Answer:
-18
Remember PEMDAS.
Step-by-step explanation:
Answer:
Louise used the most flour.
Step-by-step explanation:
Okay so first off 12% of 5 pounds would be 0.6 pounds. So we can put that Stan used 0.6 pounds. Then 0.11 of the total flour would be the same as 11% of 5 pounds, which is 0.55 pounds. So Liam used 0.55 pounds. We already know that Louise used 0.7 pounds of flour so we can order it like this.
Louise=0.7 Pounds
Stan=0.6 Pounds
Liam=0.55 Pounds
Answer:
4200
Step-by-step explanation:
Answer:
An individual's effective tax rate represents the average of all tax brackets that their income passes through as well as the total of all deductions and credits that lower their total income to their taxable income.
Step-by-step explanation:
Answer:
![AB = \sqrt{a^2 + b^2-2abCos\ C}](https://tex.z-dn.net/?f=AB%20%3D%20%5Csqrt%7Ba%5E2%20%2B%20b%5E2-2abCos%5C%20C%7D)
Step-by-step explanation:
Given:
The above triangle
Required
Solve for AB in terms of a, b and angle C
Considering right angled triangle BOC where O is the point between b-x and x
From BOC, we have that:
![Sin\ C = \frac{h}{a}](https://tex.z-dn.net/?f=Sin%5C%20C%20%3D%20%5Cfrac%7Bh%7D%7Ba%7D)
Make h the subject:
![h = aSin\ C](https://tex.z-dn.net/?f=h%20%3D%20aSin%5C%20C)
Also, in BOC (Using Pythagoras)
![a^2 = h^2 + x^2](https://tex.z-dn.net/?f=a%5E2%20%3D%20h%5E2%20%2B%20x%5E2)
Make
the subject
![x^2 = a^2 - h^2](https://tex.z-dn.net/?f=x%5E2%20%3D%20a%5E2%20-%20h%5E2)
Substitute
for h
becomes
![x^2 = a^2 - (aSin\ C)^2](https://tex.z-dn.net/?f=x%5E2%20%3D%20a%5E2%20-%20%28aSin%5C%20C%29%5E2)
![x^2 = a^2 - a^2Sin^2\ C](https://tex.z-dn.net/?f=x%5E2%20%3D%20a%5E2%20-%20a%5E2Sin%5E2%5C%20C)
Factorize
![x^2 = a^2 (1 - Sin^2\ C)](https://tex.z-dn.net/?f=x%5E2%20%3D%20a%5E2%20%281%20-%20Sin%5E2%5C%20C%29)
In trigonometry:
![Cos^2C = 1-Sin^2C](https://tex.z-dn.net/?f=Cos%5E2C%20%3D%201-Sin%5E2C)
So, we have that:
![x^2 = a^2 Cos^2\ C](https://tex.z-dn.net/?f=x%5E2%20%3D%20a%5E2%20Cos%5E2%5C%20C)
Take square roots of both sides
![x= aCos\ C](https://tex.z-dn.net/?f=x%3D%20aCos%5C%20C)
In triangle BOA, applying Pythagoras theorem, we have that:
![AB^2 = h^2 + (b-x)^2](https://tex.z-dn.net/?f=AB%5E2%20%3D%20h%5E2%20%2B%20%28b-x%29%5E2)
Open bracket
![AB^2 = h^2 + b^2-2bx+x^2](https://tex.z-dn.net/?f=AB%5E2%20%3D%20h%5E2%20%2B%20b%5E2-2bx%2Bx%5E2)
Substitute
and
in ![AB^2 = h^2 + b^2-2bx+x^2](https://tex.z-dn.net/?f=AB%5E2%20%3D%20h%5E2%20%2B%20b%5E2-2bx%2Bx%5E2)
![AB^2 = h^2 + b^2-2bx+x^2](https://tex.z-dn.net/?f=AB%5E2%20%3D%20h%5E2%20%2B%20b%5E2-2bx%2Bx%5E2)
![AB^2 = (aSin\ C)^2 + b^2-2b(aCos\ C)+(aCos\ C)^2](https://tex.z-dn.net/?f=AB%5E2%20%3D%20%28aSin%5C%20C%29%5E2%20%2B%20b%5E2-2b%28aCos%5C%20C%29%2B%28aCos%5C%20C%29%5E2)
Open Bracket
![AB^2 = a^2Sin^2\ C + b^2-2abCos\ C+a^2Cos^2\ C](https://tex.z-dn.net/?f=AB%5E2%20%3D%20a%5E2Sin%5E2%5C%20C%20%2B%20b%5E2-2abCos%5C%20C%2Ba%5E2Cos%5E2%5C%20C)
Reorder
![AB^2 = a^2Sin^2\ C +a^2Cos^2\ C + b^2-2abCos\ C](https://tex.z-dn.net/?f=AB%5E2%20%3D%20a%5E2Sin%5E2%5C%20C%20%2Ba%5E2Cos%5E2%5C%20C%20%2B%20b%5E2-2abCos%5C%20C)
Factorize:
![AB^2 = a^2(Sin^2\ C +Cos^2\ C) + b^2-2abCos\ C](https://tex.z-dn.net/?f=AB%5E2%20%3D%20a%5E2%28Sin%5E2%5C%20C%20%2BCos%5E2%5C%20C%29%20%2B%20b%5E2-2abCos%5C%20C)
In trigonometry:
![Sin^2C + Cos^2 = 1](https://tex.z-dn.net/?f=Sin%5E2C%20%2B%20Cos%5E2%20%3D%201)
So, we have that:
![AB^2 = a^2 * 1 + b^2-2abCos\ C](https://tex.z-dn.net/?f=AB%5E2%20%3D%20a%5E2%20%2A%201%20%2B%20b%5E2-2abCos%5C%20C)
![AB^2 = a^2 + b^2-2abCos\ C](https://tex.z-dn.net/?f=AB%5E2%20%3D%20a%5E2%20%2B%20b%5E2-2abCos%5C%20C)
Take square roots of both sides
![AB = \sqrt{a^2 + b^2-2abCos\ C}](https://tex.z-dn.net/?f=AB%20%3D%20%5Csqrt%7Ba%5E2%20%2B%20b%5E2-2abCos%5C%20C%7D)