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Ahat [919]
3 years ago
12

The parent function of the function g(x) = (x – h)2 + k is f(x) = x2. The vertex of the function g(x) is located

Mathematics
1 answer:
Katen [24]3 years ago
7 0

9514 1404 393

Answer:

  (h, k) = (9, -8)

Step-by-step explanation:

The function g(x) is "vertex form" for a quadratic whose vertex is (h, k). We are told the vertex is (9, -8), so we have ...

  (h, k) = (9, -8) . . . . the values of h and k

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Step-by-step explanation:

The cosine function, along with sine and tangent, is one of the three most common trigonometric functions. In any right triangle, the cosine of an angle is the length of the adjacent side (A) divided by the length of the hypotenuse (H). In a formula, it is written simply as 'cos'.

In any right angled triangle, for any angle:

The sine of the angle = the length of the opposite side

                                  the length of the hypotenuse

The cosine of the angle = the length of the adjacent side

                                     the length of the hypotenuse

The tangent of the angle = the length of the opposite side

                                     the length of the adjacent side

So in shorthand notation:

sin = o/h   cos = a/h   tan = o/a

Often remembered by: soh cah toa

7 0
3 years ago
Determine which ratio forms a proportion with 6/9
velikii [3]
Idk for sure but im thinking 8/12? idk sorry
7 0
3 years ago
Suppose $2000 is invested at 9% interest compounded continuously. How long will it take for the investment to grow to $10,000? U
Lady bird [3.3K]

Answer:

7

Step-by-step explanation:

sing the equation         >    A  =  Pe^rt

20000  =    10000e^0.1t    >       10%  =  0.1

2  = e^0.1t

log 2  =    log e^0.1t               >     log to the base e

log 2  =  0.1t * 1              log e to the base e  =1

0.6931 = 0.1t

t =   6.931

  =    7 years

Hope this helps <3

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4 0
3 years ago
How does it satisfy a linear function
Alina [70]
Multiple values of y for a single value of x is a sure giveaway that this is NOT a function.  Please review definitions of "function."  A function would be represented if no x value has more than one y value associated with it.
5 0
3 years ago
Directions: Using the digits 1 to 9, at most one time each, fill in the boxes to find the largest or smallest possible values fo
12345 [234]

9514 1404 393

Answer:

  smallest: 8x -3 = 4; 1y +9 = 2. total = -49/8

  largest: 1x -9 = 8; 2y +3 = 7. total = 19

Step-by-step explanation:

If we use variables to represent the box contents, we can write ...

  • ax -b = c
  • dy +e = f

Then the values of x and y are ...

  x = (c +b)/a

  y = (f -e)/d

For positive integer values of the variables, x will always be positive, and y may or may not be negative.

<h3>Smallest sum</h3>

For the sum to be the smallest, we must have x be as small as possible and the ratio (f-e)/d be as negative as possible.

x will be small for large 'a' and for (c+b) small. For y to be as negative as possible, we want 'd' and 'f' small and 'e' large. Best results are obtained for

  • 8x -3 = 4   ⇒   x = 7/8
  • 1y +9 = 2   ⇒   y = -7

For these coefficients, the sum is -6 1/8 = -49/8.

(note that the values of 'b' and 'c' can be swapped with no net effect)

<h3>Largest sum</h3>

For the sum to be the largest, we must have x as large as possible: (b+c) large and 'a' small. At the same time we must have y be positive and as large as possible: (f-e) positive and large, 'd' small. Best results are obtained for

  • 1x -9 = 8  ⇒   x = 17
  • 2y +3 = 7   ⇒   y = 2

For these coefficients, the sum is 19. Again, 'b' and 'c' can be swapped with no effect.

_____

<em>Additional comment</em>

These extreme values are verified by examination of the 60,480 possible permutations of the coefficients.

8 0
3 years ago
Read 2 more answers
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