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Sonbull [250]
3 years ago
9

What is a correct expansion of (3x + 2)(3x^2 + 4)

Mathematics
2 answers:
Anuta_ua [19.1K]3 years ago
5 0

All we need to do is use FOIL here to multiply these.

(3x + 2)(3x^2 + 4)

9x^3 + 12x + 6x^2 + 8

Simplify.

Rearrange terms.

9x^3 + 6x^2 + 12x + 8 is the expanded form of the original binomials.

4vir4ik [10]3 years ago
5 0

The answer is: 3x·3x^2+3x·4+2·3x^2+2·4 APEX

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A cardboard box without a lid is to have a volume of 8,788 cm3. Find the dimensions that minimize the amount of cardboard used.
Montano1993 [528]

Answer:

  x = y = 26 cm; z = 13 cm

Step-by-step explanation:

The generic solution for the minimum material in an open-top box is that the box is square and half as high as it is wide. It is half a cube of twice the volume.

The dimensions of the square base are ...

  ∛(2·8788 cm³) = 26 cm

Then the height is half that, or 13 cm.

  x = y = 26 cm; z = 13 cm

_____

If you need to see the development, you can use the method of Lagrange multipliers to find the minimum area for the given volume;

  area = xy +2(xz +yz)

  volume = xyz = 8788

We require each of the partial derivatives of L with respect to x, y, z, and λ to be zero.

  L = xy +2(xz +yz) +λ(xyz -8788)

  partial with respect to x: 0 = y+2z +λyz

  partial with respect to y: 0 = x +2z +λxz

  partial with respect to z: 0 = 2x+2y +λxy

  partial with respect to λ: 0 = xyz -8788

From the first two equations, we have ...

  λ = (y +2z)/(yz) = 1/z +2/y

  λ = (x +2z)/(xz) = 1/z +2/x

Equating these expressions for λ, we find ...

  1/z +2/y = 1/z +2/x   ⇒   x = y

The third equation then tells us ...

  λ = (2x +2y)/(xy) = 2/y +2/x

Comparing this to either of the first two expressions for λ, we see ...

  1/z +2y = 2/x +2/y   ⇒   z = x/2

This is the result we started the answer with:

  x = y = 2z = ∛(2·8788 cm³)

7 0
2 years ago
Esther uses 6.6 pints of blue paint and white paint to paint her bedroom walls. 3 5 of this amount is blue paint, and the rest i
OverLord2011 [107]

Answer:

2 16/25 or 2.64 pints.

Step-by-step explanation:

Turn the 6.6 into a fraction for calculation purposes. you get 33/5. since 3/5 is blue paint and the question wants white paint, calculate 33/5 × 2/5. You should get 66/25 as the answer.

5 0
2 years ago
If CB =3(x+8) and AD= 4(x+3), find AB
kkurt [141]

CD=CA+AB+BD

AB=CD-CA-BD

AB=CD-BD-BD

AB=CD-2.BD

AB=CD-2(BC+CD)

AB=CD-2BC-2CD

AB=-(CD+2BC)

AB=-{98-6(x+8)}

AB= 6x-50

6 0
2 years ago
determine the equation of the circle if its center is (8,-6) and which passes through the points (5,-2).
ser-zykov [4K]

Answer:

(x - 8)² + (y + 6)² = 25

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k ) are the coordinates of the centre and r is the radius

Here (h, k ) = (8, - 6 ) , then

(x - 8)² + (y - (- 6))² = r² , that is

(x - 8)² + (y + 6)² = r²

The radius is the distance from the centre to a point on the circle

Calculate r using the distance formula

r = \sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2    }

with (x₁, y₁ ) = (8, - 6 ) and (x₂, y₂ ) = (5, - 2 )

r = \sqrt{(5-8)^2+(-2-(-6))^2}

  = \sqrt{(-3)^2+(-2+6)^2}

  = \sqrt{9+4^2}

  = \sqrt{9+16}

   = \sqrt{25}

   = 5

Then equation of circle is

(x - 8)² + (y + 6)² = 5² , that is

(x - 8)² + (y + 6)² = 25

6 0
2 years ago
I need more help with 21 questions
Mariulka [41]

Answer:

45

Step-by-step explanation:

9 ÷ 1/5

9 × 5/1

9 × 5

45

7 0
3 years ago
Read 2 more answers
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