In each of the following sentences, underline the verb or helping verb in parentheses that agrees with its subject.

They (is, are) trying to save these ballads.

Find the minimum and maximum values of the function subject to the given constraint.

$$f ( x , y , z ) = x ^ { 2 } + y ^ { 2 } + z ^ { 2 },$$

x + 3y + 2z = 36

Underline the subject and the correct word or word group in parentheses in each of the following sentences.

(Who's, Who are) the student assistant today?

Circle each subject and underline each verb in the following sentences.

Christina played the guitar and sang songs from Chile.

In the following sentence, circle the subject of the underlined verb. Then, if the verb does not agree in number with its subject, write the correct form of the verb above the incorrect form. If the verb is already correct, write C above it.

Has Julie told everyone what time the movie $\underline{\text{begins}}$?

Write $U$ beside each sentence that has you as its understood subject. Write $I$ beside each sentence that is in inverted order. If the sentence is in inverted order, draw one line under the subject and two lines under each simple predicate.

Over the outfield wall sailed the ball.

Underline the subject and the correct word or word group in parentheses in each of the following sentences.

Where (is, are) the other assignments for the class?

Draw two lines under the verb in parentheses that agrees with the subject.

Through the rain (trudges, trudge) the weary travelers.

Draw two lines under the verb in parentheses that agrees with the subject.

There (lies, lie) Julia's prize rosebush.

Underline the form of the verb that agrees with the subject.
Anyone who (excavates, excavate) a dinosaur has many stories to tell.

Decide whether the words in each of the following pairs are antonyms or synonyms. Then, explain your reasoning.

subject to, prone

Maximize

$$z=f_1(x)=7x_1+14x_2$$

subject to

$$0≤x_≤6, 0≤x_2≤3, 7x_1+14x_2≤84.$$

Find the minimum value of

$$f(x, y)=x^2-2 x y+2 y^2+20$$

subject to the constraint $2 x-6 y=15$.

Find the minimum and maximum values of the function subject to the given constraint.

$$f ( x , y ) = 4 x ^ { 2 } + 9 y ^ { 2 },$$

xy = 4