Which inequality in standard form represents the shaded region?

Mathematics

1 answer:

Lubov Fominskaja [6]2 years ago

5 0

The figure is represented by the inequality y ≥ 5 · x² - 40 · x - 45. (Correct choice: C)

<h3>What inequality represents the figure</h3>

In accordance with the figure, we have an inequation of the form y ≥ f(x). Now we proceed to find the <em>quadratic</em> equation of the parabola:

f(x) = a · (x + 1) · (x - 9)

- 125 = a · (4 + 1) · (4 - 9)

- 125 = a · 5 · (- 5)

- 125 = - 25 · a

a = - 5

f(x) = 5 · (x + 1) · (x - 9)

f(x) = 5 · (x² - 8 · x - 9)

f(x) = 5 · x² - 40 · x - 45

The figure is represented by the inequality y ≥ 5 · x² - 40 · x - 45. (Correct choice: C)

To learn more on inequalities: brainly.com/question/17675534

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Which number does NOT represent an integer? A. 3 B. 20.1 C. -10 D. 20/4

guapka [62]

Answer:

the number doesnt represent an integer?

A. 3

B. 20.1

C. -10

D. 20/4

Step-by-step explanation:

We call integers the “counting numbers, their negatives and zero”. I.e. 0,1,−1,2,−2,3,−3,.. etc.

non-integers means “everything except integers”. Which is not well-defined (i.e. nonsense). Why? Because nobody said what “everything” is.

Therefore, when somebody says “non-integer” he has to specify how he defines “everything”. In this case, our “everything” is probably “real numbers”.

Real numbers have an interesting definition concerning an abstract mathematical object called “field” . Let’s forget about that and let’s focus on a high school definition: Real numbers are probably all the numbers you know. They are those represented by a decimal and their negatives e.g. 345.232… and −243.13242240… where there are “infinitely many” digits at the end. Note that 2.5 is also a real number. Integers are too. Basically, real numbers are the numbers used to measure distances and their negatives.

To summirize, your answer is the following:

“non integers” means everything except the integers, where everything is defined however we want. The most common definition of everything in this case is “real numbers” and therefore the most common interpretation of “non integers” is “reals which are not integers”.

Examples of “reals which are not integers”: 1.5,2.88,1.3333… etc

the answer is

B. 20.1

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