Triangle A B C has vertices A(1,3), B(-2,-1) and C(3,-2). Graph $\triangle$ A B C and its image after the indicated glide reflection.

Translation: along $\langle$ -1,1$\rangle$ Reflection: in y=x

Triangle A B C has vertices A(1,3), B(-2,-1) and C(3,-2). Graph $\triangle$ A B C and its image after the indicated glide reflection.

Translation: along $\langle$ 2,0$\rangle$ Reflection: in y-axis

Consider the linear function

$$f(x) = x.$$

Make a conjecture about the order in which transformations are performed.

Graph each figure and its image along the given vector.

pentagon D E F G H with vertices D(-1,-2 E(2,-1), F(5,-2), G(4,-4), and H(1,-4) $\langle$ -1,5 $\rangle$

Graph each figure and its image after the specified rotation about the origin.

$\triangle$ P Q R with vertices P(1,3), Q(3,-2) and R(4,2) ; $90^{\circ}$

Use the line of reflection. Draw the image in this line using a ruler

Find the equation(s) of the tangent line(s) at the point(s) on the graph of the equation $y^{3}-x y-x^{3}=2$ where x = 1. Round all approximate values to two decimal places.

Which of the following sets of ordered pairs are functions?

(a) $(7,11),(11,7),(4,-4),(-4,4)$

(b) $(5,-2),(-2,5),(4,-2),(-2,4)$

(c) $(7,-3),(-3,7),(5,7),(3,7)$

Some economists suggest that an extra year of education increases a person's wages, on average, by about 14%. Assume you could make $10 per hour with your current level of education and that inflation increases wages at a continuous rate of 3.5% per year. Is the difference you found in part (b) increasing with time? If so, at what rate? (Assume the number of additional years of education stays fixed at four.)

Consider $W$ and $U$ to be subspaces of vector space $V$.

(a) Show that $W \cup U$, the set of all vectors $\mathbf{v}$ that are either in $W$ or in $U$, is not always a subspace of $V$. (b) When is $W \cup U$ a subspace of $V$ ? (c) Show that $W \cap U$, the set of all vectors $\mathbf{v}$ that are in both $W$ and $U$, is a subspace of $V$.

Write yes or no. If so, draw all lines of symmetry and state their number

In the 1980s, it was generally believed that congenital abnormalities affected about 5% of the nation's children. Some people believe that the increase in the number of chemicals in the environment has led to an increase in the incidence of abnormalities. A recent study examined 384 children and found that 46 of them showed signs of an abnormality. Is this strong evidence that the risk has increased? a) Write appropriate hypotheses. b) Check the necessary assumption s and conditions. c) Perform the mechanic s of the test. What is the P-value? d) Explain carefully what the P-value mean s in context. e) What 's your conclusion? f) Do environmental chemicals cause congenital abnormalities?

If U and W are subspaces of a vector space V, let

$$U \cup W = \{ \mathbf { v } | \mathbf { v }$$

is in U or v is in W}. Show that

$$U \cup W$$

is a subspace if and only if

$$U \subseteq W$$

or

$$W \subseteq U$$

.

Two teaspoons of cough medicine equal ________ milliliters of cough medicine.