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kramer
3 years ago
5

Solve each system by elimination 6x+3y=21 -12x+y=-7

Mathematics
2 answers:
Olenka [21]3 years ago
5 0

Answer:

x=1,y=5

Step-by-step explanation:

6x+3y=21....(1)

-12x+y=-7.....(2)

From (2) make y the subject of formula

y=-7+12x...(3)

Substitute (3) into (1)

6x+3(-7+12x)=21

6x-21+36x=21

Collect like terms

6x+36x=21+21

42x=42

Divide both sides by 42

x=1

Substitute the value of x into (3)

y=-7+12(1)

y=-7+12

y=5

Therefore x=1,y=5

AnnyKZ [126]3 years ago
4 0

Answer:

(x,y)=(1,5)

Step-by-step explanation:

6x+3y=21/*2

-12x+y=-7

12x+6y=42 (1)

-12x+y=-7 (2)

(1)+(2): 7y=35

-12x+y=-7

y=35/7

-12x+y=-7

y=5

-12x+5=-7

y=5

-12x=-7-5

y=5

-12x=-12

y=5

x=-12/(-12

y=5

x=1

(x,y)=(1,5)

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Answer:

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Alternate Hypothesis, H1 = The pulse rates of men do not have a standard deviation equal to 10 beats per minute

Step-by-step explanation:

The null hypothesis is basically the problem statement i.e

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2 years ago
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

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∵ 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)

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* 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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3 years ago
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