Question

1. no calculator. simplify each expression. 4² + 1 = 6⁻¹ = 2(a² - 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. x, h(x); -2, 16; 0, 8; 2, 4; 4, 0 15. what is the domain and range of the graph below? use interval notation. domain: range: 16. the daily revenue of dave’s snowball stand for selling x snowballs is represented by the function r(x). explain the meaning of r(104).

Explanation:

Step1: Simplify $4^{2}+1$

$4^{2}+1=16 + 1=17$

Step2: Simplify $6^{-1}$

$6^{-1}=\frac{1}{6}$

Step3: Simplify $2(x^{2}-5)$

$2(x^{2}-5)=2x^{2}-10$

Step4: Solve $4 - 2(x + 1)=18$ for $x$

First, distribute the -2: $4-2x - 2=18$.
Then combine like - terms: $2-2x=18$.
Subtract 2 from both sides: $-2x=16$.
Divide both sides by -2: $x=-8$

Step5: Evaluate $mx + b$ with $m=\frac{1}{2}$, $x = - 8$ and $b = 20$

Substitute the values: $\frac{1}{2}\times(-8)+20=-4 + 20=16$

Step6: Determine non - arithmetic sequence

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

Step7: Find GCF of 15 and 40

Factor 15: $15 = 3\times5$
Factor 40: $40=2^{3}\times5$
The GCF is 5

Step8: Find $h(0)$ from the table

When $x = 0$, $h(0)=8$

Step9: Find $x$ when $h(x)=4$ from the table

When $h(x)=4$, $x = 2$

Step10: Find domain and range from the graph

The domain is the set of all $x$ - values. The graph exists from $x=-3$ to $x = 3$, so the domain is $[-3,3]$
The range is the set of all $y$ - values. The graph has a maximum around $y = 4$ and minimum around $y=-4$, so the range is $[-4,4]$

Step11: Explain $R(104)$

The function $R(x)$ represents the daily revenue of Dave's Snowball Stand for selling $x$ snowballs. $R(104)$ represents the daily revenue when 104 snowballs are sold.

Answer:

1. $4^{2}+1 = 17$
2. $6^{-1}=\frac{1}{6}$
3. $2(x^{2}-5)=2x^{2}-10$
4. $x=-8$
5. $mx + b=16$
6. C. $5,7,10,12,\cdots$
7. 5
8. $h(0)=8$
9. $x = 2$
10. Domain: $[-3,3]$, Range: $[-4,4]$
11. $R(104)$ represents the daily revenue when 104 snowballs are sold.