Algebra Word Problem Solutions

Two spelunkers (cave explorers) were exploring different branches of an underground cavern. The first was able to descend 198 ft farther than twice the second. If the first spelunker descended a 1218 ft, how far was the second spelunker able to descend?

solve given system of equation
${\displaystyle 2x+5y=-18}$
${\displaystyle y=-3x-7}$

WRITE A RULE FOR THE nth TERM OF THE ARITHMETIC SEQUENCE THEN FIND $a_{25}$: {1.6,4,6.4,8.8,11.2,…} *

Andrew and his father are scuba diving at -38 feet and Tackle Box Canyon has an elevation of -83 feet. Write an inequality to compare the depths. Explain the meaning of the inequality.

The number of houses that will be built in the new neighborthood must be at least 14 and no more than 28.

Airlines schedule about 5.5 hours of flying time for an A320 Airbus to fly from Dulles International Airport near Washington, D.C., to Los Angeles International Airport. Airlines schedule about 4.5 hours of flying time for the reverse direction. The distance between these airports is about 2,300 miles. They allow about 0.4 hour for takeoff and landing.
a. From this information, estimate (to the nearest 5 mph) the average wind speed the airlines assume in making their schedule.
b. What average airplane speed (to the nearest 5 mph) do the airlines assume in making their schedule?

Below is data collected from the growth of two different trees over time. Each tree was planted in 1960, and the trees

In the exponential growth or decay function $y=y_0{e}^{k}t$, what does $y_0$ represent? What does k represent?

Solve
y=3x−8
y=13−4x

Which expression is equivalent to the following complex fraction? ${\displaystyle -\frac{2}{x}+\frac{5}{y}/\frac{3}{y}-\frac{2}{x}}$

Determine whether the sequence ${\displaystyle \left\{an\right\}\mathrm{\infty }}$
$n=2$ with ${\displaystyle an=\frac{\ln }{n}n2}$ converges.

Show all steps.

The set of all integers under addition is

Given that point (x, y) is on the graph of y = 4 - x², express the distance from (3, 4) to (x, y) as a function of x.

Solve quadratic equation using the quadratic formula. ${\displaystyle 3x^2-3x-4=0}$

You intend to estimate a population mean with a confidence interval. You believe the population to have a normal distribution. Your sample size is 28. Find the critical value that corresponds to a confidence level of 98%. (Report answer accurate to three decimal places with appropriate rounding.) ${\displaystyle t\frac{a}{2}=}$

Find the binomial that completes the factorization.
${\displaystyle 5s^4+5000s{t}^3=5s(s^3+1000t^3)}$

Mathematical Reasoning
True or False?
There exist irrational numbers with repeating decimals?
There exists a natural number x such that $y>x$ for every naural number y?

Whether tha addition, subtraction, pultiplication and division of polynomials always result in a polynomial or not. Explain reason.

Define Absolute value.

Need to calculate:The factorization of $2x^3-8x^2-9x+36$.