Solve the linear system using substitution.

$$\left. \begin{array} { l } { x - 9 = 0.5 y } \\ { 2.2 x - 3.1 y = - 0.2 } \end{array} \right.$$

In this exercise, find the roots of the given equation by completing the square.

$$3 x^2 +6 x+6=0$$

In the graph of $x - 3 y > 1 ,$ the corresponding equation $x - 3 y = 1$ is graphed as a(n) ______ line.

Determine the value of the literal numbers in each of the given matrix equalities. If the matrices cannot be equal, explain why.

$$\begin{bmatrix} x \\ x+y \end{bmatrix} = \begin{bmatrix} 2 & 0 \\ 4 &-3 \end{bmatrix}$$

Given that

$$\frac{1}{1-x}=\sum_{n=0}^{\infty} x^{n}$$

with convergence in (−1, 1), find the power series for the function with the given center a, and identify its interval of convergence. $f(x)=\frac{1}{1-2 x} ; a=0$

Solve the right triangle named$ABC$ with altitude $a$,base $b$, hypotenuse $c$ and angle $\theta$, marked between base and hypotenuse,for all unknown sides and angles.The angle $C=90^\circ$.$A$ is in between $b$ and $c$ and $B$ is in between $a$ and $c$.Round your answers to two decimal places.

$$A=30^{\circ}, \quad b=3$$

Write the following expression using summation notation.

$$1^2+2^2+3^2+\ldots+9^2+10^2$$

Solve for x, rounding to three decimal places if necessary. Check for extraneous solutions.

$$log_2 3 + log_2 (x – 4) = 4$$

Which is NOT the equation of a parabola? $\text{ F. } y=2 x^{2}+4 x-9$ $\text { G. } 3 x+2 y^{2}+y+1=0$ $\text { H. } x^{2}+2 y^{2}+8 y=8$ $\text { J. } x=\frac{1}{2}(y-1)^{2}+5$

Solve the system of linear equations using any algebraic method.
-3x + 4y = -1
6x + 2y = 7

Explain why the vapor pressure of water $\left(2.34 \mathrm{kPa}\right.$ at $\left.20^{\circ} \mathrm{C}\right)$ is far less than the vapor pressure of pentane (59.9 kPa at $20^{\circ} \mathrm{C}$ ) which is a much bigger molecule.

Describe and correct the error made while simplifying the expression $\frac{3+\sqrt{2}}{3-\sqrt{2}}$.

$$\begin{aligned} \frac{3+\sqrt{2}}{3-\sqrt{2}}= & \frac{3+\sqrt{2}}{3-\sqrt2} \cdot \frac{3+\sqrt{2}}{3+\sqrt{2}} \\ = & \frac{3^2+(\sqrt{2})^2}{3^2-(\sqrt{2})^2}=\frac{9+2}{9-2}=\frac{11}{7}\end{aligned}$$

Use the given transformation to evaluate the integral.

$\iint_R\left(x^2-x y+y^2\right) d A$, where $R$ is the region bounded by the ellipse $x^2-x y+y^2=2$;

$$x=\sqrt{2} u-\sqrt{2 / 3} v, \quad y=\sqrt{2} u+\sqrt{2 / 3} v$$

If a pair of dice is tossed once, what is the probability that the total number rolled will be

$\text{(a)} \ 7? \qquad$ (b) a number less than $7$ ?