Answer:
<em>The dimensions of the tabletop: Length= 67.976... inches and Width= 33.988... inches and the perimeter will be 203.929... inches.</em>
Step-by-step explanation:
Suppose, the width of the rectangular tabletop is
inch.
As the tabletop has a length that is twice it’s width, so the length will be:
inch.
The tabletop measures 76 inches on its diagonal.
<u>Formula for length of diagonal of rectangle</u>: ![d=\sqrt{l^2+w^2}](https://tex.z-dn.net/?f=d%3D%5Csqrt%7Bl%5E2%2Bw%5E2%7D)
So, the equation will be..........
![76=\sqrt{(2x)^2+ x^2}\\ \\ 76=\sqrt{4x^2+x^2} \\ \\ 76=\sqrt{5x^2} \\ \\ 5x^2= 76^2= 5776\\ \\ x^2= \frac{5776}{5}=1155.2 \\ \\ x= \sqrt{1155.2} =33.988...](https://tex.z-dn.net/?f=76%3D%5Csqrt%7B%282x%29%5E2%2B%20x%5E2%7D%5C%5C%20%5C%5C%2076%3D%5Csqrt%7B4x%5E2%2Bx%5E2%7D%20%5C%5C%20%5C%5C%2076%3D%5Csqrt%7B5x%5E2%7D%20%5C%5C%20%5C%5C%205x%5E2%3D%2076%5E2%3D%205776%5C%5C%20%5C%5C%20x%5E2%3D%20%5Cfrac%7B5776%7D%7B5%7D%3D1155.2%20%5C%5C%20%5C%5C%20x%3D%20%5Csqrt%7B1155.2%7D%20%3D33.988...)
Thus, the width of the tabletop is 33.988... inches and the length will be: (2×33.988...) = 67.976... inches.
The perimeter will be: 2(33.988...+ 67.976...) inches = 203.929... inches.
Answer:
c
Step-by-step explanation:
The total surface area of a 3-dimensional object is the sum of the areas of the faces or surfaces of a 3 dimensional object
for example, the total surface area of a cube is the sum of the area of all the six faces
the total surface area of a cube = 6a²
where a = edge
if a = 6
total surface area
6(6²) = 216
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 :)
Answer:
divide both sides by 2 (to isolate the equation in parenthesis)
subtract 3 from both sides (to isolate the variable x)
x=1
Step-by-step explanation:
if you need a better explanation just let me know!