Identify the conjunctions in the following sentences by drawing one line under the coordinating conjunctions and two lines under the correlative conjunctions.

Example 1. Polar animals find food $\underline{\underline{\text{both}}}$ in water $\underline{\underline{\text{and}}}$ on land.

They are well known for their swimming abilities, but they can also run on land at high speeds.

Verify that two congruent corresponding parts are not sufficient to guarantee that two triangles are congruent by drawing the following figures: Draw $\triangle A B C$ and $\triangle X Y Z$ with $A B=8 \mathrm{~cm}, X Y=8 \mathrm{~cm}, A C=6 \mathrm{~cm}, X Z=6 \mathrm{~cm}$, but $B C=10 \mathrm{~cm}$ and $Y Z=8 \mathrm{~cm}$. How do $\angle A$ and $\angle X$ compare?

Identify the conjunctions in the following sentences by drawing one line under the coordinating conjunctions and two lines under the correlative conjunctions.

Example 1. Polar animals find food $\underline{\underline{\text{both}}}$ in water $\underline{\underline{\text{and}}}$ on land.

Polar bears have a highly developed sense of smell and can detect food up to ten miles away.

Identify the conjunctions in the following sentences by drawing one line under the coordinating conjunctions and two lines under the correlative conjunctions.

Example 1. Polar animals find food $\underline{\underline{\text{both}}}$ in water $\underline{\underline{\text{and}}}$ on land.

Unlike that of a deep hibernator, though, the polar bear’s temperature remains constant, so the bear can spring into action almost immediately.

The accompanying drawing suggests a series of manipulations starting with saturated $\mathrm{Mg}(\mathrm{OH})_2$ (aq). Calculate $\left[\mathrm{Mg}^{2+}(\mathrm{aq})\right]$ at each of the lettered stages.
(d) $25.00$ ml of the clear solution in part (b) is removed and added to $250.0 \mathrm{~mL}$ of $0.065 \mathrm{M} \mathrm{MgCl}_2(\mathrm{aq})$.

(a) By drawing the graphs of the functions

$$f ( x ) = 1 + \ln ( 1 + x ) \quad \text { and } \quad g ( x ) = \sqrt { x }$$

in a suitable viewing rectangle, show that even when a logarithmic function starts out higher than a root function, it is ultimately overtaken by the root function. (b) Find, rounded to two decimal places, the solutions of the equation

$$\sqrt { x } = 1 + \ln ( 1 + x )$$

.

Solve using the five-step plan. Write out each step. A choice of possible numbers for one unknown is given. In the problem, drawing a sketch may help you. A rectangle is 15 ft longer than it is wide and its area is $324 \mathrm{ft}^{2}$. Find its length and width. Choices for the width: 10, 12, 16

Use the information below to answer the question.

A basket of 40 pairs of pliers at a discount hardware store includes 5 pairs of 6 -inch pliers. A second basket contains 20 hammers, including 3 large hammers.

What is the probability of drawing a 6-inch pair of pliers from the first basket without looking?

Paulo is drawing plans for a set of three proportional nesting baskets, in the shape of open rectangular prisms.

The volume for the largest basket (C) can be modeled by the function $V_c(x)=2 x^3+10 x^2+8 x$. Use the graph to factor $V_{\mathrm{C}}$.

a. What are the values of x where $V_c=0$ ?

b. Use these zeros to write the factors.

(a) find the intercepts of each equation, (b) test each equation for symmetry with respect to the x-axis, the y-axis, and the origin, and (c) graph each equation by hand by plotting points. Be sure to label the intercepts on the graph and use any symmetry to assist in drawing the graph. Verify your results using a graphing utility. $x^2 + y^2 = 16$

Carlos wrote the following directions for a drawing. Follow his directions to make the drawing on your own paper. Draw segments to connect the following points in order: a. (-9, 0), b. (6, -1), c. (8, 0), d. (7, 1), e. (6,

$$\frac{1}{2}$$

), f. (6, -1), g. (9,

$$- 2 \frac { 1 } { 2 }$$

), h. (10, -2), i. (7, 1), j. (6,

$$1 \frac { 1 } { 2 }$$

), k. (

$$- 10 \frac { 1 } { 2 }$$

, 3), I. (-11, 2), m. (

$$- 10 \frac { 1 } { 2 }$$

, 0), n. (-10,

$$- 1 \frac { 1 } { 2 }$$

), o. (9,

$$- 2 \frac { 1 } { 2 }$$

), p. (-3,

$$- 3 \frac { 1 } { 2 }$$

), q. (-7, -8), r. (-10, -8), s. (-9,

$$- 1 \frac { 1 } { 2 }$$

)

Find the probability that the quadratic polynomial $Ax^2+B^x+1$, where the coefficients $A$ and $B$ are determined by drawing i.i.d. $\text{Unif}(0, 1)$ random variables, has at least one real root. Hint: By the quadratic formula, the polynomial $ax^2 +bx+c$ has a real root if and only if $b^2 − 4ac \geq 0$.

(a) By drawing the graphs of the functions

$$f(x)=1+\ln (1+x) \quad \text { and } \quad g(x)=\sqrt{x}$$

in a suitable viewing rectangle, show that even when a logarithmic function starts out higher than a root function, it is ultimately overtaken by the root function.

(b) Find, correct to two decimal places, the solutions of the equation $\sqrt{x}=1+\ln (1+x)$.

Given are five observations for two variables, x and y.

$$\begin{matrix} x_i & \text{1} & \text{2} & \text{3} & \text{4} & \text{5}\\ \hline y_i & \text{3} & \text{7} & \text{5} & \text{11} & \text{14}\\ \end{matrix}$$

Try to approximate the relationship between x and y by drawing a straight line through the data.