6x + 2y = -12 4x + 3y = 7

Solve. 6x - 2y = 10 for y when x = 2

An investment of $\$5000$ doubles in value every decade. The function $f(x)=5000\cdot 2^x$, where $x$ is the number of decades, models the growth of the value of the investment. How much is the investment worth after $30$ yr?

Find the general solution of the given system.

$$\mathbf{X}^{\prime}=\left(\begin{array}{rr}{12} & {-9} \\ {4} & {0}\end{array}\right) \mathbf{X}$$

Solve each problem, and express the answer in scientific notation. a. $\left(4 \times 10^{2}\right) \times\left(1 \times 10^{8}\right)$ b. $\left(2 \times 10^{-4}\right) \times\left(3 \times 10^{2}\right)$ c. $\left(6 \times 10^{2}\right) \div\left(2 \times 10^{\prime}\right)$ d. $\left(8 \times 10^{4}\right) \div\left(4 \times 10^{1}\right)$

Find $(f \cdot g)(-2)$ for the following functions.

$$\begin{array}{l}{f(x)=-x^{2}+2 x-2} \\ {g(x)=2 x+3}\end{array}$$

A. -20 B. 8 C. 120 D. 215

describe how to transform the graph of y =ln x into the graph of the given function. Sketch the graph by hand and support your sketch with a grapher.

$$f(x)=ln(2-x)$$

Let

$$F _ { 1 } \left( y _ { 1 } \right) \text { and } F _ { 2 } \left( y _ { 2 } \right)$$

be two distribution functions. For any

$$\alpha , - 1 \leq \alpha \leq 1$$

, consider

$$Y _ { 1 }$$

and

$$Y _ { 2 }$$

with joint distribution function

$$F \left( y _ { 1 } , y _ { 2 } \right) = F _ { 1 } \left( y _ { 1 } \right) F _ { 2 } \left( y _ { 2 } \right) \left[ 1 - \alpha \left\{ 1 - F _ { 1 } \left( y _ { 1 } \right) \right\} \left\{ 1 - F _ { 2 } \left( y _ { 2 } \right) \right\} \right]$$

. What is

$$F \left( y _ { 1 } , \infty \right)$$

, the marginal distribution function of

$$Y _ { 1 }$$

? [Hint: What is

$$F _ { 2 } ( \infty )$$

?]

Is it possible to form a triangle with the given side lengths? If not, explain why not. 3 in., 4 in., 8 in.

A geosynchronous satellite orbits Earth at a distance of 42,250.0 km and has a period of 1 day. What is the centripetal acceleration of the satellite?

The center of a ring R is the subring defined by $\{c \in R: c r=r c$ for every $r \in R\}.$ Prove that the center of $M(2, \mathbb{Z})$ consists of all matrices of the form

$$\left[\begin{array}{ll}{a} & {0} \\ {0} & {a}\end{array}\right], \quad a \in \mathbb{Z}$$

Verify that this is not an ideal of $M(2, \mathbb{Z}).$

What is the primary purpose of the Supremacy Clause? to outline why some powers must be implied rather than detailed to explain why state and federal powers are always kept equal to describe the relationship between federal and state powers to declare to American citizens the US is the supreme ruler

Air flows from a pipe into the region between two parallel circular disks. The fluid velocity in the gap between the disks is closely approximated by $V=V_{0} R / r,$ where R is the radius of the disk, r is the radial coordinate, and $V_{0}$ is the fluid velocity at the edge of the disk. Determine the acceleration for r = 1, 2, or 3 ft if $V_{0}=5 \mathrm{ft} / \mathrm{s}$ and $R=3 \mathrm{ft.}$

Find, to the nearest degree, the angles that a diagonal of a box with dimensions 10 cm x 11 cm x 25 cm makes with the edges of the box.