# Get college algebra help

Recent questions in Algebra
Vectors and spaces

### if x, y belong to R^p, than is it true that the relation norm (x+y) = norm (x) + norm (y) holds if and only if x = cy or y = cx with c>0

Transformations of functions

### Describe how the given functions can be obtained from their basic (or parent) function f using transformations. $$\displaystyle{f{{\left({x}\right)}}}=\sqrt{{{x}}},{g{{\left({x}\right)}}}=\sqrt{{{2}{x}-{10}}}$$

Transformations of functions

### The function g is related to one of the parent functions described in an earlier section. $$\displaystyle{g{{\left({x}\right)}}}={\frac{{{1}}}{{{6}}}}\sqrt{{{x}}}$$ a) Identify the parent function f. b)Describe the sequence of transformations from f to g. c)Use function notation to write g in terms of f. g(x)=(?)f(x)

Vectors and spaces

### Vectors u and v are orthogonal. If u=<3, 1+b> and v=<5, 1-b> find all possible values for b.

Vectors and spaces

### The average height of a 2 year old boy is 38 inches. an 8 year old averages 56 inches. Use this information to write a linear equation that models the height (in inches), y, in terms of the age (in years), x. Use the linear equation to predict the average height of a 5 year-old boy.

Vectors and spaces

### $Find the minimum and maximum values of $$\displaystyle{y}=\sqrt{{6}}\theta-\sqrt{{3}}{\sec{\theta}}$$ on the interval PSK[0,\frac{\text{pi}}{\text{3}}]$

Forms of linear equations

### 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 $$x_1, x_2, x_3, x_4$$ as variables. Determine whether the system is consistent or inconsistent. If it is consistent, give the solution. $$\begin{bmatrix}1 & 0 & 0 & 0 & 1\\ 0 &1 & 0 &0 & 2 \\ 0 & 0 & 1 & 2 & 3 \end{bmatrix}$$

Transformations of functions

### What transformations of the parent graph of $$\displaystyle{f{{\left({x}\right)}}}=\sqrt{{c}}$$ produce the graphs of the following functions? a) $$\displaystyle{m}{\left({x}\right)}=\sqrt{{{7}{x}-{3.5}}}-{10}$$ b) $$\displaystyle{j}{\left({x}\right)}=-{2}\sqrt{{{12}{x}}}+{4}$$

Exponential models

### In addition to quadratic and exponential models, another common type of model is called a power model. Power models are models in the form yˆ=a⋅xp. Here are data on the eight planets of our solar system. Distance from the sun is measured in astronomical units (AU), the average distance Earth is from the sun. $$\begin{array}{|l|c|c|} \hline \text { Planet } & \begin{array}{c} \text { Distance from sun } \\ \text { (astronomical units) } \end{array} & \begin{array}{c} \text { Period of revolution } \\ \text { (Earth years) } \end{array} \\ \hline \text { Mercury } & 0.387 & 0.241 \\ \hline \text { Venus } & 0.723 & 0.615 \\ \hline \text { Earth } & 1.000 & 1.000 \\ \hline \text { Mars } & 1.524 & 1.881 \\ \hline \text { Jupiter } & 5.203 & 11.862 \\ \hline \text { Saturn } & 9.539 & 29.456 \\ \hline \text { Uranus } & 19.191 & 84.070 \\ \hline \text { Neptune } & 30.061 & 164.810 \\ \hline \end{array}$$ Use the PwrReg command on your graphing calculator to find a power model relating y = period to x = distance.

Forms of linear equations

### Consider the system (*) whose coefficient matrix A is the matrix D listed in Exercise 46 and whose fundamental matrix was computed just before the preceding exercise.

Forms of linear equations

### Write the vector form of the general solution of the given system of linear equations. $$\displaystyle-{x}_{{1}}+{2}{x}_{{3}}-{5}{x}_{{4}}+{x}_{{5}}-{x}_{{6}}={0}$$

Forms of linear equations

### The row echelon form of a system of linear equations is given. a) Write the system of equations corresponding to the given matrix. Use x, y. or x, y, z. or $$x_1,x_2,x_3,x_4$$ as variables. Determine whether the system is consistent or inconsistent. If it is consistent, give the solution. $$\begin{bmatrix}1 & 2 & -1 & 0 \\ 0 & 1 & -1 & 1 \\ 0 & 0 & 0 & 2 \end{bmatrix}$$

Forms of linear equations

### Write the vector form of the general solution of the given system of linear equations. $$\displaystyle{x}_{{1}}+{2}{x}_{{2}}-{x}_{{3}}+{2}{x}_{{5}}-{x}_{{6}}={0}$$

Forms of linear equations

### The given matrix is the augmented matrix for a system of linear equations. Give the vector form for the general solution. $$\begin{bmatrix} {1}&{0}&-{1}&-{2}&-{3}&{1}\\{0}&{1}&{2}&{3}&{4}&{0}\end{bmatrix}$$

Alternate coordinate systems

### Solve the following systems of inequalities graphically on the set of axes below.The state the following coordinates of a point in the solution say $$\displaystyle{y}\leq{x}+{6}$$ $$\displaystyle{y}\succ{\frac{{{3}}}{{{2}}}}{x}-{4}$$

Forms of linear equations

### The given matrix is the augmented matrix for a system of linear equations. Give the vector form for the general solution. $$\begin{bmatrix}{1}&{0}&-{1}&-{2}&-{3}&{0}\\{0}&{1}&{2}&{3}&{4}&{0}\end{bmatrix}$$

Alternate coordinate systems

### Consider the following system. $$\begin{cases}{y}={30}-{x}\\{2}{y}=-{x}^{{{2}}}+{16}{x}-{12}\end{cases}$$

Transformations of functions

### Begin by graphing $$\displaystyle{f{{\left({x}\right)}}}={{\log}_{{{2}}}{x}}$$ Then use transformations of this graph to graph the given function. What is the graph's x-intercept? What is the vertical asymptote? Use the graphs to determine each function's domain and range. $$\displaystyle{g{{\left({x}\right)}}}={{\log}_{{{2}}}{\left({x}-{2}\right)}}$$

Transformations of functions

### Sketch a graph of the function. Use transformations of functions when ever possible. $$\displaystyle{f{{\left({x}\right)}}}={1}+\sqrt{{{x}}}$$

Forms of linear equations