When collecting like terms, what terms are alike in the expression seen

Using the bijection rule to count binary strings with even parity.

AleksandrR [38]

Answer:

Lets denote c the concatenation of strings. For a binary string a in B9, we define the element f(a) in E10 this way:

f(a) = a c {1} if a has an odd number of 1's
f(a) = a c {0} if a has an even number of 1's

Step-by-step explanation:

To show that the function f defined above is a bijective function, we need to prove that f is well defined, injective and surjective.

f is well defined:

To see this, we need to show that f sends elements fromo b9 to elements of E10. first note that f(a) has 1 more binary integer than a, thus, it has 10. if a has an even number of 1's, then f(a) also has an even number because a 0 was added. On the other hand, if a has an odd number of 1's, then f(a) has one more 1, as a consecuence it will have an even number of 1's. This shows that, independently of the case, f(a) is an element of E10. Thus, f is well defined.

f is injective (or one on one):

If a and b are 2 different binary strings, then f(a) and f(b) will also be different because the first 9 elements of f(a) form a and the first elements of f(b) form b, thus f(a) is different from f(b). This proves that f in injective.

f is surjective:

Let y be an element of E10, Let x be the first 9 elements of y, then f(x) = y:

If x has an even number of 1's, then the last digit of y has to be 0, and f(x) = x c {0} = y
If x has an odd number of 1's, then the last digit of y has to be a 1, otherwise it wont be an element of E10, and f(x) = x c {1} = y

This shows that f is well defined from B9 to E10, injective, and surjective, thus it is a bijection.

3 0

4 years ago

Check answer? My answer is x = 80

Alex

The two triangles are similar.

40/x = 32/4

x = 5

8 0

3 years ago

Pls help I need it done tonight

Ksenya-84 [330]

Answer:

ABD= 58

BDC= 32

Step-by-step explanation:

complementary = 2 angles equal 90 degrees.

8y+2=90

Subtract 2 both sides.

8y=88

y=11

That's not all, put y into the equations.

ABD

5(11)+3

Multiply

55+3=58

BDC

3(11)-1

MULTIPLY

33-1

SUBTRACT

32

4 0

3 years ago

Part A Predict what will happen to the coordinates of a point (x, y) as the point reflects across a line to produce point (x', y

mylen [45]

The list attached shows the coordinate of (x, y) after transformation when reflecting over x, y-axis, and lines y = x, y = -x

<h3>What is geometric transformation?</h3>

It is defined as the change in coordinates and the shape of the geometrical body. It is also referred to as a two-dimensional transformation. In the geometric transformation, changes in the geometry can be possible by rotation, translation, reflection, and glide translation.

We have two lines of reflection:

y = x and

y = -x

The point is (x, y)

After reflecting over line y = x the coordinate (x, y) becomes:

(y, x)

After reflecting over the line y = -x the coordinate (x, y) becomes:

(-y, -x)

Thus, the list attached shows the coordinate of (x, y) after transformation when reflecting over x, y-axis, and lines y = x, y = -x

Learn more about the geometric transformation here:

brainly.com/question/16156895

#SPJ1

7 0

2 years ago

Determine the equation of the line that is parallel to the given line, through the given point.

Verdich [7]

Answer:

$y=-\frac{3}{2}x+1$

Step-by-step explanation:

Hi there!

What we need to know:

Linear equations are typically organized in slope-intercept form: $y=mx+b$ where m is the slope and b is the y-intercept (the value of y when x is 0)
Parallel lines always have the same slope

1) Determine the slope (m)

$3x+2y = 10$

First, we must organize this given equation in slope-intercept form. This will help us identify its slope.

$3x+2y = 10$

Subtract 3x from both sides

$2y = -3x+10$

Divide both sides by 2

$y = -\frac{3}{2} x+5$

Now, we can identify clearly that $-\frac{3}{2}$ is in the place of m in $y=mx+b$ , making it the slope. Because parallel lines have the same slope, this makes the slope of the line we're currently solving for $-\frac{3}{2}$ as well. Plug this number into $y=mx+b$ :