\circ}C$

### Problem 15: Convert $-18.9^{\circ}C$ to degrees Fahrenheit using $F=\frac{9}{5}C+32$
# Explanation:
## Step 1: Substitute $C=-18.9$ into the formula
First, $\frac{9}{5}\times(-18.9)=-34.02$
## Step 2: Add 32
Then, $F=-34.02 + 32=-2.02\approx - 2.0$ (rounded to the nearest tenth)
# Answer: Approximately $-2.0^{\circ}F$

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QUESTION IMAGE

Question

Explanation:

Problem 1: \(18 - 12 + 4^2\)

Step 1: Calculate the exponent

Step 2: Perform subtraction and addition from left to right

Step 1: Perform multiplication operations

Step 2: Perform addition

Step 1: Simplify the innermost parentheses

Step 2: Perform the multiplication inside the brackets

Step 3: Perform the addition inside the brackets

Step 4: Perform the final multiplication

Answer:

Problem 2: \(5 \cdot 3 + 2(4)\)