Answer:
Scientist B
Step-by-step explanation:
1 kg = 2.2 lbs
1L = 2.11 pints
So let's convert Scientist B's data.
3.0lbs salt = 3.0/2.2 = 1.36kg
6 pints water = 6/2.11 = 2.84L water
Scientist A
1kg salt
3.0L water
We now figure out the concentration of salt in water.
Scientist A Scientist B
1kg/3.0L = .33kg/L 1.36kg/2.84L = .48kg/L
So scientist B had a more concentrated solution.
−2(6x+5)=74
Simplify both sides of the equation.
−2(6x+5)=74
−2 x 6x−2 x 5=74
−12x−10=74
Add 10 to both sides.
−12x−10=74
+10 +10
−12x=84
Divide both sides by -12.
−12x
=
84
/−12 /-12
x=-7
hope it helps!
Answer:
The estimated distance is 8.1cm.
The actual distance is 8.106cm.
Step-by-step explanation:
Given that the Pythogorean Theorem, c² = a² + b². Then substitute the following values into the formula :
![{c}^{2} = {a}^{2} + {b}^{2}](https://tex.z-dn.net/?f=%20%7Bc%7D%5E%7B2%7D%20%20%3D%20%20%7Ba%7D%5E%7B2%7D%20%20%2B%20%20%7Bb%7D%5E%7B2%7D%20)
Let a = 5.1cm,
Let b = 6.3cm,
![{c}^{2} = {5.1}^{2} + {6.3}^{2}](https://tex.z-dn.net/?f=%20%7Bc%7D%5E%7B2%7D%20%20%3D%20%20%7B5.1%7D%5E%7B2%7D%20%20%2B%20%20%7B6.3%7D%5E%7B2%7D%20)
![{c}^{2} = 26.01 + 39.69](https://tex.z-dn.net/?f=%20%7Bc%7D%5E%7B2%7D%20%20%3D%2026.01%20%2B%2039.69)
![{c}^{2} = 65.7](https://tex.z-dn.net/?f=%20%7Bc%7D%5E%7B2%7D%20%20%3D%2065.7)
![c = \sqrt{65.7}](https://tex.z-dn.net/?f=c%20%3D%20%20%5Csqrt%7B65.7%7D%20)
![c = 8.106cm \: (3d.p)](https://tex.z-dn.net/?f=c%20%3D%208.106cm%20%5C%3A%20%283d.p%29)
27 divided by 15 is 1.8, so that should be the correct answer.
- Slope-Intercept Form: y = mx + b, with m = slope and b = y-intercept
- Slope Formula:
![\frac{y_2-y_1}{x_2-x_1}](https://tex.z-dn.net/?f=%5Cfrac%7By_2-y_1%7D%7Bx_2-x_1%7D)
So firstly, to find the slope of this equation, plug the two points, (1,1) and (-3,2), into the slope formula and solve as such:
![\frac{1-2}{1-(-3)}=-\frac{1}{4}](https://tex.z-dn.net/?f=%5Cfrac%7B1-2%7D%7B1-%28-3%29%7D%3D-%5Cfrac%7B1%7D%7B4%7D)
Next, plug either one of the points into the x and y coordinates to solve for b as such:
![2=-\frac{1}{4}*-3+b\\2=\frac{3}{4}+b\\\frac{5}{4}=b](https://tex.z-dn.net/?f=2%3D-%5Cfrac%7B1%7D%7B4%7D%2A-3%2Bb%5C%5C2%3D%5Cfrac%7B3%7D%7B4%7D%2Bb%5C%5C%5Cfrac%7B5%7D%7B4%7D%3Db)
<u>Our final equation is
, or the third option.</u>