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3 years ago

Which statement could be used to conclude that this parallelogram is a rhombus? m m m m

Mathematics

1 answer:

NeX [460]3 years ago

3 0

I didn't ask the question but the answer options are:

m<GFH=45

m<DEF=70

m<DHE=90

m<GDE=100

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1. Solve the following simultaneous equations using the matrix method.

dmitriy555 [2]

(i) Use the formula for the determinant of a 2×2 matrix.

$\begin{vmatrix}a&b\\c&d\end{vmatrix} = ad-bc$

$\implies \det(A) = \begin{vmatrix}4 & -3 \\ 2 & 5\end{vmatrix} = 4\times5 - (-3)\times2 = \boxed{26}$

(ii) The adjugate matrix is the transpose of the cofactor matrix of A. (These days, the "adjoint" of a matrix X is more commonly used to refer to the conjugate transpose of X, which is not the same.)

The cofactor of the (i, j)-th entry of A is the determinant of the matrix you get after deleting the i-th row and j-th column of A, multiplied by $(-1)^{i+j}$ . If C is the cofactor matrix of A, then

$C = \begin{pmatrix}5&-2\\3&4\end{pmatrix}$

Then the adjugate of A is the transpose of C,

$\mathrm{adj}(A) = C^\top = \boxed{\begin{pmatrix}5&3\\-2&4\end{pmatrix}}$

(iii) The inverse of A is equal to 1/det(A) times the adjugate:

$A^{-1} = \dfrac1{\det(A)} \mathrm{adj}(A) = \boxed{\begin{pmatrix}\frac5{26}&\frac3{26}\\\\-\frac1{13}&\frac2{13}\end{pmatrix}}$

(iv) The system of equations translates to the matrix equation

$A\begin{pmatrix}x\\y\end{pmatrix}=\begin{pmatrix}6\\16\end{pmatrix}$

Multiplying both sides on the left by the inverse of A gives

$A^{-1}\left(A\begin{pmatrix}x\\y\end{pmatrix}\right)=A^{-1} \begin{pmatrix}6\\16\end{pmatrix}$

$\left(A^{-1}A\right)\begin{pmatrix}x\\y\end{pmatrix}=A^{-1} \begin{pmatrix}6\\16\end{pmatrix}$

$\begin{pmatrix}x\\y\end{pmatrix}=\begin{pmatrix}\frac5{26}&\frac3{26}\\\\-\frac1{13}&\frac2{13}\end{pmatrix} \begin{pmatrix}6\\16\end{pmatrix}$

$\begin{pmatrix}x\\y\end{pmatrix}=\boxed{\begin{pmatrix}3\\2\end{pmatrix}}$

4 0

2 years ago

Answer fast please important

steposvetlana [31]

Answer:

c) does not make sense, y-int is (0,-8). a) the graph does show a linear line. b) sure it works, the x-int is 3. d) yes the line is infinite both ways (x,y) x (infinite, -infinite) y (infinite, - infinite)

Step-by-step explanation:

I hope this helps

4 0

3 years ago

EXPERTS/ACE/GENIUSES

Ivan

The answer would be D

7 0

3 years ago

12. -3.24 + (-1.55) + 2.512<br> Help

Feliz [49]

Your answer is 9.722

4 0

3 years ago

Which points lie on the graph of the function f(x) = ⌈x⌉ + 2? Check all that apply. (–5.5, –4) (–3.8, –2) (–1.1, 1) (–0.9, 2) (2

shepuryov [24]

Answer:

cde

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers