Answer:
∠1 - 40°
Step-by-step explanation:
∠1 - 40°
b/c it's a right triangle and we have two angles given, 50° and 90°. Add them and subtract by 180° and get 40°.
∠2 - 140°
b/c an exterior (outside) angle is equal to the two most isolated / farthest angles added. The two most is angles are 105° and 35°, add them and get 140°.
∠3 - 40°
b/c ∠'s 1 and 3 are vertical angles meaning they're equal so since ∠1 is 40°, so is ∠3.
∠4 -
b/c ∠' s 2 and 4 are vertical angles meaning they're equal so since ∠2 is 140°, so is ∠4.
∠5 - 35°
b/c we have two angles, 105° and 40°. Add them and subtract by 180° and get 35°.
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I hope that helps you out!!
$4,950 will be paid after 3 years.
$577.50 will be paid as interest for the total loan.
Answer:
30%
Step-by-step explanation:
The unemployment rate is 30%
A vector space
is a subspace of a vector space
if
is non-empty,- for any two vectors
we have
, and - for any scalar
and
we have
.
It's easy to show the first condition is met by all the sets in parts (a-g).
(a) is a subspace of
because adding any 2x2 diagonal matrices together, or multiplying one by some scalar, gives another diagonal matrix.
(b) and (c) are also subspaces for the same reasons.
(d) is not a subspace because
because this set of matrices does not contain the zero matrix.
(e), however, is a subspace. Any linear combination of matrices in this set always yields a matrix with 0 in row 1, column 1 entry.
(f) is a subspace. A symmetric matrix is one of the form
![\begin{bmatrix}a&b\\b&c\end{bmatrix}](https://tex.z-dn.net/?f=%5Cbegin%7Bbmatrix%7Da%26b%5C%5Cb%26c%5Cend%7Bbmatrix%7D)
Adding two symmetric matrices gives another symmetric matrix:
![\begin{bmatrix}a_1&b_1\\b_1&c_1\end{bmatrix}+\begin{bmatrix}a_2&b_2\\b_2&c_2\end{bmatrix}=\begin{bmatrix}a_1+a_2&b_1+b_2\\b_1+b_2&c_1+c_2\end{bmatrix}](https://tex.z-dn.net/?f=%5Cbegin%7Bbmatrix%7Da_1%26b_1%5C%5Cb_1%26c_1%5Cend%7Bbmatrix%7D%2B%5Cbegin%7Bbmatrix%7Da_2%26b_2%5C%5Cb_2%26c_2%5Cend%7Bbmatrix%7D%3D%5Cbegin%7Bbmatrix%7Da_1%2Ba_2%26b_1%2Bb_2%5C%5Cb_1%2Bb_2%26c_1%2Bc_2%5Cend%7Bbmatrix%7D)
(g) is not a subspace. Consider the matrices
![\begin{bmatrix}1&0\\0&0\end{bmatrix},\begin{bmatrix}0&0\\0&1\end{bmatrix}](https://tex.z-dn.net/?f=%5Cbegin%7Bbmatrix%7D1%260%5C%5C0%260%5Cend%7Bbmatrix%7D%2C%5Cbegin%7Bbmatrix%7D0%260%5C%5C0%261%5Cend%7Bbmatrix%7D)
Both matrices have determinant 0, but their sum is the identity matrix with determinant 1.