Does the table represent y as a function of x? Justify Your Answer.

Answers

Answer 1

Answer:

NO. It does not represent y is a function of x.

Step-by-step explanation:

For a given table of values to be considered as representing a function, every domain value (x-value) must have exactly one range value (y-value). This implies that a function cannot have two y-values assigned it mapped to the same x-value.

Therefore, the table of values given does not represent a function because the x-value, 3.45 has two y-values, 1.72 and 3.36, assigned or mapped to it.

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Show that W is a subspace of R^3.

Answers

Answer:

Check the two conditions of Subspace.

Step-by-step explanation:

If W is a Subspace of a vector space, V then it should satisft the following conditions.

1) The zero element should be in W.

Zero element can be different for different vector spaces. For examples, zero vector in $\math{R^2}$ is (0, 0) whereas, zero element in $\math{R^3}$ is (0, 0 ,0).

2) For any two vectors, $w_1$ and $w_2$ in W, $w_1 + w_2$ should also be in W.

That is, it should be closed under addition.

3) For any vector $w_1$ in W and for any scalar, $k$ in V, $kw_1$ should be in W.

That is it should be closed in scalar multiplication.

The conditions are mathematically represented as follows:

1) 0 $\in$ W.

2) If $w_1 \in W; w_2 \in W$ then $w_1 + w_2 \in W$ .

3) $$ \forall k \in V, and \hspace{2mm} \forall w_1 \in W \implies kw_1 \in W$

Here V = $\math{R^3}$ and W = Set of all (x, y, z) such that $x - 2y + 5z = 0$

We check for the conditions one by one.

1) The zero vector belongs to the subspace, W. Because (0, 0, 0) satisfies the given equation.

i.e., 0 - 2(0) + 5(0) = 0

2) Let us assume $w_1 = (x_1, y_1, z_1)$ and $w_2 = (x_2, y_2, z_2)$ are in W.

That means: $x_1 - 2y_1 + 5z_1 = 0$ and

$x_2 - 2y_2 + 5z_2 = 0$

We should check if the vectors are closed under addition.

Adding the two vectors we get:

$w_1 + w_2 = x_1 + x_2 - 2(y_1 + y_2) + 5(z_1 + z_2)$

$= x_1 + x_2 - 2y_1 - 2y_2 + 5z_1 + 5z_2$

Rearranging these terms we get:

$x_1 - 2y_1 + 5z_1 + x_2 - 2y_2 + 5z_2$

So, the equation becomes, 0 + 0 = 0

So, it s closed under addition.

3) Let k be any scalar in V. And $w_1 = (x, y, z) \in W$

This means $x - 2y + 5z = 0$

$kw_1 = kx - 2ky + 5kz$

Taking k common outside, we get:

$kw_1 = k(x - 2y + 5z) = 0$

The equation becomes k(0) = 0.

So, it is closed under scalar multiplication.

Hence, W is a subspace of $\math{R^3}$ .

QuestionComplete the hypothesis about the product of two rational numbers.
Select the correct answer from each drop-down menu.
The product of two rational numbers is a rational
equivalent to the ratio of two integers
number
number because multiplying two rational numbers is
3 which is an irrational

Answers

The product of two rational numbers is a rational number.

What is a rational number?

"A rational number is a number that can be expressed as the quotient or fraction p/q of two integers, a numerator 'p' and a non-zerodenominator 'q'."

Therefore, when we are multiplying two rational numbers, their product must be a rational number.

This is because, numerators of both rational numbers are integers and denominators of both the numbers are non-zero integers.

Hence, the product is a rational number.

Learn more about a rational number here: brainly.com/question/9466779

#SPJ3

Find the perimeter of rectangle MNOP with vertices M (-2,5), N (-2, -4), O (3, -4), and P (3,5)Part B: Square ABCD has vertices, A (-3.5, 4), B (3.5, 4), C (3.5, -4) and D (-4.5, -4. What is the area of Square ABCD?

Answers

Answer:

(-3.5,4)b

Step-by-step explanation:

8 5/12 divided by 1 3/4

Answers

^fractions lesson^

8 5/12 : 1 3/4

step 1:

(8 × 12 + 5)/12

=101/12

step 2:

(1 × 4 + 3)/4

=7/4

ok, enter:

101/12 : 7/4

=101/12 × 4/7

=404/84

=4 68/84

=4 17/21

A college professor states that this year's entering students appear to be smarter than entering students from previous years. The college's records indicate that the mean IQ for entering students from earlier years. is 110.3. Suppose we want to sample a smaller number of this year's entering students and carry out a hypothesis test to see if the professor statement can be supported. State the null and alternative hypothesis.

Answers

Answer:

$H_(0)$ : μ = 110.3

$H_(a)$ : μ > 110.3

Step-by-step explanation:

Let μ be the mean IQ of this year's entering students.

Then null and alternative hypotheses are:

$H_(0)$ : μ = 110.3 (this year's students mean IQ is at most the mean IQ of the entering students from previous years)

$H_(a)$ : μ > 110.3 (this year's students mean IQ is higher than the mean IQ of the entering students from previous years)

What is the equation of the line

Answers

find the equation of a line given that you know points it passes through

Answer:

picture?

Step-by-step explanation: