Algebra Word Problem Solutions

absolute value of a complex number, axis of symmetry, binomial, completing the square, complex conjugate, complex number, complex plane, discriminant, imaginary number, imaginary part, imaginary unit, maximum value, minimum value, parabola, quadratic function, quadratic inequality in two variables, quadratic model, quadratic regression, real part, root of an equation, standard form, trinomial, vertex form, vertex of a parabola, zero of a function. Complete the sentences below with vocabulary words from the list above. The number 5i can be classified as both a(n)_______ and a ______.

Consider the following rational functions: ${\displaystyle r\left(x\right)=\frac{2x-1}{x^2}-x-2s\left(x\right)=\frac{x^3+27}{x^2+4}}$
${\displaystyle t\left(x\right)=\frac{\left(x^3\right)-9x}{x+2}}$
${\displaystyle u\left(x\right)=\frac{\left(x^2\right)+x-6}{x^2-25}}$
${\displaystyle w\left(x\right)=(\left(x^3\right)+\left(6x^2\right)+9x)\frac{)}{x+3}}$
Which of these functions has no vertical asymptote?

Tell whether the function represents exponential growth or exponential decay. Identify the growth or decay factor.
${\displaystyle f\left(x\right)=7\cdot {0.32}^x}$

Replace the polar equation with equivalent Cartesian equations. $(x-5{)}^2+y^2=25$

Given sequences $S_n=\frac{3n-4n^3}{5n^2+2}$ and $t_n=\cos (\frac{1}{n}).$
What conclusion we can make about each of the sequences?

How long does it take for an investment to double in value if it is invested at $14\mathrm{\%}$ compounded quarterly and compounded continuously?
a) At $14\mathrm{\%}$ compounded quarterly, the investment doubles in how many years?
b) At $14\mathrm{\%}$ compounded continuously, the investment doubles in how many years?

find the area of the largest rectangle that can be inscribed in the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$

Give an example of a context for a modeling problem where you are given that xy = 120 and you are minimizing the quantity 2x + 6y.

In January, the average high temperature for Calgary is ${9.9}^{\circ }C$ greater than Winnipeg’s average high temperature. The sum of these two temperatures is $-{15.5}^{\circ }C$. What is the average high temperature in January for each of these two cities?

For the following exercises, use the given information about the polynomial graph to write the equation. Degree 3. Zeros at $x=-2,$ $x=1$, and $x=3$. y-intercept at $(0,-4)$.

express the given percent as a decimal. 37%

What is the domain of ${\displaystyle f\left(x\right)=5\frac{x}{3-(\sqrt{x}-2)}}$?

I have $10,000 to invest for my daughter's car. I earned $215.04 when splitting the money into a 3% interest account and a 1.2% interest account. How much did I invest at each?

${\displaystyle \left(\frac{4}{k-1}\right)-\left(\frac{1}{k+4}\right)=0}$

${\displaystyle 5({10}^x-6)=7}$

Perform the following operations with real numbers. $9+(-18)$

${\displaystyle \frac{{(t+2)}^2}{3}+3\frac{{(t+2)}^1}{3}-10=0}$
how do i solve?

Replace the polar equation with equivalent Cartesian equations. $\frac{x^2}{9}+\frac{y^2}{4}=1$

Factor each polynomial. If a polynomial cannot be factored, write prime. Factor out the greatest common factor is necessary:
$10x^2-160$

Factor each polynomial by grouping.
$p^2{q}^2-10-2q^2+5p^2$