Answer:
Distance from the point to the line will be ![\sqrt{5}m](https://tex.z-dn.net/?f=%5Csqrt%7B5%7Dm)
Step-by-step explanation:
We have given the equation of the line is y = 2x\
So the equation of line will be y-2x = 0
Point from which we have to find the distance is (-2,1)
Distance from a point to line is given by
, here A = -2 , B = 1 and C = 0
And point x = -2 and y = 1
So ![d=\frac{-2\times -2+1\times 1+0}{\sqrt{(-2)^2+1^2}}=\sqrt{5}m](https://tex.z-dn.net/?f=d%3D%5Cfrac%7B-2%5Ctimes%20-2%2B1%5Ctimes%201%2B0%7D%7B%5Csqrt%7B%28-2%29%5E2%2B1%5E2%7D%7D%3D%5Csqrt%7B5%7Dm)
So distance from the point to the line will be ![\sqrt{5}m](https://tex.z-dn.net/?f=%5Csqrt%7B5%7Dm)
Original and bigger prism are similar with scale factor k = 4, so:
new surface area = k² * original surface area = 4² * 228 = 16 * 228 = 3648 m²
and
new volume = k³ * original volume = 4³ * 216 = 64 * 216 = 13824 m³
False. All points on the graph of an equation satisfies the equation.
1. Let A(a,b) be a point in the coordinate axis. The reflection of A with respect to the x-axis is the point A'(a, -b).
2. So the reflection of C(6, 4) is C'(6, -4)
3. Remark, a picture is always helpful when dealing with reflections.
The new mixture is acquired from the sum of the concentration divided by the total number of gallons. Or we could write it like this.
mix =
![\cfrac{\text{concentrate} \times gallons+\text{concentrate} \times gallons}{\text{the total number of gallons}}](https://tex.z-dn.net/?f=%20%5Ccfrac%7B%5Ctext%7Bconcentrate%7D%20%5Ctimes%20gallons%2B%5Ctext%7Bconcentrate%7D%20%5Ctimes%20gallons%7D%7B%5Ctext%7Bthe%20total%20number%20of%20gallons%7D%7D%20)
Input the numbers
mix =
![\cfrac{50 \% \times 3+30 \% \times 9}{3+9}](https://tex.z-dn.net/?f=%20%5Ccfrac%7B50%20%5C%25%20%5Ctimes%203%2B30%20%5C%25%20%5Ctimes%209%7D%7B3%2B9%7D%20)
simplify the dividend and divisor
mix =
![\cfrac{150 \%+270 \%}{12}](https://tex.z-dn.net/?f=%20%5Ccfrac%7B150%20%5C%25%2B270%20%5C%25%7D%7B12%7D%20)
mix =
![\cfrac{420 \%}{12}](https://tex.z-dn.net/?f=%20%5Ccfrac%7B420%20%5C%25%7D%7B12%7D%20)
mix =
![\cfrac{420 \%}{12}](https://tex.z-dn.net/?f=%20%5Ccfrac%7B420%20%5C%25%7D%7B12%7D%20)
mix = 35%
The new concentration is 35%