Answer:
It doesn't have a solution because if you try to graph each line y=5x+10 and y=5x-8, you will have a parallel line
Step-by-step explanation:
Answer:
![y = 1.5x - 8](https://tex.z-dn.net/?f=y%20%3D%201.5x%20-%208)
Step-by-step explanation:
<u>Step 1: Solve for y in the first equation</u>
![2y = 3x + 10](https://tex.z-dn.net/?f=2y%20%3D%203x%20%2B%2010)
![\frac{2y}{2}=\frac{3}{2}x + \frac{10}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B2y%7D%7B2%7D%3D%5Cfrac%7B3%7D%7B2%7Dx%20%2B%20%5Cfrac%7B10%7D%7B2%7D)
![y = 1.5x + 5](https://tex.z-dn.net/?f=y%20%3D%201.5x%20%2B%205)
<u>Step 2: Determine the important aspects</u>
We know that our line is parallel to the other line that has a slope of 1.5 which means that our slope is also going to be 1.5. We also know that our line crosses the point (2, -5) which means that we can use the point slope form to determine our equation
Point Slope Form → ![(y-y_1) = m(x - x_1)](https://tex.z-dn.net/?f=%28y-y_1%29%20%3D%20m%28x%20-%20x_1%29)
<u>Step 3: Plug in the information and solve</u>
![(y-(-5)) = 1.5(x - 2)](https://tex.z-dn.net/?f=%28y-%28-5%29%29%20%3D%201.5%28x%20-%202%29)
![y + 5 = 1.5x -3](https://tex.z-dn.net/?f=y%20%2B%205%20%3D%201.5x%20-3)
![y + 5 - 5 = 1.5x -3 - 5](https://tex.z-dn.net/?f=y%20%2B%205%20-%205%20%3D%201.5x%20-3%20-%205)
![y = 1.5x - 8](https://tex.z-dn.net/?f=y%20%3D%201.5x%20-%208)
Answer: ![y = 1.5x - 8](https://tex.z-dn.net/?f=y%20%3D%201.5x%20-%208)
Answer:
<h2>
![x = \frac{1}{2}](https://tex.z-dn.net/?f=x%20%3D%20%20%5Cfrac%7B1%7D%7B2%7D%20)
</h2>
Step-by-step explanation:
![30x+18=35−4x](https://tex.z-dn.net/?f=30x%2B18%3D35%E2%88%924x)
First of all using the addition property add 4x to both sides
That's
![30x + 4x + 18 = 35 + 4x - 4x \\ 34x + 18 = 35](https://tex.z-dn.net/?f=30x%20%2B%204x%20%2B%2018%20%3D%2035%20%2B%204x%20-%204x%20%5C%5C%2034x%20%2B%2018%20%3D%2035)
Next using the subtraction property subtract 18 from both sides to make 34x stand alone
We have
![34x + 18 - 18 = 35 - 18 \\ 34x = 17](https://tex.z-dn.net/?f=34x%20%2B%2018%20-%2018%20%3D%2035%20-%2018%20%5C%5C%2034x%20%3D%20%2017)
<u>Divide both sides by 34</u>
That's
![\frac{34x}{34} = \frac{17}{34}](https://tex.z-dn.net/?f=%20%5Cfrac%7B34x%7D%7B34%7D%20%20%3D%20%20%5Cfrac%7B17%7D%7B34%7D%20)
We have the final answer as
![x = \frac{1}{2}](https://tex.z-dn.net/?f=x%20%3D%20%20%5Cfrac%7B1%7D%7B2%7D%20)
Hope this helps you
Answer:
approx. 24.6 ft
Step-by-step explanation:
x=the distance of the fire from the base of the tower
200ft=the height of the tower
7 degrees=the angle of depression
Using these values you can draw a diagram that highlights that you need to use trig. to work out the answer.
Using Tan:
Tan 7=x/200 ft
multiply both sides by 200 ft
200*tan 7=24.55691218
approx. 24.6 ft