If the original angle is x degrees then its supplement is 180 - x degrees.
we have the equation:-
180 - x = 3x + 20
160 = 4x
x = 40
The original angle is 40 degrees and its supplement is 140 degrees
First make a guest check
My Guest check #9
1 donut = $1.29
Donut holes = $4.89
Dozen Donuts = $12
Donut Holes = $4.89
$1.29 + $4.89 + $12 + $4.89 = $23.07
$23.07 * 8% =<em> $24.92 is the 9th check list</em>
My Guest check #10
1 donut = $1.29
1 donut = $1.29
Dozen Donuts = $12
Donut Holes = $4.89
$1.29 + $1.29 + $12 + $4.89 = $19.47
$19.47 * 8% = <em>$21.03 is the 10th check list</em>
He can make them 6 feet long bc that’s the greatest length. so abraham will hv 3 wides that are 6 feet long
Answer:
So here is the answer to your question by using the formulae of compound amount.
Initial price( P) = $5000
Interest rate( R) = 2% pa
Time ( T) = 30 years
Compound amount (CA)=?
We have
CA=P(1+R/100)^T
=5000(1+2/100)^30
=$9056.807921
=$9057(Approx)
Thus, the money will be $9057 after 30 years.
Our first expression is
. Upon distributing the exponent 4 on all the terms, we get:
![(2p^{-3} q^{8} )^{4}=2^{4}(p^{-3})^{4}(q^{8})^{4}=16p^{-12}q^{32}=\frac{16q^{32}}{p^{12}}](https://tex.z-dn.net/?f=%282p%5E%7B-3%7D%20q%5E%7B8%7D%20%29%5E%7B4%7D%3D2%5E%7B4%7D%28p%5E%7B-3%7D%29%5E%7B4%7D%28q%5E%7B8%7D%29%5E%7B4%7D%3D16p%5E%7B-12%7Dq%5E%7B32%7D%3D%5Cfrac%7B16q%5E%7B32%7D%7D%7Bp%5E%7B12%7D%7D)
Therefore, your answer is correct for this part. :)
Second expression is
. Upon distributing the exponent -2 on all the terms, we get:
![(2m^{-4}n^{5})^{-2}=2^{-2}(m^{-4})^{-2}(n^{5})^{-2}=2^{-2}m^{8}n^{-10}=\frac{m^{8}}{4n^{10}}](https://tex.z-dn.net/?f=%282m%5E%7B-4%7Dn%5E%7B5%7D%29%5E%7B-2%7D%3D2%5E%7B-2%7D%28m%5E%7B-4%7D%29%5E%7B-2%7D%28n%5E%7B5%7D%29%5E%7B-2%7D%3D2%5E%7B-2%7Dm%5E%7B8%7Dn%5E%7B-10%7D%3D%5Cfrac%7Bm%5E%7B8%7D%7D%7B4n%5E%7B10%7D%7D)
Your second answer is correct too.
Our third expression is
. Upon distributing the exponent 2 on all the terms, we get:
![2(5g^{-4}h^{-6})^{2}=2(5^{2})(g^{-4})^{2}(h^{-6})^{2}=2(25)g^{-8}h^{-12}=\frac{50}{g^{8}h^{12}}](https://tex.z-dn.net/?f=2%285g%5E%7B-4%7Dh%5E%7B-6%7D%29%5E%7B2%7D%3D2%285%5E%7B2%7D%29%28g%5E%7B-4%7D%29%5E%7B2%7D%28h%5E%7B-6%7D%29%5E%7B2%7D%3D2%2825%29g%5E%7B-8%7Dh%5E%7B-12%7D%3D%5Cfrac%7B50%7D%7Bg%5E%7B8%7Dh%5E%7B12%7D%7D)
This one is not correct. Your answer would have been correct, if the exponent were -2 instead of 2 in this part.
Our forth and last expression is
. Upon distributing the exponent -5 on all the terms inside the parenthesis, we get:
![4(2c^{-3}d^{6})^{-5}=4(2^{-5})(c^{-3})^{-5}(d^{6})^{-5}=\frac{4}{2^{5}}(c^{15})(d^{-30})=\frac{4c^{15}}{32d^{30}}=\frac{c^{15}}{8d^{30}}](https://tex.z-dn.net/?f=4%282c%5E%7B-3%7Dd%5E%7B6%7D%29%5E%7B-5%7D%3D4%282%5E%7B-5%7D%29%28c%5E%7B-3%7D%29%5E%7B-5%7D%28d%5E%7B6%7D%29%5E%7B-5%7D%3D%5Cfrac%7B4%7D%7B2%5E%7B5%7D%7D%28c%5E%7B15%7D%29%28d%5E%7B-30%7D%29%3D%5Cfrac%7B4c%5E%7B15%7D%7D%7B32d%5E%7B30%7D%7D%3D%5Cfrac%7Bc%5E%7B15%7D%7D%7B8d%5E%7B30%7D%7D)
Therefore, your answer for this part is also correct.
Looking at your work, I don't think you made a mistake in number 3 also, probably mis-typed the question while writing here :)