Algebra Word Problem Solutions

An employment agency in temporary construction help pays heavy equipment operators $140 per day and general laborers $90 per day. If thirty-five people were hired and the payroll was $3950, how many heavy equipment operators were employed? How many laborers?

Using the following table of values for the rational functions f, s, and h. $\begin{array}{ccccccc}\text{x}& \text{-10000}& \text{-1000}& \text{-100}& \text{100}& \text{1000}& \text{10000}\\ \text{f(x)}& \text{-10001.9997}& \text{-1001.9970}& \text{-101.9694}& \text{97.9706}& \text{997.9970}& \text{9997.9997}\\ \text{g(x)}& \text{-6.0004}& \text{-6.0040}& \text{-6.0404}& \text{-5.9604}& \text{-5.9960}& \text{-5.9996}\\ \text{h(x)}& \text{-0.0005}& \text{-0.0050}& \text{-0.0506}& \text{0.0496}& \text{0.0050}& \text{0.0005}\end{array}$
Based rule that defines the functions f, g, and h. How does the degree of the numerator compare to the degree of the denominator, (e.g., greater than, less than, or equal to.)?

Determine whether each function is an example of exponential growth or decay. Then find the y-intercept. ${\displaystyle y=0.1{\left(10\right)}^x}$

Models that increase or decrease by a percentage will be exponential. Which of the following scenarios will use exponential modeling?
A) A person makes $50,000 per year and then has a salary increase of $6,000 for each year of experience.
B) A person makes $50,000 per year and their salary will increase by 2.5% each year.

For the following exercise, for each polynomial, a. find the degree; b. find the zeros, if any; c. find the y-intercept(s), if any; d. use the leading coefficient to determine the graph’s end behavior; and e. determine algebraically whether the polynomial is even, odd, or neither. ${\displaystyle f\left(x\right)=3x-x^3}$

How can you tell if an exponential function models growth or decay?

Determine whether the function represents exponential growth or exponential decay.
${\displaystyle f\left(x\right)=50{\left(1.1\right)}^{3}x}$

Construct a rational function that has a vertical asymptote at x = 3 and a removable discontinuity at x = -2. Explain how you determined your answer.

The measures of the angles of a convex polygon form an arithmetic sequence. The least measurement in the sequence is ${129}^{\circ }$. The greatest measurement is ${159}^{\circ }$. Find the number of sides in this polygon.

List the first 6 multiples of each number.
a) 6
b) 13
c) 22
d) 31
e) 45
f) 27

Use the discriminant to determine the number of real solutions of the equation.
${\displaystyle x^2=6x-9}$

Solve $\{\begin{array}{l}(x-3{)}^2+(y+1{)}^2=5\\ x-3y=7\end{array}$

Where does the helix
$r(t)=<\cos (\pi t),\sin (\pi t),t>$
intersect the paraboloid
$z=x^2+y^2$?
(x, y, z) =
What is the angle of intersection between the helix and the paraboloid?

The base of S is an elliptical region with boundary curve $9x^2+4y^2=36$. Cross-sections perpendicular to the x-asis are isosceles right triangles with hypotenuse in the base.

Find the solution of the equation rounded to two decimals.
$8.36-0.95x-9.97$

Round 2093.33 to the nearest hundredth.

Solve the equation $\log (x+3)+\log x=1$, inequality, or system of equations.

Replace the Cartesian equation with equivalent polar equations.
$x^2+(y-2{)}^2=4$

Solve the following equation. Indicate which of the values you find are allowed to be solutions to the original equation.
${\displaystyle \frac{-40}{x^2}+\frac{13}{x}=1}$

Consider the following differential equation.
2y+y-y=0