$\left \{ {{y+4x=12} \atop {3y=8-12x}} \right. \\\\ \left \{ {{y=12-4x} \atop {3y=8-12x}} \right. \\\\3(12-4x)=8-12x\\\\36-12x=8-12x\\\\-12x+12x=8-36\\\\0\neq28\\\\There\ are\ no\ solutions.$

6 0

4 years ago

17) Convert the number to scientific notation 0.00317

Masteriza [31]

Answer:

3.17x10^-3

Step-by-step explanation:

Move the decimal so there is one non-zero digit to the left of the decimal point. The number of decimal places you move will be the exponent on the

10. If the decimal is being moved to the right, the exponent will be negative. If the decimal is being moved to the left, the exponent will be positive.

6 0

3 years ago

Let FS R be a finite set. (a) Prove that F is closed (b) Prove that every point in F is an isolated point.

Lorico [155]

Answer:

a) Suppose that F is ordered in ascending order: $F = \{x_1,\ldots, x_n\}$ . Then, the complement of F can be written as

$F^c = (-\infty,x_1)\cup (x_1,x_2)\cup (x_2,x_3)\cup \cdots \cup (x_{n-1}, x_{n})\cup (x_n,+\infty)$

which is the union of a finite number of open intervals, then $F^c$ is an open set. Thus, F is a closed subset of the real numbers.

b) Take an arbitrary element of F, let us say $x_k$ . Now, choose a real number $\epsilon$ such that

$0$ there are not other element of F, because $\epsilon$ is less that the minimum distance between $x_k$ and its neighbors.

In case that $k=1$ we only consider $0$ , and if $k=n$ we only consider $0$ .

Then, all points of F are isolated.

Step-by-step explanation:

8 0

3 years ago