Recognizing Helping Verbs. In the sentences below, underline the helping verbs. I have carefully wrapped both lamps for shipment.

Write an equation in slope-intercept form of the line with the given slope and y-intercept. slope:

$$\frac { 2 } { 5 }$$

y-intercept: -2

Solve the given initial-value problem.

$$\frac { d ^ { 2 } y } { d t ^ { 2 } } - 4 \frac { d y } { d t } - 5 y=0, y(1)=0, y'(1)=2$$

Use the information provided to form complete sentences. As you do so remember that the form of the verbs conducir and ofrecer is irregular in the present tense. yo / conducir / el carro de mis padres

In the following exercise,

Point: (1, 0, 1)

Parallel to: x = 3 + 3t, y = 5 - 2t, z = -7 + t

find sets of symmetric equations of the line that passes through the given point and is parallel to the given vector or line. (For each line, write the direction numbers as integers.)

Find a unit vector that has the given property. Parallel to the line $x = 3t + 1, y = 16t − 2, z = −(t + 2)$

Write a rule for the nth term of the geometric sequence.

$$a _ { 2 } = - 72 , a _ { 6 } = - \frac { 1 } { 18 }$$

Use the quotient rule to simplify the expression. Assume that x > 0.

$$\frac { \sqrt { 72 x ^ { 3 } } } { \sqrt { 8 x } }$$

In Exercise, evaluate the integral.

$$\int \frac { x ^ { 3 } - 3 x ^ { 2 } + 2 x - 3 } { x ^ { 2 } + 1 } d x$$

Write an if statement that assigns 0 to x if y is equal to 20.

Write an equation of a line in slope-intercept form that passes through the given point and has the given slope. (-4, 2); slope -3

A shipment of eggs contains some cartons with a dozen eggs and some cartons with a half-dozen eggs. How can you represent the total number of eggs in the shipment using expressions? What variables do you use? What do they represent?

Write an equation in slope-intercept form for the line with the given slope that contains the given point. slope

$$= \frac { 1 } { 5 } ; ( - 4 , - 2 )$$

Find the characteristic polynomial of each of the following matrices using MATLAB. (a)

$$A=\left[\begin{array}{rr}1 & 2 \\ 2 & -1\end{array}\right]$$

(b)

$$A=\left[\begin{array}{lll}2 & 4 & 0 \\ 1 & 2 & 1 \\ 0 & 4 & 2\end{array}\right]$$

(c)

$$A=\left[\begin{array}{rrrr}1 & 0 & 0 & 0 \\ 2 & -2 & 0 & 0 \\ 0 & 0 & 2 & -1 \\ 0 & 0 & -1 & 2\end{array}\right]$$