Answer:
Sabrina bought 3 pounds of bananas.
Step-by-step explanation:
Given equations are:
a + b = 8 Eqn 1
0.95a + 1.10b = 8.05 Eqn 2
As we have to find the number of pounds of bananas bought, we will eliminate the variable a from the equation.
Multiplying Eqn 1 by 0.95
0.95(a+b=8)
0.95a+0.95b=7.60 Eqn 3
Subtracting Eqn 3 from Eqn 2
(0.95a+1.10b)-(0.95a+0.95b)=8.05-7.60
0.95a+1.10b-0.95a-0.95b=0.45
0.15b = 0.45
Dividing both sides by 0.15
Hence,
Sabrina bought 3 pounds of bananas.
Answer: see proof below
<u>Step-by-step explanation:</u>
Given: A + B + C = π → C = π - (A + B)
→ sin C = sin(π - (A + B)) cos C = sin(π - (A + B))
→ sin C = sin (A + B) cos C = - cos(A + B)
Use the following Sum to Product Identity:
sin A + sin B = 2 cos[(A + B)/2] · sin [(A - B)/2]
cos A + cos B = 2 cos[(A + B)/2] · cos [(A - B)/2]
Use the following Double Angle Identity:
sin 2A = 2 sin A · cos A
<u>Proof LHS → RHS</u>
LHS: (sin 2A + sin 2B) + sin 2C
![\text{Factor:}\qquad \qquad \qquad 2\sin C\cdot [\cos (A-B)+\cos (A+B)]](https://tex.z-dn.net/?f=%5Ctext%7BFactor%3A%7D%5Cqquad%20%5Cqquad%20%5Cqquad%202%5Csin%20C%5Ccdot%20%5B%5Ccos%20%28A-B%29%2B%5Ccos%20%28A%2BB%29%5D)
LHS = RHS: 4 cos A · cos B · sin C = 4 cos A · cos B · sin C 
Answer:
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Step-by-step explanation:
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Hello!!!
So we are given some number, which we will call x for simplicity purposes. They tell us that number is divided by 4 so x/4, and then 17 is added, so we now have x/4+17 and they tell us this combination is equal to 25 so set what we have so far equal to 25. So we have finally x/4+17=25. Now we just solve for x!
x/4+17=25 first we subtract 17 from both sides leaving us with, x/4=8 so now See need to multiply by 4 on both sides to clear the fraction and get x alone. So we have now
x=8*4 so x=32
Now we can check our answer by putting our value of x into equation and make sure it’s true. So we have for our check,
32/4+17=25 and 32/4 is 8 so we have 8+17=25 which is 25=25 so our equation is true and our answer is correct!!
Hope this helps you understand the concept!! Any questions please just ask!! Thank you so much!!
Distributive property
Use multiplication to simplify
Simplify using addition
Add both sides by 9 to simplify
Multiply each side by -3/4 and simplify
