Algebra Word Problem Solutions

If ${\displaystyle x^2=y^3}$ and y>1, what does ${\displaystyle x^{\frac{2}{3}}}$ equal in terms of y?

Simplify by using order of operations: ${\displaystyle \frac{10-3\cdot 2}{1+1}}$

Find a recurrence relation for the number of sequences of yellow and purple stones of length N, where each sequence has the property that no two adjacent stones are purple.

Use substitution to solve the system
${\displaystyle -3x+y=-18)}$
${\displaystyle 4x+3y=11)}$

What is the value of aa if (2a+3)−(4a−8)=7(2a+3)−(4a−8)=7?

${\displaystyle \frac{1}{2}x=\frac{7}{6}}$

Find (f o g)(x) and (g o f)(x), if
a) $f(x)=x^2–6x+2$ and $g(x)=–2x.$
b) $f(x)=x^2+3$ and $g(x)=2x–1$

The population of Riverdale is 6,735. What is the value of the 7 in the number 6,735?

A bicycle with tires of radius r=15 inches is being ridden by a boy at a constant speed - the tires are making five rotations per second. How many miles will he ride in minutes? (1mi = 5280 ft)

2x+3y=12
x−y=1x−y=1

The sum of given arithmetic sequence:
${\displaystyle \sum n=1802n-5=6080}$

17+2(x+6)=53

Given linear equation y = -1+2x
a. find the y-intercept and slope.
b. determine whether the line slopes upward, slopes downward, or is horizontal, without graphing the equation.
c. use two points to graph the equation.

${\displaystyle Q:\text{if}\{-\frac{3}{4},\sqrt{3},\frac{3}{\sqrt{3}},\sqrt{\frac{25}{5}},20,1.11222,2.5015132,\dots ,\frac{626}{262}\}}$,
find the following
1) Rational numbers?
2) Irrational numbers?

Graph the solution set for the of linear inequalities

$x+y\le 2$

$-x+y\le 2$

$y\le -2$

What are the two Special Inequalities?

Solve by completing the square ${\displaystyle x^2-x-7=0}$

The annual sales S (in millions of dollars) for the Perrigo Company from 2004 through 2010 are shown in the table. $\begin{array}{|cccccccc|}\hline \text{Year}& 2004& 2005& 2006& 2007& 2008& 2009& 2010\\ \text{Sales, S}& 898.2& 1024.1& 1366.8& 1447.4& 1822.1& 2006.9& 2268.9\\ \hline\end{array}$

a) Use a graphing utility to create a scatter plot of the data. Let t represent the year, with t=4 corresponding to 2004. b) Use the regression feature of the graphing utility to find an exponential model for the data. Use the Inverse Property $b=e^{\ln b}$to rewrite the model as an exponential model in base e. c) Use the regression feature of the graphing utility to find a logarithmic model for the data. d) Use the exponential model in base e and the logarithmic model to predict sales in 2011. It is projected that sales in 2011 will be $2740 million. Do the predictions from the two models agree with this projection? Explain.

 

Solve the given information Let ${\displaystyle f\left(x\right)=\sin x.}$ Use the following values and five-digit rounding arithmetic to construct the Hermite interpolating polynomial to approximate ${\displaystyle f\left(0.34\right)=\sin 0.34.}$
$\begin{array}{ccc}x& f(x)& f^{\prime }(x)\\ 0.30& 0.29552& 0.95534\\ 0.32& 0.31457& 0.94924\\ 0.35& 0.34290& 0.93937\end{array}$

Convert decimals and fractions to percents Write seller Bs