Perform the operation : $DF$, where matrices $A$ and $C$ are :

$$D= \begin{bmatrix} 3 & 0\\ 1 & -1 \\ 2 & 5 \end{bmatrix} \ \ \ \ F= \begin{bmatrix} 1 \\ 0 \\ -1 \end{bmatrix}$$

$$\begin{array} { l } { \text { In } \triangle \mathrm { DEF } } \\ { \mathrm { DF } = 6.0 \mathrm { km } } \\ { \angle \mathrm { E } = 44 ^ { \circ } } \\ { \angle \mathrm { F } = 90 ^ { \circ } } \end{array}$$

a) Draw this triangle and label the given information. b) Solve $\triangle \mathrm { DEF }$

Find the following ratio $\triangle D E F$ where $m \angle E$ = $90^\circ$ DE = 4, EF= 3, DF = 5.

$$\tan D$$

Find the following ratio $\triangle D E F$ where $m \angle E$ = $90^\circ$ DE = 4, EF= 3, DF = 5.

$$\tan F$$

If a parallelepiped with sides $\overline{DE}, \overline{DF}$, and $\overline{DG}$ has "7ero volume." what can you say about points D, E,F and $G$ ?

Find the following ratio $\triangle D E F$ where $m \angle E$ = $90^\circ$ DE = 4, EF= 3, DF = 5.

$$\sin F$$

If $F(x, y)=x^3-x y^2-y^4, x=2 \cos 3 t$, and $y=3 \sin t$, find dF/dt at t=0.

(a). Draw trapezoid ABCD. Let E and F be points on $\overleftrightarrow{A B}$ such that $\overrightarrow{C E} \perp \overleftrightarrow{A B}$ and $\overrightarrow{D F} \perp \overleftrightarrow{A B}$.

(b). Prove that CE=DF.

($c$). Let AB=$b_1, CD=b_2$, and CE=DF=h. Prove that the area of trapezoid ABCD is $\frac{h}{2}\left(b_1+b_2\right)$.

Find df/dx if

$$f(x)=\int_1^{e^x} \frac{2 \ln t}{t} d t$$

Use $\triangle G H J$, where D, E, and F are midpoints of the sides.

If HJ=8x-2 and DF=2x+11, what is HJ?

Find the following ratio $\triangle D E F$ where $m \angle E$ = $90^\circ$ DE = 4, EF= 3, DF = 5.

$$\cos D$$

BC=EF and AC=DF. Are the triangles congruent?

The triangle given are triangles ABC and DEF. The vertices are at A(-3,2), B(-3,4), C(1,4), D(-7,-2), E(-7,0), and (-3,0).

A. Yes

B. No

Find the following ratio $\triangle D E F$ where $m \angle E$ = $90^\circ$ DE = 4, EF= 3, DF = 5.

$$\sin D$$

In $\triangle \mathrm { DEF } ,$ find $\angle \mathrm { F }$ to the nearest degree, if $\mathrm { DE } = 15 \mathrm { cm } , \mathrm { DF } = 18 \mathrm { cm } , \text { and } \angle \mathrm { E } = 90 ^ { \circ }$