Question

1. no calculator. simplify each expression. 4² + 1 = 6⁻¹ = 2(3² - 5) = 10. solve for x. 4 - 2(x + 1) = 18 11. evaluate the expression mx + b if m = 1/2, x = -8 and b = 20. 12. which of the sequences below is not arithmetic? a) 12, 12.5, 13, 13.5, ... b) 33, 31.5, 30, 28.5, ... c) 5, 7, 10, 12, ... d) -5, -8, -11, -14, ... 13. what is the greatest common factor (gcf) of 15 and 40? 14. use the table to: find h(0). find x if h(x) = 4. 15. what is the domain and range of the graph below? use interval notation. 16. the daily revenue of daves sno - stand for selling x snowballs is represented by the function r(). explain the meaning of r(104).

Explanation:

Step1: Solve problem 9

First expression

Calculate $4^2+1$. First find $4^2 = 16$, then $16 + 1=17$.

Second expression

Calculate $6^{-1}$. By the rule of negative - exponents $a^{-n}=\frac{1}{a^{n}}$, so $6^{-1}=\frac{1}{6}$.

Third expression

Calculate $2(3^2 - 5)$. First find $3^2=9$, then $9 - 5 = 4$, and $2\times4 = 8$.

Step2: Solve problem 10

Solve the equation $4-2(x + 1)=18$.
First, distribute the $-2$: $4-2x-2 = 18$.
Combine like - terms: $2-2x=18$.
Subtract 2 from both sides: $-2x=18 - 2=16$.
Divide both sides by $-2$: $x=-8$.

Step3: Solve problem 11

Evaluate $mx + b$ with $m=\frac{1}{2}$, $x=-8$ and $b = 20$.
Substitute the values: $\frac{1}{2}\times(-8)+20$.
First, calculate $\frac{1}{2}\times(-8)=-4$.
Then, $-4 + 20=16$.

Step4: Solve problem 12

For an arithmetic sequence, the common difference $d=a_{n + 1}-a_{n}$ is constant.
For option A: $12.5-12 = 0.5$, $13 - 12.5=0.5$, $13.5 - 13 = 0.5$, it is arithmetic.
For option B: $31.5-33=-1.5$, $30 - 31.5=-1.5$, $28.5 - 30=-1.5$, it is arithmetic.
For option C: $7 - 5 = 2$, $10 - 7 = 3$, the differences are not constant, so it is not arithmetic.
For option D: $-8-(-5)=-3$, $-11-(-8)=-3$, $-14-(-11)=-3$, it is arithmetic.

Step5: Solve problem 13

Find the GCF of 15 and 40.
Factor 15: $15 = 3\times5$.
Factor 40: $40=2\times2\times2\times5$.
The common factor is 5, so the GCF is 5.

Step6: Solve problem 14

Since the table is not shown completely, assume we need to use the concept of function evaluation. If we know the values in the table corresponding to $x = 0$ to find $h(0)$ and the value of $x$ for which $h(x)=4$. But without the full table, we can't give a specific numerical answer for this part.

Answer:

1. $4^2 + 1=17$, $6^{-1}=\frac{1}{6}$, $2(3^2 - 5)=8$
2. $x=-8$
3. 16
4. C) 5, 7, 10, 12, ...
5. 5
6. Incomplete table, can't answer fully