# Algebra 1 questions and answers Recent questions in Algebra I

Functions

### Explain why the function is differentiable at the given point. Then find the linearization L(x,y) of the function at  that point. $$f(x,y)=y+sin(x/y), (0,3)$$

ANSWERED ### Find the distance between the pair of points (3.5, 8.2) and (-0.5, 6.2). If necessary, express answers in simplified radical form and then round to two decimals places.

ANSWERED ### Find, to the nearest tenth of a second, the period of a pendulum of length 3.5 feet.

ANSWERED ### Find the rectangular coordinates of the pair of points $$\displaystyle{\left({6},\pi\right)}$$ and $$\displaystyle{\left({5},{7}\frac{\pi}{{4}}\right)}$$. Then find the distance, in simplified radical form, between the points.

ANSWERED ### Simplify and express the final result using positive exponents. $$\displaystyle{\left({\frac{{{8}{y}^{{2}}}}{{{2}{y}^{{-{1}}}}}}\right)}^{{-{1}}}$$

ANSWERED ### Expand the expression and write your answer without the exponents. $$\displaystyle{{\log}_{{4}}{\frac{{{x}^{{2}}{y}^{{4}}}}{{{8}}}}}$$

ANSWERED ### Solve for the following exponential equations. Use the natural logarithm in your answer(where applicable) for full credit. Use rules for exponents, factor and simplify. $$\displaystyle{10}^{{{6}-{3}{x}}}={18}$$

Algebra I
ANSWERED ### Complete the two-way table. \begin{array}{|c|cc|c|} \hline \text{ Gender } & \text { Response } & \text { } & \text { } \ \hline & \text { Yes } & \text { No } & \text { Total } \ \hline \text { Male } & & 52 & \ \hline \text { Female } & 48 & & 110 \ \hline \text { Total } & 65 & & \ \hline \end{array}

ANSWERED ### Simplify and express the final result using positive exponents. $$\displaystyle{\left({x}^{{-{3}}}{y}^{{4}}\right)}^{{-{2}}}$$

ANSWERED ### Model the following data using an exponential function of the form $$\displaystyle{f{{\left({x}\right)}}}={A}{b}^{{x}}$$ . Set up a system of equations, and solve it to get A and b. f(x) is exponential and goes through the points (1, 2) and (4, 6).

ANSWERED ### Solve the exponential equation $$\displaystyle{6}^{{\frac{{{x}-{3}}}{{4}}}}=\sqrt{{{6}}}$$ by expressing each side as a power of the same base and then equating exponents.

Piecewise-Defined Functions
ANSWERED ### Consider the function $$\displaystyle{f{{\left({x}\right)}}}={2}{x}^{{{3}}}-{6}{x}^{{{2}}}-{18}{x}+{9}$$ on the interval [-2,4]. What is the absolute minimum of f(x) on [-2,4]? What is the absolute maximum of f(x) on [-2,4]?

ANSWERED ### Solve the exponential equation $$3^x=81$$ by expressing each side as a power of the same base and then equating exponents.

Piecewise-Defined Functions
ANSWERED ### Consider the function $$\displaystyle{f{{\left({x}\right)}}}={2}{x}^{{{3}}}+{6}{x}^{{{2}}}-{90}{x}+{8},{\left[-{5},{4}\right]}$$ find the absolute minimum value of this function. find the absolute maximum value of this function.

Exponential models
ANSWERED ### Choose the correct letter. Which of the following functions models exponential decay? A. $$f(x)=12*3^x$$ B. $$y=2*0.8^x$$ C. $$y=-3x^2$$ D. $$f(x)=1.8^x$$

ANSWERED ### Simplify and express the final result using positive exponents. $$\displaystyle{\left({\frac{{{4}{a}^{{-{2}}}}}{{{3}{b}^{{-{2}}}}}}\right)}^{{-{2}}}$$

Forms of linear equations
ANSWERED ### The reduced row echelon form of a system of linear equations is given.Write the system of equations corresponding to the given matrix. Use x, y. or x, y, z. or x1,x2,x3,x4 as variables. Determine whether the system is consistent or inconsistent. If it is consistent, give the solution.

Exponential models
ANSWERED ### Determine whether a linear, quadratic, or exponential function best models the data. Then, use regression to find the function that models the data. $$\begin{array}{|c|c|} \hline x&0&1&2&3&4\\ \hline y&10089&578&968&457&8\\ \hline \end{array}$$
ANSWERED 