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2 years ago

2X -5+3a - 5X +2a Help

Mathematics

1 answer:

Katen [24]2 years ago

6 0

Answer:

1. 2x can be seen as +2x therefore when you put it as +2x-5x the answer will be - 3x

2. +3a+2a also equals +5a

3. - 5 is left alone and there is no other similar expression

Put them together the answer becomes

-3x+5a-5

It doesn't have to be the same order of format but the numbers must be as such

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26. Define a relation ∼ ∼ on R 2 R2 by stating that ( a , b ) ∼ ( c , d ) (a,b)∼(c,d) if and only if a 2 + b 2 ≤ c 2 + d 2 . a2+

Tresset [83]

Answer:

~ is reflexive.

~ is asymmetric.

~ is transitive.

Step-by-step explanation:

~ is reflexive:

i.e., to prove $\forall (a, b) \in \mathbb{R}^2$ , $(a, b) R(a, b)$ .

That is, every element in the domain is related to itself.

The given relation is $\sim: (a,b) \sim (c, d) \iff a^2 + b^2 \leq c^2 + d^2$

Reflexive:

$(a, b) \sim (a, b)$ since $a^2 + b^2 = a^2 + b^2$

This is true for any pair of numbers in $\mathbb{R}^2$ . So, $\sim$ is reflexive.

Symmetry:

$\sim$ is symmetry iff whenever $(a, b) \sim (c, d)$ then $(c, d) \sim (a, b)$ .

Consider the following counter - example.

Let (a, b) = (2, 3) and (c, d) = (6, 3)

$a^2 + b^2 = 2^2 + 3^2 = 4 + 9 = 13$

$c^2 + d^2 = 6^2 + 3^2 = 36 + 9 = 42$

Hence, $(a, b) \sim (c, d)$ since $a^2 + b^2 \leq c^2 + d^2$

Note that $c^2 + d^2 \nleq a^2 + b^2$

Hence, the given relation is not symmetric.

Transitive:

$\sim$ is transitive iff whenever $(a, b) \sim (c, d) \hspace{2mm} \& \hspace{2mm} (c, d) \sim (e, f)$ then $(a, b) \sim (e, f)$

To prove transitivity let us assume $(a, b) \sim (c, d)$ and $(c, d) \sim (e, f)$ .

We have to show $(a, b) \sim (e, f)$

Since $(a, b) \sim (c, d)$ we have: $a^2 + b^2 \leq c^2 + d^2$

Since $(c, d) \sim (e, f)$ we have: $c^2 + d^2 \leq e^2 + f^2$

Combining both the inequalities we get:

$a^2 + b^2 \leq c^2 + d^2 \leq e^2 + f^2$

Therefore, we get: $a^2 + b^2 \leq e^2 + f^2$

Therefore, $\sim$ is transitive.

Hence, proved.

3 0

3 years ago

What is the slope of the line through (-1, 4) and (1, -2)

Vesna [10]

Answer:

6/2

Step-by-step explanation:

(y2-y1)/(x2-x1)

4-(-2) over 1-(-1)

4+2 over 1+1

6/2

5 0

3 years ago

Read 2 more answers

A small orchestra has 3 stringed instruments. What is the ratio of violins to cellos?

mylen [45]

Violin to Celio.

Violin : Celio

Violin = 6

Celio = 5

6:5

D. 6/5

5 0

3 years ago

3/4(n+3)=9 how do I find n

katrin [286]

It's one of the ways to count it:

3/4 (n + 3) = 9
3/4n + 3/4 * 3 = 9
3/4n + 9/4 = 9
3/4n + 2 1/4 = 9 / - 2 1/4 (both sides)
3/4n = 6 3/4 / : 3/4 (both sides)
n = 9

8 0

3 years ago

Read 2 more answers

How do you find the equation that is perpendicular to 2x-5y=20, passing through the point (7,-8)?

IrinaK [193]

To find a perpendicular line you first need to see the equation in slope intercept form. To do that you need to solve for y.

2x - 5y = 20 ---> subtract 2x from both sides
-5y = -2x + 20 ---> divide by -5
y = 2/5x - 4

Now that you have this, note that a perpendicular line has opposite and reciprocal slope. Since the slope in our equation is 2/5, that means the new line will have -5/2 slope. So we use the point given and the slope to find the y intercept.

y = mx + b
-8 = -5/2(7) + b ---> multiply
-8 = -35/2 + b ---> add 35/2 to both sides
19/2 = b

Now use our new slope and new y intercept to write the new equation.

y = -5/2x + 19/2

8 0

3 years ago