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Rashid [163]
3 years ago
6

What is a paragraph proof of the triangle inequality theorem

Mathematics
1 answer:
Licemer1 [7]3 years ago
6 0
It is a proof that is explained in one paragraph
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The following function represents the profit P(n), in dollars, that a concert promoter makes by selling tickets for n dollars ea
Gre4nikov [31]
A) zeroes

P(n) = -250 n^2 + 2500n - 5250

Extract common factor:

P(n)= -250 (n^2 - 10n + 21)

Factor (find two numbers that sum -10 and its product is 21)

P(n) = -250(n - 3)(n - 7)

Zeroes ==> n - 3 = 0  or n -7 = 0
Then n = 3 and n = 7 are the zeros.

They rerpesent that if the promoter sells tickets at 3  or 7 dollars the profit is zero.

B) Maximum profit

Completion of squares

n^2 - 10n + 21 = n^2 - 10n + 25 - 4 = (n^2 - 10n+ 25) - 4 = (n - 5)^2 - 4

P(n) = - 250[(n-5)^2 -4] = -250(n-5)^2 + 1000

Maximum ==> - 250 (n - 5)^2 = 0 ==> n = 5 and P(5) = 1000

Maximum profit =1000 at n = 5

C) Axis of symmetry

Vertex = (h,k) when the equation is in the form A(n-h)^2 + k

Comparing A(n-h)^2 + k with - 250(n - 5)^2 + 1000

Vertex = (5, 1000) and the symmetry axis is n = 5.



8 0
3 years ago
A car drives 195 miles in 3 hours and 15 minutes. what is the average speed of the car?
g100num [7]
1 mpm or 0.0166666666 repeating mph
5 0
3 years ago
What four consecutive intergers have a sum of -34
Ivenika [448]

Answer:

-7, -8 , -9 and -10 are such four integers.

Step-by-step explanation:

Let the first integer = k

So, the next three consecutive integers are ( k+1), ((k + 1) + 1)  and (((k + 1) + 1) +1)

or, k , (k +1), (k +2) and (k +3) are four consecutive integers.

Now, their sum is -34.

⇒k   + (k +1) +  (k +2) +  (k +3)  = -34

or, 4k  + 6 = -34

or, 4k = - 34 - 6 = -40

⇒  k = -40/ 4 = -10

Hence, the first integer k = -10

The next integer = k + 1 = -10 + 1 = -9

Similarly next two integers are -8 and - 7.

So -7, -8 , -9 and -10 are such four integers.

7 0
3 years ago
Solve the inequality: -2z - 3 < 5
Ghella [55]

Answer:

z>-4

Step-by-step explanation:

6 0
2 years ago
Read 2 more answers
5x + 3 = 6x – 1<br> Solve for the solution
Genrish500 [490]

Answer: x=4

Step-by-step explanation:

Subtract 6x from both sides.

5x+3−6x=6x−1−6x

−x+3=−1

Step 2: Subtract 3 from both sides.

−x+3−3=−1−3

−x=−4

Step 3: Divide both sides by -1.

−x/−1 = −4/−1

x=4

4 0
2 years ago
Read 2 more answers
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