College Algebra Solutions for Your Success

Find the matrix of the linear mapping. ${\displaystyle L(x,y,z)=(x+y+z)}$

The coefficient matrix for a system of linear differential equations of the form $y_1=Ay$
has the given eigenvalues and eigenspace bases. Find the general solution for the system
${\lambda }_1=3+i\Rightarrow \left\{\left[\begin{array}{c}2i\\ i\end{array}\right]\right\},{\lambda }_2=3-i\Rightarrow \left\{\left[\begin{array}{c}-2i\\ -i\end{array}\right]\right\}$

To calculate: The probability that a student chosen randomly from the class is going to college if the number of students in a high school graduating class is 128, out of which 52 are on the honor roll, and out of these, 48 are going to college. The number of students who are not on the honor roll is 76, out of these 56 are going to college.

Let R be a commutative ring with identity and let I be a proper ideal of R. proe that ${\displaystyle \frac{R}{I}}$ is a commutative ring with identity.

Consider the following two bases for ${\displaystyle R^3}$ :
$\alpha :=\{\left[\begin{array}{c}2\\ 1\\ 3\end{array}\right],\left[\begin{array}{c}-1\\ 0\\ 1\end{array}\right],\left[\begin{array}{c}3\\ 1\\ -1\end{array}\right]\}and\beta :=\{\left[\begin{array}{c}1\\ 1\\ 1\end{array}\right],\left[\begin{array}{c}-2\\ 3\\ 1\end{array}\right],\left[\begin{array}{c}2\\ 3\\ -1\end{array}\right]\}$ If $[x{]}_{\alpha }={\left[\begin{array}{c}1\\ 2\\ -1\end{array}\right]}_{\alpha }thenfind[x{]}_{\beta }$
(that is, express x in the ${\displaystyle \beta }$ coordinates).

To calculate: The intercepts on the coordinate axes of the straight line with the given equation ${\displaystyle 2y-4=3x}$

class council determined that its profit from the upcoming homecoming dance is directly related to the ticket price for the dance. Looking at past dances, the council determined that the profit pp can be modeled by the function $p(t)=-12t^2+480t+30$, where tt represents the price of each ticket. What should be the price of a ticket to the homecoming dance to maximize the council's profit? Price

Use sigma notation to express the following 1 - 2 + 3 - 4 + 5 - 6 + 7 - 8

Given f(x)=6x+5​, describe how the graph of g compares with the graph of f. g(x)=6(0.2x)+5
Select the correct choice below, and fill in the answer box to complete your choice.
A. The graph of​ g(x) is translated _ ​unit(s) to the left compared to the graph of​ f(x).
B. The graph of​ g(x) is translated _ ​unit(s) down compared to graph of​ f(x).
C. g(x) has a scale factor of _ compared to​ f(x). Because it scales the vertical​ direction, the graph is stretched vertically.
D. g(x) has a scale factor of _ compared to​ f(x). Because it scales the vertical​ direction, the graph is compressed vertically.
E. g(x) has a scale factor of _ compared to​ f(x). Because it scales the horizontal​ direction, the graph is stretched horizontally.
F. g(x) has a scale factor of _ compared to​ f(x). Because it scales the horizontal​ direction, the graph is compressed horizontally.
G. The graph of​ g(x) is translated _ ​unit(s) to the right compared to the graph of​ f(x).
H. The graph of​ g(x) is translated _ ​unit(s) up compared to graph of​ f(x).

Describe the transformations of
${\displaystyle f\left(x\right)=\sqrt{3}\left\{x\right\}}$ and ${\displaystyle h\left(x\right)=x^3}$
that result in the functions listed below.
${\displaystyle g\left(x\right)=-\sqrt{3}\{x-3\}}$ and ${\displaystyle j\left(x\right)=-{(x-3)}^3}$
${\displaystyle p\left(x\right)=4\sqrt{3}\{-x\}-1}$ and ${\displaystyle q\left(x\right)=0.25{(-4x)}^3-1}$

Let ${\displaystyle \gamma =\{t^2-t+1,t+1,t^2+1\}\text{and}\beta =\{t^2+t+4,4t^2-3t+2,2t^2+3\}be\text{or}deredbasesf\text{or}{P}_2\left(R\right).}$ Find the change of coordinate matrix Q that changes $\beta \text{ coordinates into }\gamma -\text{ coordinates}$

To draw: The conclusion and internet the decision.

Give a full correct answer for given question 1- Let W be the set of all polynomials ${\displaystyle a+bt+c{t}^2\in P_2}$ such that ${\displaystyle a+b+c=0}$ Show that W is a subspace of ${\displaystyle P_2,}$ find a basis for W, and then find dim(W) 2 - Find two different bases of ${\displaystyle R^2}$ so that the coordinates of $b=\left[\begin{array}{c}5\\ 3\end{array}\right]$ are both (2,1) in the coordinate system defined by these two bases

The equivalent polar coordinates for the given rectangular coordinates.
A rectangular coordinate is given as (0, -3).

Find the x-and y-intercepts of the graph of the equation algebraically.
${\displaystyle y=-3(2x+1)}$

Find the x-and y-intercepts of the graph of the equation algebraically.
${\displaystyle y=\frac{3}{4}x-\frac{1}{4}}$

The given matrix is the augmented matrix for a system of linear equations. Give the vector form for the general solution.
${\displaystyle \left[\begin{array}{cccccc}1& -1& 0& -2& 0& 0\\ 0& 0& 1& 2& 0& 0\\ 0& 0& 0& 0& 1& 0\end{array}\right]}$

[Pic] Describe a combination of transformations.

Find the x-and y-intercepts of the graph of the equation algebraically.
${\displaystyle y=2(x-4)}$

Need to find a variable.
$ax+5=6x+3$
solve for x