Answer:
The 7th term of the sequence is 0.000768
Step-by-step explanation:
As given, the sequence is : 12, -2.4 , 0.48, ....
The first term = 12
Second term = -2.4
Third term = 0.48
Common ratio = ![\frac{-2.4}{12} = \frac{0.48}{-2.4} = -0.2](https://tex.z-dn.net/?f=%5Cfrac%7B-2.4%7D%7B12%7D%20%3D%20%5Cfrac%7B0.48%7D%7B-2.4%7D%20%3D%20-0.2)
Fourth term = 0.48(-0.2) = -0.096
Fifth term = -0.096(-0.2) = 0.0192
Sixth term = 0.0192(-0.2) = -0.00384
Seventh term = -0.00384(-0.2) = 0.000768
Answer:
15 pounds
Step-by-step explanation:
5 bags @ 3 pounds
5 x 3 = 15 lbs.
Answer:
1.)1.3
2.)0.13
3.)13
4.)0.13
5.)True, because multiplying by .001 is the same as dividing by 1000
Step-by-step explanation:
Use point-slope formula---> y-y1=m(x-x1)
Let y1 equal -9, let x1 equal -10, and let m equal 3
Plug in and solve
y-(-9)=3(x-(-10)
y+9=3(x+10)
y+9=3x+30
Subtract nine from both sides
y=3x+21(This is slope form, i might have gone too far)
Answer:
![x\approx24^\circ](https://tex.z-dn.net/?f=x%5Capprox24%5E%5Ccirc)
Step-by-step explanation:
We know that r and s have a combined length of 70. Therefore:
![r+s=70](https://tex.z-dn.net/?f=r%2Bs%3D70)
Notice that we can determine r by using the Pythagorean Theorem. In this case, r is the hypotenuse, and 20 and 8 are the legs. Therefore:
![a^2+b^2=c^2](https://tex.z-dn.net/?f=a%5E2%2Bb%5E2%3Dc%5E2)
Substituting 20 and 8 for a and b and r for c yields:
![20^2+8^2=r^2](https://tex.z-dn.net/?f=20%5E2%2B8%5E2%3Dr%5E2)
Compute:
![464=r^2](https://tex.z-dn.net/?f=464%3Dr%5E2)
Therefore:
![r=\sqrt{464}=\sqrt{16\cdot 29}=4\sqrt{29}](https://tex.z-dn.net/?f=r%3D%5Csqrt%7B464%7D%3D%5Csqrt%7B16%5Ccdot%2029%7D%3D4%5Csqrt%7B29%7D)
Now, we can determine s. We know that:
![s+r=70](https://tex.z-dn.net/?f=s%2Br%3D70)
So, by substitution:
![s+4\sqrt{29}=70](https://tex.z-dn.net/?f=s%2B4%5Csqrt%7B29%7D%3D70)
Therefore:
![s=70-4\sqrt{29}](https://tex.z-dn.net/?f=s%3D70-4%5Csqrt%7B29%7D)
Now, notice that, with respect to x, 20 is the opposite side and s is the hypotenuse.
Therefore, we can use the sine ratio. The sine ratio is the ratio between a right triangles opposite side to its hypotenuse.
In this case, the opposite to x is 20, and the hypotenuse is s, or 70-4√29. Therefore:
![\displaystyle \sin(x^\circ)=\frac{20}{s}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Csin%28x%5E%5Ccirc%29%3D%5Cfrac%7B20%7D%7Bs%7D)
By substitution:
![\displaystyle \sin(x^\circ)=\frac{20}{70-4\sqrt{29}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Csin%28x%5E%5Ccirc%29%3D%5Cfrac%7B20%7D%7B70-4%5Csqrt%7B29%7D%7D)
Take the inverse sine of both sides:
![\displaystyle x^\circ=\sin^{-1}\Big(\frac{20}{70-4 \sqrt{29}} \Big)](https://tex.z-dn.net/?f=%5Cdisplaystyle%20x%5E%5Ccirc%3D%5Csin%5E%7B-1%7D%5CBig%28%5Cfrac%7B20%7D%7B70-4%20%5Csqrt%7B29%7D%7D%20%5CBig%29)
Use a calculator. Therefore:
![x\approx24.37^\circ\approx24^\circ](https://tex.z-dn.net/?f=x%5Capprox24.37%5E%5Ccirc%5Capprox24%5E%5Ccirc)