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2 years ago

50p thanks to whoever helps :)

Mathematics

1 answer:

barxatty [35]2 years ago

4 0

Answer:

1. 1+(2+3)

2. (1 +2)+3

3. (2*3)*4

4. 2*(3*4)

5. 3*2

6. 2+1

7. 2(x+3)

8. 4x+3

9. (4*3)+(4*2)

10. (-2*5)+(-2*x)

11. (3*10)-(3*y)

12. (-3*4)-(-3*x)

13. commutative property

14. commutative property

15. distributive property

16. associative property

17. 1+(-3)

18. 4+3

19. -(-4-3)

20. -4+3

Hope this helps

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Step-by-step explanation:

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The graph of which function has a minimum located at (4, –3)?

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Answer:

None of the options is the answer to the question

Step-by-step explanation:

we know that

The equation of a vertical parabola into vertex form is equal to

$f(x)=a(x-h)^{2}+k$

where

(h,k) is the vertex of the parabola

case A) we have

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In this case the x-coordinate of the vertex will be negative

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case B) we have

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This case is a vertical parabola open downward (the vertex is a maximum)

The vertex is the point $(4,-3)$ <u>but is not a minimum</u>

see the attached figure

therefore

case B is not the solution

case C) we have

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Convert into vertex form

Group terms that contain the same variable, and move the constant to the opposite side of the equation

$f(x)-5=x^{2}-4x$

Complete the square. Remember to balance the equation by adding the same constants to each side

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Rewrite as perfect squares

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The vertex is the point $(2,1)$

therefore

case C is not the solution

case D) we have

$f(x)=2x^{2}-16x+35$

Convert into vertex form

Group terms that contain the same variable, and move the constant to the opposite side of the equation

$f(x)-35=2x^{2}-16x$

Factor the leading coefficient

$f(x)-35=2(x^{2}-8x)$

Complete the square. Remember to balance the equation by adding the same constants to each side

$f(x)-35+32=2(x^{2}-8x+16)$

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Rewrite as perfect squares

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$f(x)=2(x-4)^{2}+3$ --------> vertex form

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therefore

case D is not the solution

The answer to the question will be the function

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