Master Algebra 1 Word Problems with our Comprehensive Practice

A computer is worth $2400 when it is new. After each year it is worth half what it was the previous year. What will its worth be after 4 years?

Alternative for calculating the nth of quadratic sequence
Given the quadratic sequence
$f(n)=1,7,19,37,\cdots <!--\; \cdots \; -->$
To calculate the f(n) for $n\ge <!--\; \ge \; -->1$.
$f(n)=a{n}^2+bn+c$
We start with the general quadratic function, then sub in for $n:=1,2$ and 3
$f(1)=a+b+c$
$f(2)=4a+2b+c$
$f(3)=9a+3b+c$
Now solve the simultaneous equations
$\begin{array}{}\text{(1)}& a+b+c=1\end{array}$
$\begin{array}{}\text{(2)}& 4a+2b+c=7\end{array}$
$\begin{array}{}\text{(3)}& 9a+3b+c=19\end{array}$
$(2)-<!--\; -\; -->(1)$ and $(3)-<!--\; -\; -->(2)$
$\begin{array}{}\text{(4)}& 3a+b=6\end{array}$
$\begin{array}{}\text{(5)}& 5a+b=12\end{array}$
$(5)-<!--\; -\; -->(4)$
$a=3$
$b=-<!--\; -\; -->3$
$c=1$
$f(n)=3n^2-<!--\; -\; -->3n+1$
This method is very long. Is there another easy of calculating the f(n)?

Find the common ratio of ${\displaystyle -\frac{1}{4},\frac{1}{8},-\frac{1}{16},\frac{1}{32},...}$

Find the slope of any line perpendicular to the line passing through (12,−3) and (−1,4)

Given an irrational number $x\in <!--\; \in \; -->\mathbb{R}\setminus <!--\; \setminus \; -->\mathbb{Q}$, is it possible to find a map $T:\mathbb{N}\to <!--\; \to \; -->\mathbb{N}$ strictly increasing such that $\{T(n)x\}\to <!--\; \to \; -->0$ as $n\to <!--\; \to \; -->\mathrm{\infty <!--\; \infty \; -->}$, where $\{\cdot <!--\; \cdot \; -->\}$ is the fractional part?

Why is e used in exponential growth functions?
Now I'm aware that $e^x$ is its own derivative, which makes it convenient to use in calculus. However, I have a question about this function:
Intuitively, an exponential growth function could be written as $a\ast <!--\; \ast \; -->(1+k{)}^t$, where a is the initial amount, k is the growth rate and t is the time.
However, it can also be rewritten as $a\ast <!--\; \ast \; -->e^{kt}$, same thing, but with Euler's number added to it.
In what way are these both the same? They yield the same answer. Why not 2, or 4, or 10? I know that one would need to change the growth constant if using one of those bases, the one I called k, but how come one doesn't need to change it when it's in base e?

Find the integers if the sum of two consecutive even integers is 106

How do you find the first five terms of each sequence ${\displaystyle a_1=1}$, ${\displaystyle a_2=2}$, ${\displaystyle a_{n+2}=4\left(a_{n+1}\right)-3a_n}$?

${\displaystyle 4x^2>12x-9}$

Show that the roots of $x^2+bx+ac=0$ are a times the roots of the quadratic $a{x}^2+bx+c=0$ by using transformation of the function $f(x)=a{x}^2+bx+c$
Let $f(x)=a{x}^2+bx+c$ and $g(x)=x^2+bx+ac$
The graph of $y=g(ax)$ results from shifting the graph of $y=g(x)$ horizontally b a factor of $1/a$
Does that mean $g(ax)=f(x)$?

Write an equation of a line going through (1,7) parallel to the x-axis

Find the 9th term of the geometric sequence where a1 = -7 and a6 = -7,168

The sum of the measures of two exterior angles of a triangle is 255. Find the measure of the third

Consider the following system of linear equations:
$x_1+2x_2+x_3-<!--\; -\; -->2x_4=10$
$-<!--\; -\; -->x_1+2x_2+x_3-<!--\; -\; -->x_4=6$
$+x_2+x_3=2$
Find all its canonical forms and basic solutions.

Is it possible to intuitively explain, how the three irrational numbers $e,i$ and $\mathrm{\pi <!--\; \pi \; -->}$ are related?

A rational number that is a infinite product of distinct irrational numbers?

Write an equation in point slope form that passes through (-3, 3/4) and has no slope

Rewrite in standard form and give the vertex
$f(x)=2x^2-<!--\; -\; -->6x$

Find the integers if the sum of 2 consecutive integers of 9

Find the common ratio if the first two terms of a geometric series are 1/3 + 1/9 + ...