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Svetllana [295]
3 years ago
14

20-90x-50x^2 find the vertex

Mathematics
2 answers:
Leni [432]3 years ago
6 0

20-90x-50x^2, written in standard form, would be -50x^2 - 90x + 20. Let's use the method of completing the square to determine the vertex:

Divide all terms in -50x^2 - 90x + 20 by -50, obtaining -50(x^2 + (9/5)x - 2/5)

The coefficient of x is 9/5. Divide this by 2, obtaining 9/10, and then square this result: (9/10)^2 = 81/100. Add this to x^2 + (9/5)x - 2/5 and then subtract it, resulting in x^2 + (9/5)x - 2/5 + 81/100 - 81/100, or

x^2 + (9/5)x + 81/100 - 2/5 - 81/100, or

(x + 9/10)^2 - 12100

Then the vertex location is (-9/10, -12100).

A faster approach would be to use x = -b / (2a) to determine the x-coordinate of the vertex and then to evaluate the function at this x-value to determine the y-coordinate. Here x = -(-90) / (-100) = -9/10 (same as before).

lawyer [7]3 years ago
4 0
I think it’s your answer

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In Graph x-axis represents number of visits and y-axis represents cost.

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Answer:

3

Step-by-step explanation:

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Match the property name with the appropriate equation. Use each once.
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Answer:

19. Opposite of a Difference     ↔    E. -(8 - 3·m) = 3·m - 8

20. Opposite of a sum               ↔    A.  -[(-r) + 2p] = -(-r) - 2p

21. Opposite of an Opposite     ↔   F. -1[ -1(9 - 2w)] =  9 - 2w

22. Multiplication by 0               ↔   B.  160 - (3d + 2)(0) = 160 - 0

23. Multiplication by                   ↔   D. -1 -(4r + 3s) + t = (-1)(4r + 3s) + t

21. Distributive property             ↔   C.  5(2 - x) = 10 - 5x

Step-by-step explanation:

19. Opposite of a difference is the difference of the opposites

20. Opposite of a sum is the sum if the opposites

21. Opposite of an opposite is the original number

22. Multiplication by 0- The result of multiplication by 0 is 0

23. Multiplication by -1 results in the change in sign of a number

24. Distributive property - Multiplying the sum or difference of two numbers  by a number, will have the same result as multiplying each each of the addends by the number individually and adding the product together.

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