<h3>
Answer: Choice A</h3>
Arrow from 0 to -8 (pointing left). Another arrow from -8 to -6 (pointing right)
See diagram below
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Explanation:
Let's think of this in terms of money. Writing -8 means we are 8 dollars in debt. Since -8 is listed first, this means we start at 0 and go 8 units to the left along the number line, to land on -8.
Then we'll go 2 units to the right to land ultimately at -6. This is because of the "-(-2)" portion, which is the same as "+2". Subtracting a negative is the same as adding. The two negatives cancel each other out.
Going back to the money example, if we have a balance of -8 (we're 8 dollars in debt) and taking away 2 IOU notes means we're 6 dollars in debt. Subtracting a negative can be thought of as taking away debt.
Side note: If we had -8-2, then we would go 2 units to the left of -8 to land on -10 instead.
Answer:
![JL=54](https://tex.z-dn.net/?f=JL%3D54)
Step-by-step explanation:
We are given that K is the midpoint of JL. Using this information, we want to find JL.
By the definition of midpoint, this means that:
![JK=KL](https://tex.z-dn.net/?f=JK%3DKL)
Substitute them for their equations:
![8x+11=14x-1](https://tex.z-dn.net/?f=8x%2B11%3D14x-1)
Solve for <em>x.</em> Subtract 8<em>x</em> from both sides:
![11=6x-1](https://tex.z-dn.net/?f=11%3D6x-1)
Add 1 to both sides:
![6x=12](https://tex.z-dn.net/?f=6x%3D12)
And divide both sides by 6. Hence:
![x=2](https://tex.z-dn.net/?f=x%3D2)
JL is the sum of JK and KL. Hence:
![JK+KL=JL](https://tex.z-dn.net/?f=JK%2BKL%3DJL)
Since JK = KL, substitute either one for the other:
![JK+(JK)=2JK=JL](https://tex.z-dn.net/?f=JK%2B%28JK%29%3D2JK%3DJL)
Substitute JK for its equation:
![2(8x+11)=JL](https://tex.z-dn.net/?f=2%288x%2B11%29%3DJL)
Since we know that <em>x</em> = 2:
![2(8(2)+11)=2(16+11)=2(27)=54=JL](https://tex.z-dn.net/?f=2%288%282%29%2B11%29%3D2%2816%2B11%29%3D2%2827%29%3D54%3DJL)
Thus:
![JL=54](https://tex.z-dn.net/?f=JL%3D54)
Answer:
v_top = 2400 mi/hr
v_w = 400 mi/h
Step-by-step explanation:
Given:
- Total distance D = 4800 mi
- Headwind journey time taken t_up= 3 hr
- Tailwind journey time taken t_down = 2 hr
Find:
Find the top speed of Luke's snow speeder and the speed of the wind.
Solution:
- The speed of Luke v_l is in stationary frame is given by:
v_l = v_w + v_l/w
Where,
v_w: Wind speed
v_l/w: Luke speed relative to wind.
- The top speed is attained on his returned journey with tail wind. We will use distance time relationship to calculate as follows:
v_top = D / t_down
v_top = 4800 / 2
v_top = v_down = 2400 mi/hr
- Similarly his speed on his journey up with head wind was v_up:
v_up = D / t_up
v_up = 4800 / 3
v_up = 1600 mi/hr
- Now use the frame relations to find the wind speed v_w:
v_down = v_w + v_l/w
v_up = -v_w + v_l/w
- Solve equations simultaneously:
2400 = v_w + v_l/w
1600 = -v_w + v_l/w
4000 = 2*v_l/w
v_l/w = 2000 mi/h
v_w = 400 mi/h
Since the cost of the spray paint is approx $1.50,
The range for the cost of the spray paint is'
![\pm0.05\text{ dollars}](https://tex.z-dn.net/?f=%5Cpm0.05%5Ctext%7B%20dollars%7D)
Therefore, the coach budget should be between,
![\begin{gathered} \text{for }+0.05\text{ dollars,} \\ =1.5+0.05=1.55\text{ dollars and,} \\ \text{for -0.05 dollars,} \\ =1.5-0.05=1.45\text{ dollars} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%5Ctext%7Bfor%20%7D%2B0.05%5Ctext%7B%20dollars%2C%7D%20%5C%5C%20%3D1.5%2B0.05%3D1.55%5Ctext%7B%20dollars%20and%2C%7D%20%5C%5C%20%5Ctext%7Bfor%20-0.05%20dollars%2C%7D%20%5C%5C%20%3D1.5-0.05%3D1.45%5Ctext%7B%20dollars%7D%20%5Cend%7Bgathered%7D)
Hence, the budget of the coach should be between $1.45 and $1.55.