Answer:
![z =3\sqrt{13}](https://tex.z-dn.net/?f=z%20%3D3%5Csqrt%7B13%7D)
Step-by-step explanation:
In the figure you can identify up to 3 straight triangles.
To solve the problem, write the Pythagorean theorem for each triangle.
<em>Triangle 1</em>
![13^2 = z^2 + x^2](https://tex.z-dn.net/?f=13%5E2%20%3D%20z%5E2%20%2B%20x%5E2)
<em>Triangle 2</em>
![z^2 = y^2 + 9^2](https://tex.z-dn.net/?f=z%5E2%20%3D%20y%5E2%20%2B%209%5E2)
<em>Triangle 3</em>
![x^2 = y^2 + 4^2](https://tex.z-dn.net/?f=x%5E2%20%3D%20y%5E2%20%2B%204%5E2)
Now substitute equation 2 and equation 3 in equation 1 and solve for y.
![13^2 = y^2 + 9^2 + y^2 + 4^2](https://tex.z-dn.net/?f=13%5E2%20%3D%20y%5E2%20%2B%209%5E2%20%2B%20y%5E2%20%2B%204%5E2)
![13^2 = 2y^2 + 9^2 + 4^2](https://tex.z-dn.net/?f=13%5E2%20%3D%202y%5E2%20%2B%209%5E2%20%2B%204%5E2)
![169 = 2y^2 + 81 + 16](https://tex.z-dn.net/?f=169%20%3D%202y%5E2%20%2B%2081%20%2B%2016)
![2y^2 =72](https://tex.z-dn.net/?f=2y%5E2%20%3D72)
![y^2 =36](https://tex.z-dn.net/?f=y%5E2%20%3D36)
![y =6](https://tex.z-dn.net/?f=y%20%3D6)
substitute the value of y in the second equation and solve for z
![z^2 = 6^2 + 9^2](https://tex.z-dn.net/?f=z%5E2%20%3D%206%5E2%20%2B%209%5E2)
![z^2 = 36 + 81](https://tex.z-dn.net/?f=z%5E2%20%3D%2036%20%2B%2081)
![z^2 = 117](https://tex.z-dn.net/?f=z%5E2%20%3D%20117)
![z = \sqrt{117}](https://tex.z-dn.net/?f=z%20%3D%20%5Csqrt%7B117%7D)
![z =3\sqrt{13}](https://tex.z-dn.net/?f=z%20%3D3%5Csqrt%7B13%7D)
Answer:
just use factoring and you will get your answer
Step-by-step explanation:
The height of the balloon above the ground is about 7.07 feet.
<h3>
What is trigonometric ratio</h3>
Trigonometric ratio is used to show the relationship between the sides and angles of a right angled triangle.
Let h represent the height of the balloon from the ground, hence:
sin(45) = h/10
h = 7.07 feet
The height of the balloon above the ground is about 7.07 feet.
Find out more on trigonometric ratio at: brainly.com/question/1201366
We can use the point-slope equation:
![y = mx + b](https://tex.z-dn.net/?f=y%20%3D%20mx%20%2B%20b)
m, the slope, is 3/4:
![y = \frac{3}{4} x + b](https://tex.z-dn.net/?f=y%20%3D%20%20%5Cfrac%7B3%7D%7B4%7D%20x%20%2B%20b)
To find b, we plug in the point (4,1/3):
![( \frac{1}{3} ) = \frac{3}{4} (4) + b \\ \frac{1}{3} = 3 + b \\ \frac{1}{3} = \frac{9}{3} + b](https://tex.z-dn.net/?f=%28%20%5Cfrac%7B1%7D%7B3%7D%20%29%20%3D%20%20%5Cfrac%7B3%7D%7B4%7D%20%284%29%20%2B%20b%20%5C%5C%20%20%5Cfrac%7B1%7D%7B3%7D%20%20%3D%203%20%2B%20b%20%5C%5C%20%20%5Cfrac%7B1%7D%7B3%7D%20%3D%20%20%5Cfrac%7B9%7D%7B3%7D%20%20%2B%20b)
![- \frac{8}{3} = b](https://tex.z-dn.net/?f=%20-%20%20%5Cfrac%7B8%7D%7B3%7D%20%20%3D%20b)
Therefore, the point-slope equation is
![y = \frac{3}{4} x - \frac{8}{3}](https://tex.z-dn.net/?f=y%20%3D%20%20%5Cfrac%7B3%7D%7B4%7D%20x%20-%20%20%5Cfrac%7B8%7D%7B3%7D%20)
Now we have to see which answer matches.
