Algebra Word Problem Solutions

Write a polynomial function f of least degree that has rational coefficients, a leading coefficient of 1, and the given zeros. Write the polynomial in standard form. -2, 1, 3

Factor the GCF from the polynomial.
${\displaystyle x^2(x-1)+y^2(x-1)}$

Factor each polynomial. If a polynomial cannot be factored, write prime. Factor out the greatest common factor is necessary:
${\displaystyle 24x^4+36x^{3}y-60x^2{y}^2}$

R.A. Moyer of lowa State College found. in comprehensive tests carried out on 41 wet pavements, that the braking distance d(in feet) for a particular automobile traveling at v miles per hour was given approximately by
$d=0.0212v^{\frac{7}{3}}$
Approximate the braking distance to the ncarest foot for the car traveling on wet pavement at 70 miles per hour.

$An=n-\frac{1}{2}a11=?$ Given the nth term find the indicated term.

Tell whether the function represents exponential growth or exponential decay. Explain.
${\displaystyle y=3{\left(0.85\right)}^x}$

Simplify the following:
(a+10)(a+10)

$y=-3x-13$ and $4x+3y=-24$

Find the weighted average of a data set where 10 has a weight of 5, 30 has a weight of 3, and 50 has a weight of 2.

A gondola on an amusement park ride, similar to the Spin Cycle at Silverwood Theme Park, spins at a speed of 13 revolutions per minute. If the gondola is 25 feet from the ride's center, what is the linear speed of the gondola in miles per hour?

Simplify the expression, answering with rational exponents and not radicals. To enter ${\displaystyle x^{\frac{m}{n}},}$ type ${\displaystyle x^{\left(\frac{m}{n}\right)}.}$
${\displaystyle \sqrt{7}\left\{n\right\}\sqrt{7}\left\{n\right\}=?}$

Mr. Maxwell bought new basketball shows with the discount shown. He has a $10-off coupon he can use after the percentage off. If Mr. Maxwell bought the shows for $61.25, what was the original price? A. If the shoes are discounted 25%, what percent of the original price is the original price? 25% discount is the same as 75% of the original price. B. Fill in the boxes to set up the equation to find the original price of the shoes. Original Price =61.25 C. What would be the price without a $10-off coupon?

${\displaystyle a^7\times b^8=a{b}^{15}}$

Solve the equations and inequalities. Write the solution sets to the inequalities in interval notation. ${\displaystyle {\log }_2(3x-1)={\log }_2(x+1)+3}$

For the following exercises, use a graphing utility to create a scatter diagram of the data given in the table. Observe the shape of the scatter diagram to determine whether the data is best described by an exponential, logarithmic, or logistic model. Then use the appropriate regression feature to find an equation that models the data. When necessary, round values to five decimal places.
$\begin{array}{|ccccccccccc|}\hline x& 1& 2& 3& 4& 5& 6& 7& 8& 9& 10\\ f(x)& 409.4& 260.7& 170.4& 110.6& 74& 44.7& 32.4& 19.5& 12.7& 8.1\\ \hline\end{array}$

Consider the following system of llinear equations.
${\displaystyle \frac{1}{3}x+y=\frac{5}{4}}$
${\displaystyle \frac{2}{3}x-\frac{4}{3}y=\frac{5}{3}}$
Part A: ${\displaystyle \frac{Whatproptoerty}{proptoerties}}$ can be used to write an equivalent system?
Part B: Write an equivalent system and use elimination method to solve for x and y.

Use an inverse matrix to solve system of linear equations.
$x+2y=-1$
$x-2y=3$

A given polynomial has a root of $x=3$, an zero of $x=-2$, and an x-intercept of $x=-1$.
The equation of this polynomial in factored form would be $f(x)=$
The equation of this polynomial in standard form would be $f(x)=$

Need to calculate:The factorization of $8x^3+20x^2+2x+5$.

State the fundamental theorem of arithmetic.