Deck 1: Topics From Algebra

Solve the inequality and graph the solution on the real number line
​ $x ^ { 3 } + 6 x ^ { 2 } - 36 x - 216 \leq 0$ ​

Write the complex conjugate of the complex number. Then multiply the number by its complex conjugate.
​ $3 - 11 i$ ​

A stream of water moving at the rate of v feet per second can carry particles of size $0.03 \sqrt { v }$ inches. Find the size of the largest particle that can be carried by a stream flowing at the rate of $\frac { 7 } { 6 }$ foot per second. (Round your answer to three decimal places.)
​

Solve the inequality and graph the solution on the real number line.
​ $\frac { 1 } { x } \geq \frac { 1 } { x + 5 }$ ​

Plot the following real number on the real number line.

Find the distance between a and b.
​
a = 173, b = 57
​

Use inequality notation to describe the set.
​
q is at least 6 but less than 22
​

Factor the perfect square trinomial.
​ $x ^ { 2 } + 8 x + 16$ ​

Write the complex conjugate of the complex number. Then multiply the number by its complex conjugate.
​ $\sqrt { - 24 }$ ​

Do the operation and express the answer in a + bi form.
​ $\frac { - 9 } { i ^ { 12 } }$ ​

Determine which number/s in the set is/are natural number/s.
​
{2.65, 0.669..., -2, 0.019937247..., 35, -20}
​

Write the quotient in standard form.
​ $\frac { 7 } { 1 - i }$ ​

Use the properties of radicals to simplify the following expression.
​ $\sqrt [ 5 ] { 160 x ^ { 5 } }$ ​