![y - \frac{3}{4} = \frac{1}{3} (x - 4) \\ y - \frac{3}{4} = \frac{1}{3} x - \frac{4}{3} \\ y - \frac{9}{12} = \frac{1}{3} x - \frac{16}{12}](https://tex.z-dn.net/?f=y%20-%20%20%5Cfrac%7B3%7D%7B4%7D%20%20%3D%20%20%5Cfrac%7B1%7D%7B3%7D%20%28x%20-%204%29%20%5C%5C%20y%20-%20%20%5Cfrac%7B3%7D%7B4%7D%20%20%3D%20%20%5Cfrac%7B1%7D%7B3%7D%20x%20-%20%20%5Cfrac%7B4%7D%7B3%7D%20%20%5C%5C%20y%20-%20%20%5Cfrac%7B9%7D%7B12%7D%20%20%3D%20%20%5Cfrac%7B1%7D%7B3%7D%20x%20-%20%20%5Cfrac%7B16%7D%7B12%7D)
![y = \frac{1}{3} x - \frac{7}{12}](https://tex.z-dn.net/?f=y%20%3D%20%20%5Cfrac%7B1%7D%7B3%7D%20x%20-%20%20%5Cfrac%7B7%7D%7B12%7D%20)
Since this is not the same, we try the next one.
![y - \frac{1}{3} = \frac{3}{4} (x - 4) \\ y - \frac{1}{3} = \frac{3}{4} x - 3 \\ y - \frac{1}{3} = \frac{3}{4} x - \frac{9}{3}](https://tex.z-dn.net/?f=y%20-%20%20%5Cfrac%7B1%7D%7B3%7D%20%20%3D%20%20%5Cfrac%7B3%7D%7B4%7D%20%28x%20-%204%29%20%5C%5C%20y%20-%20%20%5Cfrac%7B1%7D%7B3%7D%20%20%3D%20%20%5Cfrac%7B3%7D%7B4%7D%20x%20-%203%20%5C%5C%20y%20-%20%20%5Cfrac%7B1%7D%7B3%7D%20%20%3D%20%20%5Cfrac%7B3%7D%7B4%7D%20x%20-%20%20%5Cfrac%7B9%7D%7B3%7D)
![y = \frac{3}{4} x - \frac{8}{3}](https://tex.z-dn.net/?f=y%20%3D%20%20%5Cfrac%7B3%7D%7B4%7D%20x%20-%20%20%5Cfrac%7B8%7D%7B3%7D%20)
This is the same, so this is the answer. We should still double-check the other answers.
![y - \frac{1}{3} = 4(x - \frac{3}{4} ) \\ y - \frac{1}{3} = 4x - 3 \\ y - \frac{1}{3} = 4x - \frac{9}{3}](https://tex.z-dn.net/?f=y%20-%20%20%5Cfrac%7B1%7D%7B3%7D%20%20%3D%204%28x%20-%20%20%5Cfrac%7B3%7D%7B4%7D%20%29%20%5C%5C%20y%20-%20%20%5Cfrac%7B1%7D%7B3%7D%20%20%3D%204x%20-%203%20%5C%5C%20y%20-%20%20%5Cfrac%7B1%7D%7B3%7D%20%20%3D%204x%20-%20%20%5Cfrac%7B9%7D%7B3%7D)
![y = 4x - \frac{8}{3}](https://tex.z-dn.net/?f=y%20%3D%204x%20-%20%20%5Cfrac%7B8%7D%7B3%7D%20)
This one is not equivalent.
![y - 4 = \frac{3}{4} (x - \frac{1}{3} ) \\ y - 4 = \frac{3}{4} x - \frac{1}{4} \\ y - \frac{16}{4} = \frac{3}{4} x - \frac{1}{4}](https://tex.z-dn.net/?f=y%20-%204%20%3D%20%20%5Cfrac%7B3%7D%7B4%7D%20%28x%20-%20%20%5Cfrac%7B1%7D%7B3%7D%20%29%20%5C%5C%20y%20-%204%20%3D%20%20%5Cfrac%7B3%7D%7B4%7D%20x%20-%20%20%5Cfrac%7B1%7D%7B4%7D%20%20%5C%5C%20y%20-%20%20%5Cfrac%7B16%7D%7B4%7D%20%20%3D%20%20%5Cfrac%7B3%7D%7B4%7D%20x%20-%20%20%5Cfrac%7B1%7D%7B4%7D%20)
![y = \frac{3}{4} x + \frac{15}{4}](https://tex.z-dn.net/?f=y%20%3D%20%20%5Cfrac%7B3%7D%7B4%7D%20x%20%2B%20%20%5Cfrac%7B15%7D%7B4%7D%20)
This one also does not work.
The answer is the second one: