Answer:
Step-by-step explanation:
Given:
To find: points of intersection of the given lines
Solution:
In substitution method, the system of equations is solved by expressing one variable in terms of another, as a result, removing one variable from an equation.
Put 
in the equation 
![2x+8y=7\\2[\frac{1+2y}{5}]+8y=7\\ 2+4y+40y=35\\44y=35-2\\44y=33\\y=\frac{33}{44}\\ =\frac{3}{4}](https://tex.z-dn.net/?f=2x%2B8y%3D7%5C%5C2%5B%5Cfrac%7B1%2B2y%7D%7B5%7D%5D%2B8y%3D7%5C%5C%202%2B4y%2B40y%3D35%5C%5C44y%3D35-2%5C%5C44y%3D33%5C%5Cy%3D%5Cfrac%7B33%7D%7B44%7D%5C%5C%20%3D%5Cfrac%7B3%7D%7B4%7D)
Put 
in the equation
![x=\frac{1+2y}{5}\\=\frac{1}{5}[1+2(\frac{3}{4})]\\=\frac{1}{5}[1+(\frac{3}{2})]\\\\=\frac{1}{5}(\frac{2+3}{2}) \\\\=\frac{1}{5}(\frac{5}{2})\\\\=\frac{1}{2}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B1%2B2y%7D%7B5%7D%5C%5C%3D%5Cfrac%7B1%7D%7B5%7D%5B1%2B2%28%5Cfrac%7B3%7D%7B4%7D%29%5D%5C%5C%3D%5Cfrac%7B1%7D%7B5%7D%5B1%2B%28%5Cfrac%7B3%7D%7B2%7D%29%5D%5C%5C%5C%5C%3D%5Cfrac%7B1%7D%7B5%7D%28%5Cfrac%7B2%2B3%7D%7B2%7D%29%20%5C%5C%5C%5C%3D%5Cfrac%7B1%7D%7B5%7D%28%5Cfrac%7B5%7D%7B2%7D%29%5C%5C%5C%5C%3D%5Cfrac%7B1%7D%7B2%7D)
Therefore,
Answer:
Step-by-step explanation:
Pythagorean theorem: base ² +altitude² = hypotenuse²
1) hypotenuse² = base² + altitude²
x² = 6² + 3²
= 36 + 9
= 45
x = √45
x = 6.7 cm
4) base ² +altitude² = hypotenuse²
x ² + 3.7 ² = 4.2 ²
x ² + 13.69 = 17.64
x ² = 17.64 - 13.69 = 3.95
x = √3.95
x = 1.99 cm
10)c ² = a ² + b ²
= 3 ² +4 ²
= 9 + 16
c ² = 25
c = √25 = 5
11) a ² + b ² = c ²
9 ² +b² = 13 ²
81 + b² = 169
b² = 169 - 81 = 88
b = 9.38
12) a² + b² = c²
12² + b² = 22²
144 + b² = 484
b² = 484 - 144 = 340
b =√340 = 18.44
Acceleration = change in velocity / time
a: acceleration
Vf: final velocity
Vi: initial velocity
t: time
a = (Vf - Vi) / t
a = (3.3 - 0) / 15
a = 0.22 m/s^2
5x-40=3x+8
Add 40 to both sides
5x=3x+48
Subtract 3x from both sides
2x=48
Divide by two on both sides
X=24
<h2>
Horizontal distance when projectile strikes water surface is 170 .02 feet</h2>
Step-by-step explanation:
The height is given by
We need to find when it strikes the water surface,
At water surface h = 0 feet
Substituting
Solving this quadratic equation to get x.
-32x² + 2500x + 500000 = 0
32x² - 2500x - 500000 = 0
x = 170 .02 feet or x = -91.90 feet
Negative x is not possible
Horizontal distance when projectile strikes water surface = 170 .02 feet
