Answer : 16 kites
David Made 4
Stephan Made : 3*4 = 12
Altogether the boys made : 16 kites
Make a system of equations.
![\sf0.10d+0.25q=6](https://tex.z-dn.net/?f=%5Csf0.10d%2B0.25q%3D6)
![\sf~q = 2d](https://tex.z-dn.net/?f=%5Csf~q%20%3D%202d)
Plug in 2d for 'q' in the first equation:
![\sf0.10d+0.25q=6](https://tex.z-dn.net/?f=%5Csf0.10d%2B0.25q%3D6)
![\sf0.10d+0.25(2d)=6](https://tex.z-dn.net/?f=%5Csf0.10d%2B0.25%282d%29%3D6)
Multiply:
![\sf0.10d+0.50d=6](https://tex.z-dn.net/?f=%5Csf0.10d%2B0.50d%3D6)
Combine like terms:
![\sf0.60d=6](https://tex.z-dn.net/?f=%5Csf0.60d%3D6)
Divide 0.60 to both sides:
![\sf~d=10](https://tex.z-dn.net/?f=%5Csf~d%3D10)
Now plug this into any of the two equations to find 'q':
![\sf~q = 2d](https://tex.z-dn.net/?f=%5Csf~q%20%3D%202d)
![\sf~q = 2(10)](https://tex.z-dn.net/?f=%5Csf~q%20%3D%202%2810%29)
![\sf~q = 20](https://tex.z-dn.net/?f=%5Csf~q%20%3D%2020)
So she has 10 dimes and 20 quarters.
Following are simplifications to the given expression:
Given:
![\bold{(3x-1)(x-3)}](https://tex.z-dn.net/?f=%5Cbold%7B%283x-1%29%28x-3%29%7D)
To find:
simplify=?
Solution:
![\to \bold{(3x-1)(x-3)}\\\\\to \bold{(3x^2-9x-x+3)}\\\\\to \bold{(3x^2-10x+3)}\\\\](https://tex.z-dn.net/?f=%5Cto%20%5Cbold%7B%283x-1%29%28x-3%29%7D%5C%5C%5C%5C%5Cto%20%5Cbold%7B%283x%5E2-9x-x%2B3%29%7D%5C%5C%5C%5C%5Cto%20%5Cbold%7B%283x%5E2-10x%2B3%29%7D%5C%5C%5C%5C)
Therefore, the final answer is "
".
Learn more:
brainly.com/question/1661958
the horizontal distance between the child and the crackers is 2.9 ft .
<u>Step-by-step explanation:</u>
Here we have , A child spots crackers in a cabinet at an angle of elevation of 50. The crackers are 3.5 ft above the child. We need to find what is the horizontal distance between the child and the crackers . Let's find out:
According to question , we have a right angle triangle with parameters as :
, Where x is angle of elevation !
We know that , ![Tanx = \frac{Perpendicular}{Base}](https://tex.z-dn.net/?f=Tanx%20%3D%20%5Cfrac%7BPerpendicular%7D%7BBase%7D)
⇒ ![Tanx = \frac{Perpendicular}{Base}](https://tex.z-dn.net/?f=Tanx%20%3D%20%5Cfrac%7BPerpendicular%7D%7BBase%7D)
⇒ ![Tan50 = \frac{3.5}{Base}](https://tex.z-dn.net/?f=Tan50%20%3D%20%5Cfrac%7B3.5%7D%7BBase%7D)
⇒ ![Base = \frac{3.5}{Tan50}](https://tex.z-dn.net/?f=Base%20%3D%20%5Cfrac%7B3.5%7D%7BTan50%7D)
⇒ ![Base = \frac{3.5}{1.19}](https://tex.z-dn.net/?f=Base%20%3D%20%5Cfrac%7B3.5%7D%7B1.19%7D)
⇒ ![Base =2.9ft](https://tex.z-dn.net/?f=Base%20%3D2.9ft)
Therefore , the horizontal distance between the child and the crackers is 2.9 ft .
0.9 + 0.02 + 0.004 is the expanded form of 0.924, it is just taking apart each place in the number.