Answer:
PR = 24.5
Step-by-step explanation:
Since the triangles are similar then the ratios of corresponding sides are equal, that is
=
, that is
=
( cross- multiply )
18PR = 28 × 15.75 = 441 ( divide both sides by 18 )
PR = 24. 5
Answer:
Width = 40 yards
Length = 80 yards
Step-by-step explanation:
Width = x
Length = 2x
2x + 2(2x) = 240 yd
2x + 4x = 240 yd
6x = 240 yd
x = 40
Answer:
S is not the subspace of 
Step-by-step explanation:
Let us suppose two vectors u and v belong to the S such that the property of xy≥0 is verified than
![v=\left[\begin{array}{c}0 \\1\end{array}\right]](https://tex.z-dn.net/?f=v%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D0%20%5C%5C1%5Cend%7Barray%7D%5Cright%5D)
Both the vectors satisfy the given condition as follows and belong to the S

Now S will be termed as subspace of R2 if
- u+v also satisfy the condition
- ku also satisfy the condition
Taking u+v
![u+v=\left[\begin{array}{c}-1 \\0\end{array}\right]+\left[\begin{array}{c}0 \\1\end{array}\right]\\u+v=\left[\begin{array}{c}-1+0 \\0+1\end{array}\right]\\u+v=\left[\begin{array}{c}-1 \\1\end{array}\right]](https://tex.z-dn.net/?f=u%2Bv%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D-1%20%5C%5C0%5Cend%7Barray%7D%5Cright%5D%2B%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D0%20%5C%5C1%5Cend%7Barray%7D%5Cright%5D%5C%5Cu%2Bv%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D-1%2B0%20%5C%5C0%2B1%5Cend%7Barray%7D%5Cright%5D%5C%5Cu%2Bv%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D-1%20%5C%5C1%5Cend%7Barray%7D%5Cright%5D)
Now the condition is tested as

This indicates that the condition is not satisfied so S is not the subspace of 
Answer:
2
Step-by-step explanation: