Algebra Word Problem Solutions

A canyon is 900 meters deep at its deepest point. A rock is dropped from the rim above this point. Write the height of the rock as a function of time t in seconds. (Use -9.8 m/s2 as the acceleration due to gravity.) How long will it take the rock to hit the canyon floor? (Give your answer correct to 1 decimal place.)

Consider the exponential function $f(x)=1,250\cdot {1.08}^x$ which models the amount of money invested in a bond fund where x represents the number of years since the money was invested. a. What is the rate of growth or decay?
b. What does 1,250 represent?

Let a, b and c be a real numbers such that a>0, b<0 and c<0. Find the sign of each expression.
a) -b
b) a+c
c) c-a
d) $a{b}^2$

Solve ${\displaystyle \{\begin{array}{ccccc}x& +& 2y& =& 9\\ y& =& -2x\end{array}}$

Identify each function as exponential growth or decay, and find the growth or decay factor.
${\displaystyle y=3\cdot {\left(\frac{1}{2}\right)}^x}$

For the following exercises, determine whether the equation represents exponential growth, exponential decay, or neither. Explain. $y=11,701(0.97{)}^t$

To find the equation $4\sqrt{8}\times \sqrt{10}=?$

write the general forms of the equations of the lines that pass through the point and are (a) parallel to the given line and (b) perpendicular to the given line.
${\displaystyle (\frac{3}{4},\frac{7}{8})5x-3y=0}$

${\displaystyle (\frac{y}{y^2-16}-\left(\frac{2}{y^2+9y+20}\right)=\frac{1}{y-4}}$

A coffee manufacturer wants to market a new brand of coffee that sells for $4.10 per pound by mixing two coffees that sell for $2.75 and $5.00 per pound, respectively. What amounts of each coffee should be blended to obtain the desired mixture?

A rational expression whose numerator or denominator or both contain rational expressions is called $a/an$_________ rational expression or $a/an$ fraction___________.

63:27 = 49: ?

$\begin{array}{|ccc|}\hline \text{ Original Price }& \text{ Percent of Discount }& \text{ Sale Price}\\ \\ \$20& 20\mathrm{\%}& \$16\\ \\ \$95& 35\mathrm{\%}& \$41.75\\ \\ & 75\mathrm{\%}& \$55.50\\ \\ & 40\mathrm{\%}& \$78\\ \hline\end{array}$

Solve the following simultaneous equations. 3a+5b=26, a+5b=22

Simplification Basic Concepts with Examples Simplification is very easy and important topic according to banking, SSC and other govt. exam perspective. Simplification is based on basic math calculations and some other algebraic topics. Simplification is less time consuming and having higher accuracy.

Use the following quadratic function to answer the question below: ${\displaystyle y=x^2-14x+5}$
a. Showing all work, find the vertwx of the quadratic.
b. Write the quadratic in the vertex form

A function is a ratio of quadratic functions and has a vertical asymptote x =4 and just one -intercept, x =1. It is known f that has a removable discontinuity at x =- 1 and ${\displaystyle \underset{x\to 1}{lim}f\left(x\right)=2}$. Evaluate
a) f(0)
b) ${\displaystyle lim{x}_{x\to \mathrm{\infty }}f\left(x\right)}$

Find the quadratic polynomial ${\displaystyle g\left(x\right)-a{x}^2+bx+c\text{which best fits the function}f\left(x\right)=e^x\text{at}x=0,\text{in the sense that}g\left(0\right)=f\left(0\right),\text{and}{g}^{\prime }\left(0\right)=f^{\prime }\left(0\right),\text{and}g{}^{″}\left(0\right)=f{}^{″}\left(0\right).}$ Using a computer or calculator, sketch graphs of f and g on the same axes. What do you notice?

Solve:
${\displaystyle x^3-3x^2+27}$ is congruent to 0 (mod 225)

Answer true or false to each of the following statements and explain your answers.
a. Polynomial regression equations are useful for modeling more complex curvature in regression equations than can be handled by using the method of transformations.
b. A polynomial regression equation can be estimated using the method of least squares, the same method used in multiple linear regression.
c. The term “linear” in “multiple linear regression” refers to using only first-degree terms in the predictor variables.