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Aneli [31]
4 years ago
14

How can you tell whether an ordered pair is a solution of a linear inequality?

Mathematics
1 answer:
sweet-ann [11.9K]4 years ago
7 0

Hello from MrBillDoesMath!

Answer:

Suppose the ordered pair is (x.y). Substitute these values in the linear equality to see if it is true,

Example. Consider the point (7, -4). Is it a solution of the linear inequality

3x < 4y - 9?   Let's check to find out.

Check:

Is  3 (7) < 4 (-4) - 9    true ?

Is    21  < -16     -9 =  -25   ??  

NO!

So (7,-4) is NOT a solution of the linear inequality.


Thank you,

MrB


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Given f(x) =
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The end behavior of the given function (range) is x< 4 or x > 4. So, f(x) < 4 or f(x) > 4. The solution in interval notation is \mathbf{(-\infty, 4) \cup (4, \infty)}.

The last option is correct.

<h3>What is the range of the function?</h3>

The end behavior of the given function f(x) = (8x+1)/2x-9 wants us to identify the range of the given function.

The range is the set of values of the dependent variable for which a function is defined. The function range is the combined domain of the inverse function.

From the information given:

\mathbf{f(x) = \dfrac{8x +1}{2x -9 }}

Inverse of \mathbf{\dfrac{8x +1}{2x -9 }} becomes \mathbf{f(x) = \dfrac{1+9x}{2(-4+x) }}

The domain of the inverse is x< 4 or x > 4. So, f(x) < 4 or f(x) > 4. Now, representing the solution in interval notation, we have:

\mathbf{(-\infty, 4) \cup (4, \infty)}

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2 years ago
Grace has a scale of 3 cm as 90 miles on a map. If the distance between the two cities are 10 cm apart on the map, how many mile
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300 miles

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What about.,.

10 cm : ? (x) miles

We cross-multiply the ratios;

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X = 300 miles

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6 0
4 years ago
The number of basketball games that must be scheduled in a league with n teams is given by G(n) = (n2 - n)/2 where each team pla
Pani-rosa [81]

Answer:

There are 7 teams in the league

Step-by-step explanation:

Given that the number of games is given by:

G(n) = \frac{(n^2-n)}{2}

The equation will be used to determine the number of games. As we already know, that 21 games are scheduled which means G(n) is 21 so we have to find n when G(n) is 21

Putting this mathematically

21 = \frac{n^2-n}{2}

Multiplying equation by 2

2*21 = 2*\frac{n^2-n}{2}\\42 = n^2-n\\n^2-n-42 = 0\\n^2-7n+6n-42 = 0\\n(n-7)+6(n-7) = 0\\(n-7)(n+6)=0\\n-7 = 0 => n=7\\n+6=0 => n=-6

As the number of teams cannot be negative, the number of teams in league are 7.

Hence,

There are 7 teams in the league

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3 years ago
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