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stiv31 [10]
3 years ago
15

Place each of the key aspects under the function it describes

Mathematics
2 answers:
melamori03 [73]3 years ago
5 0

Answer:

range: {y: y ≥ 0} ⇒ h(x)

decreasing over(-∞ , 1) ⇒ h(x)

increasing over (-∞ , 0) ⇒ g(x)

range: {y: y ≤ 1} ⇒ g(x)

increasing over (1 , ∞) ⇒ h(x)

decreasing over(0 , ∞) ⇒ g(x)

Step-by-step explanation:

∵ h(x) = (x - 1)²

∴ Its vertex is (1 , 0)

∴ The parabola is opened upward

∴ The range: {y: y ≥ 0}

∴ It's decreasing over (-∞ , 1)

∴ It's increasing over (1 , ∞)

∵ g(x) = -(x - 1)(x + 1) = -(x² - 1) = -x² + 1

∴ Its vertex is (0 , 1)

∴ The parabola is opened downward

∴ The range: {y: y ≤ 1}

∴ It's increasing over (-∞ , 0)

∴ It's decreasing over (0 , ∞)

RideAnS [48]3 years ago
5 0
<h2>Answer with explanation:</h2>

First function h(x) is given by:

h(x)=(x-1)^2

The function is a quadratic function

and also we know that:

(x-1)^2\geq 0

Hence, the range is: {y | y≥0}

Also, we know that the graph of the function decreases continuously in the interval (-∞,1) and then it increases continuously in the interval (1,∞)

and the vertex is at (1,0)

Second function is:

       g(x)=-(x+1)(x-1)

which could also be written by:

g(x)=-(x^2-1)

since we know that:

(a+b)(a-b)=a^2-b^2

Also,we know that:

x^2\geq 0\\\\x^2-1\geq -1\\\\-(x^2-1)\leq 1

i.e.

g(x)\leq 1

Hence, we get the range of this function is:  {y | y≤1}

The graph of this function is a downward open parabola with vertex at (0,1) and hence, the graph is increasing in the interval (-∞,0) and decreasing over the interval (0,∞).

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Step-by-step explanation:

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3 years ago
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If two fair dice are rolled, what is the probability that the total showing is either even or less than five?
snow_tiger [21]

The Probability that the total showing is either even or less than five = 5/6

<h3>What is Probability?</h3>

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. The probability of an event is a number between 0 and 1, where, broadly speaking, 0 represents the event's impossibility and 1 implies certainty.

<h3>According to the given data:</h3>

The example space for rolling two dice is:

(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)

(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)

(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)

(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)

(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)

(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)

36 events total.

Events that have a sum that is even or less than Five .

Total instances when the aggregate is even or less than Five equals 30.

P(sum is even or less than 5)

= (Total no of favorable event)/(Total no of event)

= 30/36

=5/6

probability that the total showing is either even or less than five = 5/6

To know more about probability visit :

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6 0
1 year ago
Help me plz I can’t figure it out
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Answer:

m = 60

Step-by-step explanation:

The context is very important, the 'm' represents the minutes late the parents are and from this we can eliminate some options :

- The last one because then a parent would drop their child off earlier

- The first one and the third one because it is too long

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Answer:

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