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sergejj [24]
2 years ago
14

What is the largest number in the form x987yz that is divisible by 12?

Mathematics
2 answers:
Sever21 [200]2 years ago
7 0

Answer:

998796

Step-by-step explanation:

For a number to be divisible by 12. it must be divisible by 3 and  4

Since we need the largest 6 digit number, we will take x = 9

So the number is 9987yz

Again since we need the largest number we will consider the largest 2 digit number multiple of 4 and 3.

Largest 2 digit number divisible by 4 is 96, which is also divisible by 3.

So, yz  = 96

Therefore , the largest number in the form will be : 998796

vodomira [7]2 years ago
4 0

Answer:

The largest number is 998796

------------------------------------------------------

The largest digit you could use is 9 so, our number would be, 998799,

but the thing is that it's not divisible by 12.

The next largest would be 8. (998798) Not divisible.

7, so our number would be, 998797. Not divisible.

6, 998796. 998796/12= 83233, which means that it is divisble, so, the largest number in the form x987yz that is divisble by 12 is 998796

Please correct me if I'm wrong.

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The function f(x) = x2 + 22x + 58 is translated 4 units to the right and 16 units up. What is the vertex form of the new functio
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Answer:

The new function is (x + 7)² - 47 ⇒ the 3rd answer

Step-by-step explanation:

* Lets put the function f(x) in the vertex form at first and then make

 the translation

∵ The general form of the quadratic function is

  f(x) = ax² + bx + c

∵ The x-coordinate of the vertex of the function is -b/2a

∵ The y-coordinate of the vertex of the function is f(-b/2a)

- Lets find a , b from the function two find the vertex point

∵ f(x) = x² + 22x + 58

∴ a = 1 , b = 22 , c = 58

∵ x-coordinate of the vertex = -b/2a

∴ x-coordinate of the vertex = -22/2(1) = -11

∵ y-coordinate of the vertex = f(-11)

∴ f(-11) = (-11)² + 22(-11) + 58 = 121 - 242 + 58 = -63

∴ The vertex point is (-11 , -63)

- The vertex form of the quadratic function is f(x) = (x - h)² + k , where

  (h , k) are the coordinates of the vertex point

∵ The vertex point is (-11 , -63)

∴ h = -11 , k = -63

∴ f(x) = (x - -11)² + -63

∴ f(x) = (x + 11)² - 63

* lets revise the rules of the translation

- If the function f(x) translated horizontally to the right  

 by m units, then the new function g(x) = f(x - m)

- If the function f(x) translated horizontally to the left  

 by m units, then the new function g(x) = f(x + m)

- If the function f(x) translated vertically up  

 by n units, then the new function g(x) = f(x) + n

- If the function f(x) translated vertically down  

 by n units, then the new function g(x) = f(x) – n

∵ f(x) will translate 4 units to the right

∴ m = 4

∵ f(x) ⇒ f(x - m)

∴ (x + 11)²  ⇒ (x + 11 - 4)² = (x + 7)²

∵f(x) will translate 16 units up

∴ -63 will add by 16

∴ n = 16

∴ f(x) ⇒ f(x) + n

∵ -63 + 16 = -47

∴ The new function is (x + 7)² - 47

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Answer:

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Step-by-step explanation:

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