The minerals shown in Figure 1.14 are fluorite and topaz that have been tested for hardness using a wire nail. Use the Mohs scale in Figure 1.13 to identify which is fluorite and which is topaz.

Specimen A:

Specimen B:

What do we mean when we refer to a mineral's tenacity? List three terms that describe tenacity.

Indiquez l'article correct.

Voici $\rule{1cm}{0.2pt}$ eau minérale.

To some observers, the mineral shown in Figure 1.9 exhibits a metallic luster, while others describe its luster as nonmetallic. Based on the streak of this sample, how would you describe its luster?

Select one of the following terms to describe the crystal shape, or habit, of each specimen given: cubic crystals, hexagonal crystals, fibrous habit, banded habit, blocky habit, bladed habit, tabular habit.

Specimen A: _______________________________ Specimen B: _______________________________ Specimen C: _______________________________ Specimen D: _______________________________

a Are these triangles congruent?

The given triangles are $\triangle ABC$ and $\triangle DEF$. The vertices of the $\triangle ABC$ are at A(-2,-2), B(-2,1), and C(3,-2) while the length of the $\triangle DEF$ are $\overline{DF}$=3, $\overline{DE}$=4, and $\overline{FE}$=5.

A. Yes

B. No

b What if C in the triangle above was at (2,-2)? Would the triangles be congruent in that case?'

A. Yes

B. No

If in $\triangle \mathrm{A B C}$ and $\triangle \mathrm{D E F}$, AB = DE, $\mathrm{m} \angle \mathrm{A B C=\mathrm{m} \angle E D F}$, BC = DF, $\mathrm{A C}=(20 x-10)$, and $\mathrm{E F}=(15 x+15)$, what is the value of x?

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

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

To some observers, the given mineral exhibits a metallic luster, while others describe its luster as nonmetallic. Based on the streak of this sample, how would you describe its luster?

Luster: ________________________________________

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

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

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

$\triangle A B C \sim \triangle F D E$. What is DE?

Given that the length of $\overline{AC}=12$, $\overline{BC}=8$, $\overline{EF}=18$, and $\overline{DF}=6$

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

$$\tan D$$

Find df/dx if

$$f(x)=\int_{1}^{e^{x}} \frac{2 \ln t}{t} d t.$$