Which rule has a scale factor of 3 and shifts the shape 4 units left and 2 units down?

Given the quadratic equation below, the standard form of it is

kotykmax [81]

Answer:

Step-by-step explanation:

2x^+9x=10

2x^2+9x-10=0 is standard form

8 0

3 years ago

Prove De Morgan's law by showing that each side is a subset of the other side by considering x ∈ A⎯⎯⎯ A ¯ ∩ B⎯⎯⎯ B ¯ .

adelina 88 [10]

Solution :

We have to prove that $\overline{A \cup B} = \overline{A} \cap \overline{B}$ (De-Morgan's law)

Let $x \in \bar{A} \cap \bar{B},$ then $x \in \bar{A}$ and $x \in \bar{B}$

and so $x \notin \bar{A}$ and $x \notin \bar{B}$ .

Thus, $x \notin A \cup B$ and so $x \in \overline{A \cup B}$

Hence, $\bar{A} \cap \bar{B} \subset \overline{A \cup B}$ .........(1)

Now we will show that $\overline{A \cup B} \subset \overline{A} \cap \overline{B}$

Let $x \in \overline{A \cup B}$ ⇒ $x \notin A \cup B$

Thus x is present neither in the set A nor in the set B, so by definition of the union of the sets, by definition of the complement.

$x \in \overline{A}$ and $x \in \overline{B}$

Therefore, $x \in \overline{A} \cap \overline{B}$ and we have $\overline{A \cup B} \subset \overline{A} \cap \overline{B}$ .............(2)

From (1) and (2),

$\overline{A \cup B} = \overline{A} \cap \overline{B}$

Hence proved.

3 0

3 years ago

The number of hours, t, that bacteria spread 10-fold can be modeled by the equation B(t) = B0(10)2t. There are 25 bacteria prese

nordsb [41]

Answer: 1.67 hours.

Explanation:

1) Function that models the number of bacteria:

$B(t)=B_0(10)^{2t}$

2) Bo = 25, then the function is:

$B_0=25(10)^{2t}$

3) To know how many hours will elpase until the number of bactaria is 55,00, you equals B to 55,500 in the equation and solve for t, in this way:

i) start

$55000=25(10)^{2t)$

ii) division property

$2200=10^{2t}$

iii) antilogarithm property

$2t = log_{10}2200$

iv) division property

$t=\frac{log_{10}2200}{2}$

v) Due the operations:

t = 1.67 hours.

Note that the time is less than 2 hours. That sounds fine since after 1 hour there will be 10 times 25 (250 bacteria), and after 2 hours 100 times 25 (2500 bacteria).