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3 years ago

Factor this expression and show the steps12x^2+14x-6

Mathematics

1 answer:

Minchanka [31]3 years ago

6 0

$\boxed{\bold{2\left(3x-1\right)\left(2x+3\right)}}$

$\bold{----------------------------------}$

$\bold{Factor \ Out \ Common \ Term \ 2: \ 2\left(6x^2+7x-3\right)}$

$\bold{2\left(6x^2+7x-3\right)}$

$\bold{Factor \ 6x^2+7x-3: \ \left(3x-1\right)\left(2x+3\right)}$

$\bold{2\left(3x-1\right)\left(2x+3\right)}$

$\boxed{\bold{Eclipsed}}$

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3 years ago

Jennifer earns $7.60 per hour working after school. She wants to buy a musical instrument and she needs at least $500. Write an

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3 years ago

What are the common factors of 10 25 and 75

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3 years ago

Mating eagle pairs typically have two baby eagles (called eaglets). When there are two eaglets, the parents always feed the olde

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Answer:

C. x 0 1 2 p(x) 0.35 0.60 0.05

Step-by-step explanation:

50% chance of survival

Let:

x = older eaglet survive

y = younger eaglet survive

Hence,

P(x = 0) (none of the eaglet survive)

P(x = 1) (only one survive)

P(x = 2) (both survive)

P(x) = 0.5

P(x') = 1 - 0.5 = 0.5

P(x n y) = 0.5 * 0.1 = 0.05 ( both survive)

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(0.5 * 0.3) + (0.5 * (1 - 0.1))

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= 0.35

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3 years ago

A piece of wire of length L will be cut into two pieces, one piece to form a square and the other piece to form an equilateral t

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Answer:

(a) square: L; triangle: 0.

(b) square: L·(-16+12√3)/11; triangle: L·(27-12√3)/11

Step-by-step explanation:

Strategy: First we will write each area in terms of its perimeter. Then we will find the total area in terms of the amount devoted to the square. Differentiating will give a way to find the minimum total area.

In terms of its perimeter p, the area of a square is ...

A_square = p^2/16

In terms of its perimeter p, the area of an equilateral triangle is ...

A_triangle = p^2/(12√3)

Then the total area of the two figures whose total perimeter is L with "x" devoted to the square is ...

A_total = x^2/16 + (L-x)^2/(12√3)

(a) We know when polygons are regular, the one with the most area for the least perimeter is the one with the most sides. Hence, the total area is maximized when all of the wire is devoted to the square.

(b) The derivative of A_total with respect to x is ...

dA/dx = x/8 -(L-x)/(6√3)

This will be zero when ...

x/8 = (L-x)/(6√3)

x(6√3) = 8L -8x

x(8 +6√3) = 8L

x = L·8/(6√3 +8) = 8L(6√3 -8)/(64-108)

x = L·(12√3 -16)/11

The total area is minimized when L·(12√3 -16)/11 is devoted to the square, and the balance is devoted to the triangle.

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3 years ago

Factor this expression and show the steps12x^2+14x-6​

Factor this expression and show the steps12x^2+14x-6