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3 years ago

What is the difference between bounded above and bounded below?

1 answer:

8 0

The set EE is said to be bounded above if and only if there is an M∈RM∈R such that a≤Ma≤Mfor all a∈Ea∈E, in which case MM is called an upper bound of EE.A number ss is called a supremum of the set EE if and only if ss is an upper bbound of EE and s≤Ms≤M for all upper bounds MM of EE (In this case we shall say that EE has a finite supremum ss and write s=supEs=supE.

Let E⊂RE⊂R be nonempty.

the set EE is said to be bounded below if and only if there is an m∈Rm∈R such that a≥ma≥m for all a∈Ea∈E, in which case mm is called a lower bound of the set EE.A number tt is called an infimum of the set EE if and only if tt is a lower bound of EE and t≥mt≥m for all lower bounds mm of EE. In this case we shall say that EE has an infimum tt and write t=infE

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Answer this and I give more points

SVEN [57.7K]

9) C.

10)A.

11) $75

Those are all the answers that you needed.

5 0

2 years ago

Read 2 more answers

Consider the quadratic function f(x) = x2 – 5x + 12. Which statements are true about the function and its graph? Select three op

klasskru [66]

The graph of the quadratic function f(x)=x² - 5x + 12 is a parabola which opens up.

<h3>What is an equation?</h3>

An equation is an expression that shows the relationship between two or more numbers and variables.

The standard form of a quadratic equation is:

y = ax² + bx + c

The graph of a quadratic equation is a parabola.

The graph of the quadratic function f(x)=x² - 5x + 12 is a parabola which opens up.

Find out more on equation at: brainly.com/question/2972832

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4 0

1 year ago

Functions f(x) and g(x) are shown below:

AlekseyPX

Consider f(x) = -4(x - 6)² + 3
This is a parabola with vertex at (6, 3).
Because the leading coefficient of -4 is negative, the curve opens downward, and the vertex is the maximum value.

Answer: Maximum of f(X) = 3

Consider the function g(x) = 2 cos(2x - π) + 4
The maximum value of the cosine function is 1.
Therefore the maximum value of g(x) is
2*1 + 4 = 6

Answer: Maximum of g(x) = 6

5 0

3 years ago

Helen had $12 but spent $3 of it. What per cent did she spend?

Bezzdna [24]

Answer:

25%

Step-by-step explanation:

Its basic division really. The easiest way to think of it is how many times can 3 fit into 12 three fits into 12 four times in fraction that's 1/4 or 1 over 4. Just like the quarter (United States quarter) each one is 25 cents and you need 4 of then to make 1 US dollar or 100% so each group of three is 25 percent. This under standing could work with a variety of numbers 5 is what percent of 20 or 7 is what percent of 28 if it comes in 4s each is 25%. Hope this helps.

4 0

2 years ago

Read 2 more answers

Find a and b if the point p(6,0) and Q(3,2) lie on the graph of ax+ by=12

tiny-mole [99]

to get the equation of any straight line we only need two points off of it, hmmm let's use P and Q here and then let's set the equation in standard form, that is

standard form for a linear equation means

• all coefficients must be integers, no fractions

• only the constant on the right-hand-side

• all variables on the left-hand-side, sorted

• "x" must not have a negative coefficient

$(\stackrel{x_1}{6}~,~\stackrel{y_1}{0})\qquad (\stackrel{x_2}{3}~,~\stackrel{y_2}{2}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{2}-\stackrel{y1}{0}}}{\underset{run} {\underset{x_2}{3}-\underset{x_1}{6}}}\implies \cfrac{2}{-3}\implies -\cfrac{2}{3} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{0}=\stackrel{m}{-\cfrac{2}{3}}(x-\stackrel{x_1}{6})$

$\stackrel{\textit{multiplying both sides by }\stackrel{LCD}{3}}{3(y-0)~~ = ~~3\left( -\cfrac{2}{3}(x-6) \right)}\implies 3y=-2(x-6) \\\\\\ 3y=-2x+12 \implies \stackrel{a}{2} x+\stackrel{b}{3} y=12$

5 0

1 year ago