Solve the system of linear equations.

$$\begin{align*} 0.05x_1 - 0.03x_2 &= 0.21 \\ 0.07x_1+0.02x_2 &= 0.17 \\ \end{align*}$$

Solve the formula for the red variable. Surface area of cylinder: $S=2 \pi r^{2}+2 \pi r h$

Solve. Check to justify your answer. In softball, a player's batting average is computed by dividing the number of hits by the number of times at bat. So far this season, Charlotte has gotten 18 hits out of 44 times at bat. What is her batting average in decimal form?

Express as a fraction in simplest form. $2 . \overline{16}$

Solve the system of linear equations by graphing.

$$\begin{array}{l}{y=3 x+1} \\ {y=-2 x-4}\end{array}$$

Use Cramer's Rule to solve (if possible) the system of linear equations.

$$18x_1+12x_2=13\\30x_1+24y_2=23$$

solve the exponential equation algebraically. Approximate the result to three decimal places. e^4x = e^x^2+3

Write the given percent as a fraction in simplest form.

$$85 \%=$$

Solve the system of linear equations by graphing. Check your answer. 3x + 2y = 12 y = 6 - 3/2x

use an inverse matrix to solve (if possible) the system of linear equations. {-3x + 10y = 8 , 5x - 17y = -13

Solve the system of linear equations by graphing.

$$\begin{array} { l } { x - y = - 2 } \\ { 2 x - 3 y = - 2 } \end{array}$$

Solve the exponential equation algebraically. Approximate the result to three decimal places.

$$\frac{119}{e^{6x}-14}=7$$

Plot the graphs of $T_{R}$ versus the dimensionless ratio $\omega / \omega_{0}$ for $\zeta=0.1,0.5,1,2$. For what values of $\omega / \omega_{0} \text { is } T_{R}=1$? Explain why the graphs imply that it is desirable that the mountings have a low natural frequency in order to isolate the vibration source from the equipment platform, and that using low-stiffness isolators is one way to achieve this.

Solve the system of linear equations.

$$\begin{align*} 0.02x_1 - 0.05x_2 &= -0.19 \\ 0.03x_1+0.04x_2 &= 0.52 \\ \end{align*}$$