We have that
<span>f(x)=2x</span>²<span>+12x+16
using a graph tool
see the attached figure</span>
<span>f(x)=2x</span>²<span>+12x+16
using a graph tool
see the attached figure</span>
Which graph represents the piecewise-defined function?
2 answers:
Answer: The first option is correct.
Explanation:
The given piecewise function is,
From the piecewise function we can say that if x<0, then
If , then
Since the f(x) is defined for x<0 and , therefore the function f(x) is not defined for
.
In the graph 2, 3 and 4 for each value of x there exist a unique value of y, therefore the function is defined for all values of x, which is not true according to the given piecewise function.
Only in figure the value of y not exist when x lies between 0 to 2, including 0. It means the function is not defined for , hence the first option is correct.
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Answer:
The unknown sides are 60.81cm and 51.57cm while the unknown angle is 58degrees
Step-by-step explanation:
4a) Given the following
Opposite side = 38cm (side facing the given angle)
Required
Adjacent and hypotenuse side
According to SOH CAH TOA
Next is to get the adjacent
Next is to get the missing
Since sum of angle in the triangle is 180degrees
32 + 90 + x = 180
122 + x = 180
x = 180 - 122
x = 58degrees
Using a discrete probability distribution, it is found that:
a) There is a 0.3 = 30% probability that he will mow exactly 2 lawns on a randomly selected day.
b) There is a 0.8 = 80% probability that he will mow at least 1 lawn on a randomly selected day.
c) The expected value is of 1.3 lawns mowed on a randomly selected day.
<h3>What is the discrete probability distribution?</h3>Researching the problem on the internet, it is found that the distribution for the number of lawns mowed on a randomly selected dayis given by:
- P(X = 0) = 0.2.
- P(X = 1) = 0.4.
- P(X = 2) = 0.3.
- P(X = 3) = 0.1.
Item a:
P(X = 2) = 0.3, hence, there is a 0.3 = 30% probability that he will mow exactly 2 lawns on a randomly selected day.
Item b:
There is a 0.8 = 80% probability that he will mow at least 1 lawn on a randomly selected day.
Item c:
The expected value of a discrete distribution is given by the <u>sum of each value multiplied by it's respective probability</u>, hence:
E(X) = 0(0.2) + 1(0.4) + 2(0.3) + 3(0.1) = 1.3.
The expected value is of 1.3 lawns mowed on a randomly selected day.
More can be learned about discrete probability distributions at brainly.com/question/24855677
Answer:
7,11
Step-by-step explanation:
The width is x. x+4= the length. The area is side times side, so it’s
x × (x+4) = 77
We can simplify this to:
x × x + x × 4 = 77
x^2 + 4x = 77
x^2 + 4x - 77 = 0 This is a quadratic equation. So we can solve using the quadratic formula:
x = ->
That’s the positive solution and that’s x, the width. So the width is 7 and the length is 7+4=11