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Nina [5.8K]
3 years ago
7

(x^2 - 4)(x^2 + x - 12) = 0

Mathematics
1 answer:
tatiyna3 years ago
3 0

Answer:

is that a T or F

Step-by-step explanation:

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Ahmed wrote an expression as 12x + 24, find all the equivalent expressions using the distributive property.
xeze [42]

Answer:

12x + 24 = 2(6x + 12)

12x + 24 = 3(4x +  8)

12x + 24 = 4(3x +  6)

12x + 24 = 6(2x +  4)

12x + 24 = 12(x +  2)

Step-by-step explanation:

Given

12x + 24

Required

Equivalent expressions

No option were given; So, I will list out some possible equivalent expressions.

Using distributive property:

AB + AC = A*(B + C)

So, we have:

12x + 24 = 2*6x + 2 * 12

12x + 24 = 2(6x + 12) ----- (1)

Another:

12x + 24 = 3*4x + 3 * 8

12x + 24 = 3(4x +  8)

Another:

12x + 24 = 4*3x +  4*6

12x + 24 = 4(3x +  6)

Another:

12x + 24 = 6*2x +  6*4

12x + 24 = 6(2x +  4)

Another:

12x + 24 = 12*x +  12*2

12x + 24 = 12(x +  2)

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2 years ago
The pet store has 8 rabbits for sale. Each morning the owner feeds the rabbits a total of 2 cups of pellets. If each rabbits rec
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Each rabbit receives 4 pellets
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Teresa counted the number of tomatoes in 9 baskets at a vegetable stand. The list shows the data. 11, 12, 8, 12, 8, 8, 11, 11, 9
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Mean is 4
Median is 11
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Find the value of |5| - 4(3 to the second power - 2).
geniusboy [140]

Answer:

4.55

Step-by-step explanation:

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Find the extremum of f(x,y) subject to the given constraint, and state whether it is a maximum or a minimum. f(x,y)=4x2 2y2; 3x
nevsk [136]

For given f(x, y) the extremum: (12, 24) which is the minimum.

For given question,

We have been given a function f(x) = 4x² + 2y² under the constraint 3x+3y= 108

We use the constraint to build the constraint function,

g(x, y) = 3x + 3y

We then take all the partial derivatives which will be needed for the Lagrange multiplier equations:

f_x=8x

f_y=4y

g_x=3

g_y=3

Setting up the Lagrange multiplier equations:

f_x=\lambda g_x

⇒ 8x = 3λ                                        .....................(1)

f_y=\lambda g_y

⇒ 4y = 3λ                                         ......................(2)

constraint: 3x + 3y = 108                .......................(3)

Taking (1) / (2), (assuming λ ≠ 0)

⇒ 8x/4y = 1

⇒ 2x = y

Substitute this value of y in equation (3),

⇒ 3x + 3y = 108

⇒ 3x + 3(2x) = 108

⇒ 3x + 6x = 108

⇒ 9x = 108

⇒ x = 12

⇒ y = 2 × 12

⇒ y = 24

So, the saddle point (critical point) is (12, 24)

Now we find the value of f(12, 24)

⇒ f(12, 24) = 4(12)² + 2(24)²

⇒ f(12, 24) = 576 + 1152

⇒ f(12, 24) = 1728                             ................(1)

Consider point (18,18)

At this point the value of function f(x, y) is,

⇒ f(18, 18) = 4(18)² + 2(18)²

⇒ f(18, 18) = 1296 + 648

⇒ f(18, 18) = 1944                            ..............(2)

From (1) and (2),

1728 < 1944

This means, given extremum (12, 24) is minimum.

Therefore, for given f(x, y) the extremum: (12, 24) which is the minimum.

Learn more about the extremum here:

brainly.com/question/17227640

#SPJ4

6 0
2 years ago
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