Exam 8: Systems of Linear Equations and Inequalities

Write the form of the partial fraction decomposition for the given rational expression. Do not solve for the constants.

Write the form of the partial fraction decomposition for the given rational expression. Do not solve for the constants.

Find A^-1 given that

Calculate AB if And

Leticia has been tacking two volatile stocks. Stock A over the last year has increased 7%, and stock B has increased 10% (using a simple interest model). She has $14,300 to invest and would like to split it between the two stocks. If the stocks continue to perform the same rate, how much should she invest in each to result in a balance of $15,559.

Use row operations to transform the matrix to reduced row-echelon form.

In chemistry lab, Bevan has to make a 495 milliliter solution that is 12% HCl. All that is in the lab is 2% and 20% HCl. How many milliliters of each solution should he use to obtain the desired mix?

Use Cramer's Rule to either solve the system of equations, determine if the system is inconsistent (no solutions), or dependent (infinitely many solutions). 7x + 6y = 61 14x + 12y = -122

Evaluate the 2 x 2 determinant.

Calculate If And

Solve the system of linear equations for x, y, and z.

An object is thrown upward, and the following table depicts the height of the ball t seconds after the projectile is released. Find the initial height, initial velocity, and acceleration due to gravity.

Solve the system by linear equations by elimination.

Use Cramer's Rule to either solve the system of equations, determine if the system is inconsistent (no solutions), or dependent (infinitely many solutions). -14x - 6y = -78 14x + 6y = 78

Solve the system of linear equations by graphing the following equations. 4x - 5y = 55 7x - 2y = 49

Graph the system of inequalities.

An equation of a line that passes through two points (x₁, y₁) and (x₂, y₂) can be expressed as a determinant Apply the determinant to write an equation of the line joining through the points (-2, 3) and (-7, -6). Expand the determinant and express the equation of the line in slope-intercept form.

Perform the row operation -6R₁ + R₂ $\rightarrow$ R₂ on the matrix and write the resulting matrix.

Write the system of linear equations as an augmented matrix. -8x + 9y = 1 -2x + 5y = -5

Find A^-1 given that