Resources

Resources

Solve higher-degree inequalities

Solve the compound inequality:

6 \leq 2 x-8<10

\newline

Enter the exact answer in interval notation.

\newline

\infty

, type infinity. To enter

\cup

Solve the compound inequality. Give the solution set in both interval and graph forms.

\newline

-4 x \leq-8 \text { or }-4 x \geq 0

\newline

Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

\newline

A. The solution set is

\square

\newline

(Type your answer in interval notation.)

\newline

B. The solution set is

\varnothing

Finding the Domain and Range of a Graph

\newline

Determine the Domain and Range for the graph below. Write your answer in Interval Notation and as a Compound Inequality.

\newline

\begin{tabular}{|l|l|l|l|l|}

\newline

\hline & & & \\

\newline

\hline & & & & \\

\newline

\hline & & & & \\

\newline

\hline & & & & \\

\newline

\newline

A triangle has side lengths

=8 \mathrm{~m}, \sqrt{15} \mathrm{~m}, 7 \mathrm{~m}

\newline

A) Is the triangle a right triangle? (type yes or no in the blank)

\qquad

\newline

B) Give the number proof for your answer in

Which two numbers occur on both lists?

\qquad

and These numbers are common multiples of

3

4

\newline

Write down the next two numbers which are common multiplies of

3

4

\qquad

\Delta R W S \cong \Delta T U V

, find the values of

\mathrm{x}

\mathrm{y}

. Be sure to clearly label each of your variables in your answer.

\newline

\begin{array}{l} x= \\ y= \end{array}

\newline

\mathrm{U}=2,5,7,9,10

\newline

2

\newline

What is the complement of Set B in Set U?

\newline

\{2,5,7,9,10\}

\newline

\{5,7,9,10\}

\newline

\{2,5,7,10\}

\newline

\{2\}

\newline

\mathrm{U}=4,5,7,8,10

\newline

=8

\newline

What is the complement of Set B in Set U?

\newline

\{4,5,7,8,10\}

\newline

\{8\}

\newline

\{4,5,8\}

\newline

\{4,5,7,10\}

\newline

\mathrm{U}=4,5,6,7,11,12

\newline

4

\newline

What is the complement of Set B in Set U?

\newline

\{4,5,6,7,11,12\}

\newline

\{5,6,7,11,12\}

\newline

\{4,5,6,11\}

\newline

\{4\}

\newline

\mathrm{U}=5,6,10,11,12

\newline

=10

\newline

What is the complement of Set B in Set U?

\newline

\{5,6,11,12\}

\newline

\{5,6,10,11\}

\newline

\{10\}

\newline

\{5,6,10,11,12\}

\newline

\mathrm{U}=2,4,5,6

\newline

4

\newline

What is the complement of Set B in Set U?

\newline

\{4\}

\newline

\{2,4,5,6\}

\newline

\{2,5,6\}

\newline

\{2,4,5\}

5

b. Suppose the universal set is

\xi=\{0,1,2,3,4,5,6,7,8\}

\newline

i. Write in enumerated form the set that is represented by the bit string

011011001

\newline

A

y

110101110

B

is represented by the bit string

101011000

, write the sets AUB and A as bit strings.

The Hodge conjecture is that for projective algebraic varieties, Hodge cycles are rational linear combinations of algebraic cycles.

\newline

\text{Hdg}^{(k)}(X) = \text{H}^{(2k)}(X,\mathbb{Q}) \cap \text{H}^{(k,k)}(X)

\newline

We call this the group of Hodge classes of degree

2k

X

\newline

The modern statement of the Hodge conjecture is:

\newline

X

be a non-singular complex projective manifold. Then every Hodge class on

X

is a linear combination with rational coefficients of the cohomology classes of complex subvarieties of

X

at Slide Arrange Tools Extensions Help Accessibility

\newline

\newline

\newline

\newline

\newline

x

represent any number in the set of even integers greater than

1

\newline

Which inequality is true for all values of

x

\newline

\frac{4 x-2}{x-1} \leq 3

\newline

x \in

(Enter your answer in INTERVAL notation, using

U

to indicate a union of intervals; or enter DNE if no solution exists)

f

g

are defined as follows.

\newline

\begin{align*} &f(x) = \frac{x-2}{x^2 + 4x - 12},\ &g(x) = \frac{x}{x^2 + 64} \end{align*}

\newline

For each function, find the domain.

\newline

Write each answer as an interval or union of intervals.

Graph the solution set.

\newline

3(4x-8)+12 > 11x-14

\newline

Express the solution in set-builder notation. Select the correct choice below to complete your choice.

\newline

A. The solution set is

\newline

\{x\mid x \geq \}

\newline

Use integers or fractions for any numbers in the expression

\newline

B. The solution is all real numbers.

\newline

C. The solution is the empty set

Find the solution of the linear inequality. Express the solution set in set-builder notation. Select the correct choice below to complete your choice.

\newline

A. The solution set is

\{x \mid \}

\newline

(Use integers or fractions for any numbers in the expression)

\newline

B. The solution is all real numbers.

\newline

C. The solution set is the empty set.

Solve the equation. Check your solution.

\newline

\frac{1}{4}(-16 k+52)=8+10 k

\newline

The solution set is \{\} . Type an integer or a simp