How can i write 1 as a power in three different ways?

Over what interval is the function of the graph

Svet_ta [14]

Answer:

1 ≤ x ≤ 6 Option A

Step-by-step explanation:

When graph is constant it means, value of graph ( y-values) not to be change different values of x in given interval.

In other words, graph must be parallel to the x axis is known as the constant graph.

A function is a measure of the rate of change of function values with respect to change in input values.

In given graph horizontal line is lie on the interval from x ≥ 1 to x ≤ 6.

So, option A is correct.

6 0

4 years ago

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

35% of x is 3.5 What is the value of x

docker41 [41]

Answer: x =10

Step-by-step explanation:

I'm sorry if its not right

4 0

3 years ago

Mitchell took a math exam today.If he got 63 out of 84 questions correct, what percentage did Mitchell get wrong?

NISA [10]

Answer:

The answer is x = 25%

Step-by-step explanation:

84 represents 100% of the questions.

63 represents x% of the correct answers.

x = (63x100)/84

x = 6300/84

x = 75% correct answers.

percentage of the wrong answers:

100% - 75% = 25%

5 0

3 years ago

Read 2 more answers

A bucket contains 50 lottery balls numbered 1-50. One is drawn at random. What is the probability that it is a multiple of 6 giv

never [62]

The probability is 7/41.

We are looking for
P(multiple of 6 given 2 digit) = P(2 digit & multiple of 6)/P(2 digit)

There are 7 2-digit numbers that are multiples of 6 between 1 and 50, out of 50 numbers; P(2 digit & multiple of 6) = 7/50

There are 41 2-digit numbers out of 50; P(2 digit) = 41/50

This gives us 7/50 ÷ 41/50 = 7/50 × 50/41 = 7/41

3 0

3 years ago