Answer:
81x^2 + 12x + 4
Step-by-step explanation:
This expression doesn't factor
Answer:
7.21 units
Step-by-step explanation:
The shortest length needed to connect the house to the existing pipeline is the perpendicular distance between the location of the house (2,9) and the line y = 2/3x - 1.
The perpendicular distance (d) between a point (
) and the line Ax + By + C = 0 is given as:
![d=\frac{|Ax_1+By_1+C|}{\sqrt{A^2+B^2} }](https://tex.z-dn.net/?f=d%3D%5Cfrac%7B%7CAx_1%2BBy_1%2BC%7C%7D%7B%5Csqrt%7BA%5E2%2BB%5E2%7D%20%7D)
The line is given by y = 2/3 x - 1; 2/3x - y - 1 = 0. The point = (2, 9)
hence A = 2/3, B = -1, C = -1,
. Therefore:
![d=\frac{|\frac{2}{3}(2)+(-1)(9)+(-1) |}{\sqrt{\frac{2}{3}^2+(-1)^2 } } \\\\d=7.21](https://tex.z-dn.net/?f=d%3D%5Cfrac%7B%7C%5Cfrac%7B2%7D%7B3%7D%282%29%2B%28-1%29%289%29%2B%28-1%29%20%7C%7D%7B%5Csqrt%7B%5Cfrac%7B2%7D%7B3%7D%5E2%2B%28-1%29%5E2%20%7D%20%7D%20%5C%5C%5C%5Cd%3D7.21)
Set Lauren's age equal to L.
Using what the problem gave us, we can quickly set up an equation:
5L - 2 = 2L
Solving this equation, we get 3L = 2. L = 2/3 Lauren is 2/3 of a year old.
Use desmos it's a great app.
Answer:
<h3>
m∠A = 46°</h3>
Step-by-step explanation:
∠A and∠B being complementary means m∠A+m∠B=90°
m∠A = (4x+6)° and m∠B = (4x+4)°
so:
4x+6 + 4x+4 = 90
8x + 10 = 90
8x = 80
x = 10
m∠A = (4•10+6)° = 46°