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4 years ago

Pre algebra Simplify 32 ⋅ 35.

1 answer:

3 0

32x35=1,120
To solve this equation, all you have to do is put the two numbers in a calculator connected by multiplication sign,

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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

9,648 in standard form

AlekseyPX

9x100

i hope i helped

6 0

3 years ago

Ik that no one would like to help me with this but my friend is not feeling well today. hes out with a cold today so can yall ma

Natali [406]

Answer:

will do

Step-by-step explanation:

5 0

3 years ago

If the parent function f(x) = (2x − 3)3 is transformed to g(x) = (-2x + 3)3, which type of transformation occurs?

zimovet [89]

Answer:

it reflect over y axis.

Step-by-step explanation

Given: If the parent function f(x) = (2x − 3)³ is transformed to g(x) = (-2x + 3)³.

To find: Which type of transformation occurs.

Solution: We have given that

parent function f(x) = (2x − 3)³ .

transformed to g(x) = (-2x + 3)³.

By the transformation rule ; f(x)→→ f(-x) it mean function is reflect over y axis.

We can see from given functions g(x) →→ f(-x).

Therefore, it reflect over y axis.

4 0

3 years ago

I have been stuck on this math equation for 15 minutes. Someone please help me!

Alja [10]

Answer:

(x−9)²+(y− $\frac{17}{2}$ )²= $\frac{441}{4}$

Step-by-step explanation:

8 0

3 years ago