Improve Your Algebra Skills with Practice Problems

For each of the sets below, determine whether {2} is an element of that set.

a) ${\displaystyle \{x\in R\mid \text{x is an integer greater than 1}\}}$
b) ${\displaystyle \{x\in R\mid \text{x is the square of an integer}\}}$

c) $\{2,\{2\}\}$

d) $\{\{2\},\{\{2\}\}\}$

e) $\{\{2\},\{2,\{2\}\}\}$

f) $\{\{\{2\}\}\}$

To find:
Unit price for given rates and decide which s the better buy.

To find: The importance of Golden Ratio.

Whether the ratios ${\displaystyle \frac{8.4}{9.2}}$ and ${\displaystyle \frac{8.8}{9.6}}$ are equivalent ratios

The solution of the given proportion.
Given: ${\displaystyle \frac{9b-3}{9}=\frac{5b+5}{3}}$

The distance between the cities.
The given scale is: 1 inch ${\displaystyle =12}$ miles.

The solution of the given proportion ${\displaystyle \frac{8}{13}=\frac{v}{21}}$

Whether the proportion ${\displaystyle \frac{7}{4}=\frac{5}{3}}$ is true.

The total cost C (in dollars) to participate in a ski club is given by the literal equation C = 85x + 60, where x is the number of ski trips you take. How many ski trips do you take if you spend a total of $315?

Find the minimum and maximum values of ${\displaystyle y=\sqrt{6}\theta -\sqrt{3}\sec \theta }$
on the interval $[0,\frac{\pi }{\text{3}}]$

According to one source, the amount of data passing through mobile phone networks doubles each year.
Explain why the amount of data passing through mobile phone networks is an exponential function of time. The amount of data grows by a factor of_________________ each year, this is an exponential function because the amount is growing by _____________________ multiples.
Use ${\displaystyle D_o}$ for the initial amount of data and find a formula that gives the data D as an exponential function of the time t in years.
If this trend continues, how long will it be before the amount of data is 100 times its initial value? Round to three decimal places.

Identify, whether ${\displaystyle –4x\ge -8,x\ge 2}$ are equivalent inequalities or not equivalent ones?

What are the factors of 6?

Find the outcome.
${\displaystyle \frac{3+2\times 5-4}{\frac{8}{4}+1}}$

A vihacle valued at $35,795 originally, depreciates at a rate of 17%/year. The equation ${\displaystyle y=35795{\left(0.83\right)}^x}$ represents the vehicle's value. x is time passed since purchase (in years) and y is the woth (in dollars). How much will the car be worth ten years after the purchase?

Write expression as a sum and/or difference or logarithms, express powers as factors:
${\displaystyle {\log }_3(\frac{x^4}{2}-x)}$

Let M,N and K be matrices of type ${\displaystyle 3\times 2,2\times 3}$ and ${\displaystyle 3\times 3}$ respectively, such that det (MN) ${\displaystyle =2}$ and ${\displaystyle det\left(K\right)=6}$. Then which of the following is the value of the det ${\displaystyle {\left[{(-3MN)}^T{K}^{-1}\right]}^{-1}}$?
a) ${\displaystyle -3^2.2}$ b)${\displaystyle \frac{-1}{3^3.2}}$ c) ${\displaystyle \frac{2}{3^2}}$ d)${\displaystyle \frac{-3^2}{4}}$ e) ${\displaystyle \frac{-1}{3^2}}$

A ball is tossed upward from the ground. Its height in feet above ground after t seconds is given by the function ${\displaystyle h\left(t\right)=-16t^2+24t}$. Find the maximum height of the ball and the number of seconds it took for the ball to reach the maximum height.

add or subtract as indicated, and express answers in lowest terms. ${\displaystyle \frac{1}{6}+\frac{1}{8}}$.

A polynomial P is given. (a) Factor P into linear and irreducible quadratic factors with real coefficients. (b) Factor P completely into linear factors with complex coefficients.
${\displaystyle P\left(x\right)=x^4+8x^2-9}$