First blank: sin. C = h/a
The ratio for sin. is opposite (the height) over hypotenuse (a).
Second blank: Area = (1/2)b(a sin. C)
In this substitution, we are substituting the value of h into the traditional area of a triangle formula.
Third Blank: Area = (1/2)ab(sin C)
We are using the commutative property to move the position of a.
Hope this helps and good luck in your classes!
157 degrees ... set 4x-5 = x+16 then solve, you should get x=7, plug in 7 for one of the equations and you'll get 23. subtract 23 from 180 and get 157. hope that helped :)
• So we know that.....
x represent bags of snack and y is bottles of water.
This equations shows the total amount and the cost of each water bottle and snack:
20.00 = 2.50x + 1.00y
Total: $20.00
Snack: $2.50
Water Bottle: $1.00
And this question shows the total items:
11 = x + y
Which there will be some snack + some water bottle = 11 items
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• Now I’m going to first solve for x, which is the amount of bags of snack.
I will use the equation, 11 = x + y.
(First, we’ll subtract y from both side, since we’re solving for x [UNDO])
11 = x + y
-y = - y
_______
11 - y = x —> so x is equal to 11 minus y.
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• Now we’re going to plug the 11 - y as x in the equation: 20.00 = 2.50x + 1.00y to solve for y.
20.00 = 2.50 (11 - y) + 1.00y
20.00 = 27.5 - 2.50y + 1.00y (Distributed)
20.00 = 27.5 - 1.50y (Combine like terms)
20.00 = 27.5 - 1.50y
-27.5 = -27.5 (Subtract -27.5 both side)
——————————
-7.5 = - 1.50y
-7.5 = -1.50y
—— ——— (Divide both side by -1.50)
- 1.50 = -1.50
5 = y
y is equals to 5, which means that there are 5 water bottles.
Now we know there are 11 items total and because there are 5 water bottles, there will be 6 bags of snacks. 11-5=6
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ANSWER:
They bought 6 bags of snacks! :)
The answer is 31.5 in.^3 because
4.5 • 3.5 • 2 = 31.5in.^3
The volume of a cone is (1/3) that of its similar cylinder.
Thus the volume of the cone B would be:
