Let's take the non-linear equation:
![{x}^{2} = \sqrt{3} y](https://tex.z-dn.net/?f=%20%7Bx%7D%5E%7B2%7D%20%20%3D%20%20%5Csqrt%7B3%7D%20y)
First Make The Equation To Be In Terms of Y
*Divide Both sides by
![\sqrt{3}](https://tex.z-dn.net/?f=%20%5Csqrt%7B3%7D%20)
![\frac{ {x}^{2} }{ \sqrt{3} } = \frac{ \sqrt{3} y}{ \sqrt{3} }](https://tex.z-dn.net/?f=%20%5Cfrac%7B%20%7Bx%7D%5E%7B2%7D%20%7D%7B%20%5Csqrt%7B3%7D%20%7D%20%20%3D%20%20%5Cfrac%7B%20%5Csqrt%7B3%7D%20y%7D%7B%20%5Csqrt%7B3%7D%20%7D%20)
*Simplify
![\frac{ {x}^{2} }{ \sqrt{3} } = y](https://tex.z-dn.net/?f=%20%5Cfrac%7B%20%7Bx%7D%5E%7B2%7D%20%7D%7B%20%5Csqrt%7B3%7D%20%7D%20%20%3D%20y)
You shouldn't keep a radical in the denominator, however we leave it for the purpose of the reciprocal.
*Take The Reciprocal Of Both Sides
![\frac{ \sqrt{3} }{ {x}^{2} } = \frac{1}{y}](https://tex.z-dn.net/?f=%20%5Cfrac%7B%20%5Csqrt%7B3%7D%20%7D%7B%20%7Bx%7D%5E%7B2%7D%20%7D%20%3D%20%20%5Cfrac%7B1%7D%7By%7D%20%20)
A Linear Equation Takes The Format:
![y = mx + b](https://tex.z-dn.net/?f=y%20%3D%20mx%20%2B%20b)
So,
![\frac{1}{y} = y](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7By%7D%20%20%3D%20y)
![b = 0](https://tex.z-dn.net/?f=b%20%3D%200)
![m(slope) = \frac{ \sqrt{3} }{x}](https://tex.z-dn.net/?f=m%28slope%29%20%3D%20%20%5Cfrac%7B%20%5Csqrt%7B3%7D%20%7D%7Bx%7D%20)
![x = \frac{1}{x}](https://tex.z-dn.net/?f=x%20%3D%20%20%5Cfrac%7B1%7D%7Bx%7D%20)
Resulting in :
Answer:
51
Step-by-step explanation:
90-39 = 51
The car's average rate is 43.7 mph. The bicycle's average rate is 12.3 mph.
To get this solution, let the bicycle's average rate be (x) and the car's average rate be (x + 31.4) mph.
Distance= Speed x Time
364 = (x + x + 31.4) 6.5
364 = (2x + 31.4) 6.5
364/6.5 = 2x + 31.4
56 = 2x + 31.4
56 - 31.4 = 2x
24.6 = 2x
24.6/2 = x
12.3 = x
x = 12.3 mph
x+31.4 = 43.7 mph
Answer:
13) 2 g
14) 5,000 mL
15) 104,000 m
16) 160 mm
17) 5,600,000 mg
19) 0.25 km
Step-by-step explanation:
13. Convert 2,000 mg to g:
1 mg = 0.001 g
(2,000 mg * 0.001 g) / 1 mg = 2 g
14. Convert 5 L to mL:
1 L = 1000 mL
(5 L * 1000 mL) / 1 L = 5,000 mL
15. Convert 104 km to m:
1 km = 1000 m
(104 km * 1000 m) / 1 km = 104,000 m
16. Convert 16 cm to mm:
1 cm = 10 mm
(16 cm * 10 mm) / 1 cm = 160 mm
17. Convert 5.6 kg to mg:
1 kg = 1,000,000 mg
(5.6 kg * 1,000,000 mg) / 1 kg = 5,600,000 mg
19) Convert 250 m to km:
1 m = 0.001 km
(250 m * 0.001 km) / 1 m = 0.25 km