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4 years ago

Determine the equation of the graph, and select the correct answer below.

Mathematics

1 answer:

Hunter-Best [27]4 years ago

8 0

Vertex is (h,k)
Equation is ..
Y = (x -h)^2 + k
Put in vertex (-4,-1) gives the equation
Y = (x+4)^2 - 1

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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

In 1990, the average monthly bill for cellular telephone service was $80.90. From 1990-1997, the monthly bill decreased by 8.6%

lapo4ka [179]

A)The formula for the average monthly cellular telephone bill in terms of the year will be A = 80.90(0.914)ⁿ⁻¹

B)The average monthly bill in 1993 willl be $ 61.77

<h3>What is the percentage?</h3>

The quantity of anything is stated as though it were a fraction of a hundred. A fraction of 100 can be used to express the ratio.

The formula for the average monthly cellular telephone bill in terms of the year willl be,

A=P(R/100)ⁿ

A = 80.90(0.914)ⁿ⁻¹

The average monthly bill in 1993 is found as ;

n=4 for 1993

A=P(R/100)ⁿ

A = 80.90(0.914)³⁻¹

A=$ 61.77

Hence the formula for the average monthly cellular telephone bill in terms of the year will be A = 80.90(0.914)ⁿ⁻¹ and the average monthly bill in 1993 willl be $ 61.77.

To learn more about percentages, refer to:

brainly.com/question/13450942

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