The equation for the shadow length L.
Is L=0.72*h
Therefore at 123 feet the shadow length would be 88.56 feet
SOLUTION:
PQR is a right-angle triangle.
Therefore, to solve this problem, we will use Pythagoras theorem which is only applicable to right-angle triangles.
Pythagoras theorem is as displayed below:
a^2 + b^2 = c^2
Where c = hypotenuse of right-angle triangle
Where a and b = other two sides of right-angle triangle
Now we will simply substitute the values from the problem into Pythagoras theorem in order to obtain the length of QR.
c = PQ = 16cm
a = PR = 8cm
b = QR = ?
a^2 + b^2 = c^2
( 8 )^2 + b^2 = ( 16 )^2
64 + b^2 = 256
b^2 = 256 - 64
b^2 = 192
b = square root of ( 192 )
b = 13.8564...
b = 13.86 ( to 2 decimal places )
FINAL ANSWER:
Therefore, the length of QR is 13.86 centimetres to 2 decimal places.
Hope this helps! :)
Have a lovely day! <3
Answer:
D. 4
Step-by-step explanation:
![[(p^2) (q^{-3}) ]^{-2}.[(p)^{-3}(q)^5] ^{-2}\\\\=[(p^2) (q^{-3}) \times(p)^{-3}(q)^5 ]^{-2}\\\\=[(p^{2}) \times(p)^{-3} \times (q^{-3}) \times(q)^5 ]^{-2}\\\\=[(p^{2-3}) \times (q^{5-3}) ]^{-2}\\\\=[(p^{-1}) \times (q^{2}) ]^{-2}\\\\=(p^{-1\times (-2)}) \times (q^{2\times (-2) }) \\\\=p^{2}\times q^{-4} \\\\= \frac{p^2}{q^4}\\\\= \frac{(-2)^2}{(-1)^4}\\\\= \frac{4}{1}\\\\= 4](https://tex.z-dn.net/?f=%20%5B%28p%5E2%29%20%28q%5E%7B-3%7D%29%20%5D%5E%7B-2%7D.%5B%28p%29%5E%7B-3%7D%28q%29%5E5%5D%20%5E%7B-2%7D%5C%5C%5C%5C%3C%2Fp%3E%3Cp%3E%3C%2Fp%3E%3Cp%3E%3D%5B%28p%5E2%29%20%28q%5E%7B-3%7D%29%20%5Ctimes%28p%29%5E%7B-3%7D%28q%29%5E5%20%5D%5E%7B-2%7D%5C%5C%5C%5C%3C%2Fp%3E%3Cp%3E%3C%2Fp%3E%3Cp%3E%3D%5B%28p%5E%7B2%7D%29%20%5Ctimes%28p%29%5E%7B-3%7D%20%5Ctimes%20%28q%5E%7B-3%7D%29%20%5Ctimes%28q%29%5E5%20%5D%5E%7B-2%7D%5C%5C%5C%5C%3C%2Fp%3E%3Cp%3E%3C%2Fp%3E%3Cp%3E%3D%5B%28p%5E%7B2-3%7D%29%20%5Ctimes%20%28q%5E%7B5-3%7D%29%20%5D%5E%7B-2%7D%5C%5C%5C%5C%3C%2Fp%3E%3Cp%3E%3C%2Fp%3E%3Cp%3E%3D%5B%28p%5E%7B-1%7D%29%20%5Ctimes%20%28q%5E%7B2%7D%29%20%5D%5E%7B-2%7D%5C%5C%5C%5C%3C%2Fp%3E%3Cp%3E%3C%2Fp%3E%3Cp%3E%3D%28p%5E%7B-1%5Ctimes%20%28-2%29%7D%29%20%5Ctimes%20%28q%5E%7B2%5Ctimes%20%28-2%29%20%7D%29%20%5C%5C%5C%5C%3C%2Fp%3E%3Cp%3E%3C%2Fp%3E%3Cp%3E%3Dp%5E%7B2%7D%5Ctimes%20q%5E%7B-4%7D%20%5C%5C%5C%5C%3C%2Fp%3E%3Cp%3E%3C%2Fp%3E%3Cp%3E%3D%20%5Cfrac%7Bp%5E2%7D%7Bq%5E4%7D%5C%5C%5C%5C%3C%2Fp%3E%3Cp%3E%3C%2Fp%3E%3Cp%3E%3D%20%5Cfrac%7B%28-2%29%5E2%7D%7B%28-1%29%5E4%7D%5C%5C%5C%5C%3C%2Fp%3E%3Cp%3E%3C%2Fp%3E%3Cp%3E%3D%20%5Cfrac%7B4%7D%7B1%7D%5C%5C%5C%5C%3C%2Fp%3E%3Cp%3E%3C%2Fp%3E%3Cp%3E%3D%204)
Answer:
7y + 5z + 10
Step-by-step explanation:
2y + 7z - 2z + 4y + 8 + y + 2
Like terms are terms that have the same variable part.
2y, 4y, y are like terms (remember that y is the same as 1y when you add)
7z, -2z are like terms
8, 2 are like terms
2y + 7z - 2z + 4y + 8 + y + 2 =
= 2y + 4y + y + 7z - 2z + 8 + 2
= 7y + 5z + 10
