Answer:
∠EFG = 48°
Step-by-step explanation:
As FH bisects ∠EFG , ∠EFH = ∠HFG .
We know that ∠EFH = (-5x + 89)° . So ∠HFG = ∠EFH = (-5x + 89)°
Also, ∠HFG + ∠EFH = ∠EFG
=> 2(-5x + 89)° = (61 - x)°
=> -10x + 178 = 61 - x
=> 10x - x = 178 - 61
=> 9x = 117
=> x = 117 / 9 = 13
Putting the value of 'x' in ∠EFG gives :-
(61 - x)° = (61 - 13)° = 48°
<u>the question is </u> Calculate the value of the copper in the coin
Step 1
Find the volume of the coin
we know that
the volume of a cylinder is equal to
![V=\pi r^{2}h](https://tex.z-dn.net/?f=V%3D%5Cpi%20r%5E%7B2%7Dh)
where
r is the radius of the coin
h is the thickness of the coin
in this problem we have
Diameter=19 mm=1.9 cm
r=D/2------> r=1.9/2=0.95 cm
h=1.5 mm=0.15 cm
substitute the values in the formula
![V=\pi*0.95^{2}*0.15=0.425\ cm^{3}](https://tex.z-dn.net/?f=V%3D%5Cpi%2A0.95%5E%7B2%7D%2A0.15%3D0.425%5C%20cm%5E%7B3%7D)
Step 2
<u>Find the mass of copper in the coin</u>
we know that
the density is equal to
![Density=mass/volume](https://tex.z-dn.net/?f=Density%3Dmass%2Fvolume)
Solve for the mass
![mass=Density*volume](https://tex.z-dn.net/?f=mass%3DDensity%2Avolume)
we have
![Density=8.9\ gr/cm^{3}\\Volume=0.425\ cm^{3}](https://tex.z-dn.net/?f=Density%3D8.9%5C%20gr%2Fcm%5E%7B3%7D%5C%5CVolume%3D0.425%5C%20cm%5E%7B3%7D)
substitute in the formula
![mass=8.9*0.425=3.785\ gr](https://tex.z-dn.net/?f=mass%3D8.9%2A0.425%3D3.785%5C%20gr)
Step 3
<u>Find the cost</u>
we know that
the market price of the copper is $2.15 per pound
1 pound=453.592 grams
convert gram to pounds
3.785 gr=3.785/453.592=0.0083 pounds
0.0083*$2.15=$0.018=$0.02
therefore
<u>the answer is</u>
$0.02
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Hope it helps.
The answer to your question is x = -3
Answer:
![(g\cdot f) = -3x^2-3](https://tex.z-dn.net/?f=%28g%5Ccdot%20f%29%20%3D%20%20-3x%5E2-3)
Step-by-step explanation:
![f(x) = x^2 + 1](https://tex.z-dn.net/?f=f%28x%29%20%3D%20x%5E2%20%2B%201)
![g(x) = -3](https://tex.z-dn.net/?f=g%28x%29%20%3D%20-3)
The problem state to multiply the function
and
so the symbol seems to be incorrect.
We actually want to calculate
![g(x) f(x) =gf(x) = (-3) \cdot (x^2+1)= -3x^2-3](https://tex.z-dn.net/?f=g%28x%29%20%20f%28x%29%20%3Dgf%28x%29%20%3D%20%20%28-3%29%20%20%5Ccdot%20%28x%5E2%2B1%29%3D%20-3x%5E2-3)
Note
![g\circ f(x)=g(f(x))=g(x^2+1)=-3](https://tex.z-dn.net/?f=g%5Ccirc%20f%28x%29%3Dg%28f%28x%29%29%3Dg%28x%5E2%2B1%29%3D-3)