Functions

### Does $$\displaystyle\sum−{1}^{{{n}}}{\ln{{2}}}{n}^{{{\frac{{{1}}}{{{n}}}}}}{)}$$ converge or diverge?

Equations and inequalities

### Prove by contraposition that if x does not equal 5 and is irrational then $$\displaystyle{3}\frac{{x}}{{x}}-{5}$$ is irrational.

Linear equations and graphs

### Describe the relationship between the two quantities. 1 [Graph] 2 [Graph]

Equations and inequalities

### The product of a number and seven is equal to two more than the number

Linear equations and graphs

Sequences

### Determine whether the sequence is arithmetic, geometric, or neither. If the sequence is arithmetic or geometric, calculate its common difference or ratio, respectively. 5, 9, 13, 17,

Piecewise-Defined Functions

### Write each expression without using absolute value symbols. $$|0|$$

Equations and inequalities

Functions

### What is the degree of a quadratic function f? What is the standard form of a quadratic function? How do you put a quadratic function into standard form?

Irrational numbers

### Find a) a rational number and b) a irrational number between the given pair. $$\displaystyle{3}\frac{{1}}{{7}}$$ and $$\displaystyle{3}\frac{{1}}{{6}}$$

Forms of linear equations

### Determine whether the ordered pair is a solution to the given system of linear equations. (5,3) x-y=2 x+y=8

Forms of linear equations

### Find the augmented matrix for the following system of linear equations: 5x+7y-36z=38 -8x-11y+57z=-60

Forms of linear equations

### in number 7, Is the exponent of (-1) n right? I thought that the exponent of (-1) is n-1 because it changed from n=0 to n=1, and if $$(-1)^{n}$$, there will be a change of sign between negative sign and positive sign.

Equations and inequalities

### Solve the equations and inequalities below. Write your solutions in exact form. $$a. \frac{3}{4}-\frac{x}{3}=\frac{7x}{4}$$ $$b. (b−4)2<12$$ $$c. ∣3+x∣−9\leq21$$ $$d. 5n^{2}−11n+2=0$$

Exponential growth and decay

### Tell whether the function represents exponential growth or exponential decay. Identify the growth or decay factor. $$\displaystyle{y}={0.15}{\left(\frac{{3}}{{2}}\right)}^{{x}}$$

Exponential growth and decay

### Identify each of the following functions as exponential growth or decay. Then give the rate of growth or decay as a percent. $$\displaystyle{y}={a}{\left(\frac{{5}}{{4}}\right)}^{{t}}$$

Forms of linear equations