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3 years ago

What is the equation written in a function notation with x as the independent variable x-y=3

Mathematics

1 answer:

Aleksandr [31]3 years ago

4 0

we are given

$x-y=3$

Here , we are given

x as the independent variable

so, y is dependent variable

so, we will solve for y

$x-y=3$

Add both sides by y

$x-y+y=3+y$

$x=3+y$

Subtract both sides by 3

$x-3=3+y-3$

$x-3=y$

so, our function is

$f(x)=x-3$ ................Answer

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Given a function I and a subset A of its domain, let I(A) represent the range of lover the set A; that is, I(A) = {I(x) : x E A}

Ede4ka [16]

Step-by-step explanation:

(a)

Using the definition given from the problem

$f(A) = \{x^2 \, : \, x \in [0,2]\} = [0,4]\\f(B) = \{x^2 \, : \, x \in [1,4]\} = [1,16]\\f(A) \cap f(B) = [1,4] = f(A \cap B)\\$

Therefore it is true for intersection. Now for union, we have that

$A \cup B = [0,4]\\f(A\cup B ) = [0,16]\\f(A) = [0,4]\\f(B)= [1,16]\\f(A) \cup f(B) = [0,16]$

Therefore, for this case, it would be true that $f(A\cup B) = f(A)\cup f(B)$ .

(b)

1 is not a set.

(c)

To begin with

$A\cap B \subset A,B$

Therefore

$g(A\cap B) \subset g(A) \cap g(B)$

Now, given an element of $g(A) \cap g(B)$ it will belong to both sets, therefore it also belongs to $g(A\cap B)$ , and you would have that

$g(A)\cap g(B) \subset g(A \cap B)$ , therefore $g(A)\cap g(B) = g(A \cap B)$ .

(d)

To begin with $A,B \subset A \cup B$ , therefore

$g(A) \cup g(b) \subset g(A\cup B)$

7 0

4 years ago

-9/10 divided by -6/15

Yanka [14]

-9/10 divided by -6/15
Convert the division sign to multiplication while flipping the fraction -6/15 to -15/6.
-9/10 * -15/6
Multiply the numerator(-9) by the other numerator(-15) while multiplying the denominator(10) by the other denominator(6)
Final Answer: 135/60 or 2.25 or 2 1/4 *All answers are equivalent to each other.

7 0

3 years ago

X -9 -5 -1 3 Y - 2 0 2 4 What is the slope of the line?

Mekhanik [1.2K]

ok done. Thank to me :>

5 0

2 years ago

Use the diagram below to answer parts B, and C.

expeople1 [14]

Answer:

The volume of the triangular prism in the diagram is:

105.5 $in^{3}$

The surface area of the triangular prism in the diagram is:

10.75 $in^{2}$

Step-by-step explanation:

First, we're gonna calculate the surface area to obtain the volume, then, to calculate the area of a triangle (because the surface o a triangular prism is just a triangle), you can use the formula:

Area of a triangle = (base * height) / 2

We have this data from the diagram, where the base of the triangles is 5 inches and, the height is 4.3 inches, replacing this in the formula:

Area of a triangle = ( 5 in * 4.3 in) / 2
Area of a triangle = ( 21.5 $in^{2}$ ) / 2
Area of a triangle = 10.75 $in^{2}$

Now, we can calculate the volume of the triangular prism with the next formula:

Volume of a triangular prism = surface area * depth

In the diagram, we can see the depth is 14 inches, then:

Volume of a triangular prism = 10.75 $in^{2}$ * 14 in
Volume of a triangular prism = 105.5 $in^{3}$

How you can see with the calculations perfomed, the surface area is 10.75 $in^{2}$ and the volume of that triangular prism is 105.5 $in^{3}$ .

7 0

3 years ago

Is this rational or irrational I really need help ASAP! Will mark brainlist.

vichka [17]

Answer: Rational

A rational number is, as the name implies, any number that can be expressed as a ratio, or fraction. ... 4.5 is a rational number, as it can be represented as 9/2.

I hope this is good enough:

4 0

3 years ago