Answer:
b = ![\frac{7}{12}](https://tex.z-dn.net/?f=%5Cfrac%7B7%7D%7B12%7D)
Step-by-step explanation:
b +
= 1
← change to an improper fraction
b +
= ![\frac{5}{4}](https://tex.z-dn.net/?f=%5Cfrac%7B5%7D%7B4%7D)
Multiply through by 12 ( the LCM of 3 and 4 ) to clear the fractions
12b + 8 = 15 ( subtract 8 from both sides )
12b = 7 ( divide both sides by 12 )
b = ![\frac{7}{12}](https://tex.z-dn.net/?f=%5Cfrac%7B7%7D%7B12%7D)
Answer:
Step-by-step explanation:
cos (2α)*sin (α-β)-cos(β-α)*sin(2α)
cos (β-α)=cos {-(α-β)}=cos (α-β)
[cos (-x)=cos x]
sin(α-β)*cos (2α)-cos (α-β)*sin (2α)=sin (α-β-2α)=sin (-α-β)
=sin {-(α+β)}
=-sin (α+β)
Answer:
Approximately 7.8 units
Step-by-step explanation:
To find the distance between any two points, we can use the distance formula:
![d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B%28x_2-x_1%29%5E2%2B%28y_2-y_1%29%5E2%7D)
From the graph, we can see that A is (0,0). Let's let this be x₁ and y₁.
B is (-5,6). Let's let this be x₂ and y₂. So, substitute:
![d=\sqrt{(-5-0)^2+(6-0)^2}](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B%28-5-0%29%5E2%2B%286-0%29%5E2%7D)
Simplify:
![d=\sqrt{(-5)^2+(6)^2}](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B%28-5%29%5E2%2B%286%29%5E2%7D)
Square:
![d=\sqrt{25+36}](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B25%2B36%7D)
Add:
![d=\sqrt{61}](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B61%7D)
Take the square root. Use a calculator:
![d\approx7.8](https://tex.z-dn.net/?f=d%5Capprox7.8)
So, the distance between them is about 7.8 units.
And we're done!