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Nezavi [6.7K]
2 years ago
12

A combination lock has 6 different numbers. You can use any number 0 - 9 in the combination, but each number can only be used ON

CE. How many different combinations are possible?
Mathematics
1 answer:
Zarrin [17]2 years ago
7 0
There are 151,200 possible combinations. If you'd like an explanation of my answer, please let me know.
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Y=-x^2-12x-37 find the 1) Roots 2) Factors 3) Vertex (x,y) 4) Interception with 'Y" axis 5) Axis of Symmetry 6)Direction of Open
kakasveta [241]

Answer:

1) The roots of the equation Y = -x² - 12·x - 37 are x = -6 - √73 and -6 + √73

2) The factors of the function Y = -x² - 12·x - 37 are (x + (-6 - √73)) and (x - (-6 + √73))

3) The vertex is (-6, -1)

4) The Y-intercept is (0, -37)

5) The axis of symmetry is x = -6

6) The parabola opens downward

7) The maximum point is (-6, -1)

8) The graph of the function created with Microsoft Excel is attached

9) The domain of the function is -∞ < x < ∞

10) The range of the function is -∞ < Y ≤ -1

Step-by-step explanation:

The given function is Y = -x² - 12·x - 37

1) The roots of the equation Y = -x² - 12·x - 37 is given as follows;

0 = -x² - 12·x - 37

∴ -x² - 12·x - 37 = 0

The roots are;

x = (12 ± √((-12)² - 4 × 1 × (-37)))/(-2)

∴ x = -6 - √73 and -6 + √73

2) The factors are (x + (-6 - √73)) and (x - (-6 + √73))

3) The vertex is given by h = -b/(2·a) = 12/(2) = -6

k = c - b²/(4·a) = -37 - 144/(-4) = -1

The vertex = (h, k) = (-6, -1)

4) The intercept with the "Y" axis is given when x = 0, therefore, the y-intercept is (0, -37)

5) The axis of symmetry can be found at the vertex or the line x = -6

6) The sign of the coefficient of x² is negative therefore, the parabola opens downward

7) The maximum point is given as follows;

At the maximum point, dY/dx = d(-x² - 12·x - 37)/dx = -2·x - 12 = 0

x = 12/(-2) = -6, which is the vertex, therefore Y = -(-6)² - 12×(-6) - 37 = -1

The maximum point is the vertex (-6, -1)

8) Please find attached the graph of the function created with Microsoft Excel

9) The domain of the function is -∞ < x < ∞

10) The range of the function is -∞ < Y ≤ -1

4 0
2 years ago
1. Camille received $1000 in graduation gifts. He found a savings plan that will pay him 4% interest compounded continuously. Us
Tems11 [23]

Answer:

10,000-$10,500

Step-by-step explanation:

The answer will be between $10,000-$10,500

7 0
3 years ago
2p Determine the value of a such that the system of equations below would have an infinite number of solutions?
Alona [7]


2p Determine the value of a such that the system of equations below would have an infinite number of solutions?
18x + 12y = 36
ax – 8y =- 24

Answer: a=-12
6 0
2 years ago
+23+-26 RESPUESTA PORFIS
den301095 [7]

Answer:

-3

Step-by-step explanation:

7 0
2 years ago
Read 2 more answers
What decimal is equal to 31/100
BlackZzzverrR [31]

Answer:

0.31

Step-by-step explanation:

So if you divide 31 by 100 all you have to do is move the decimal from right to left the number of zeros you have. Here we have 2 zeros so we move from right to left twice.

0.31

4 0
3 years ago
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