Mathematics, 12.08.2020 05:01 Ayomide19

Help will mark brainlist if it correct If each edge of a cube is increased by 2 inches, the A. volume is increased by 8 cubic inches
B. area of each face is increased by 4 square

C. diagonals of each face is increased by 2 inches
D. sum of these edges is increased by 24 inches

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Answer from: bsheepicornozj0gc

D. sum of these edges is increased by 24 inches -- True

Step-by-step explanation:

Given a cube and its edge is increased by 2 inches.

To study the effect of this increase in the Volume, area of each face, diagonal and sum of edges.

Solution:

Let the side of original cube = a inches.

Formula for volume of cube:

V =side^3 = a^3

If the side is increased by 2 inches, the side becomes (a+2) inches.

So, new volume, V' = (a+2)^3

Using the formula:

(x+y)^3 =x^3+y^3+3xy(x+y)

$V' = (a+2)^3 = a^3+8+3\times 2 \times a(a+2)=a^3+8+6a(a+2)$

So, V' = V + 8+6a(a+2)

Volume increased by 8+6a(a+2) [which is not equal to 8]

So, statement is false:

A. volume is increased by 8 cubic inches -- False

Each face in a cube is a square.

Area of each face, A = side^2 = a^2

New area, A' = (a+2)^2

Using the formula: (x+y)^2 =x^2+y^2+2xy

A' = a^2+4+4a

Area increased by 4+4a [which is not equal to 4 sq inches]

B. area of each face is increased by 4 square inches -- False

Diagonal of each face = $a\sqrt2$

Increase of 2 in the edge:

New diagonal = $(a+2)\sqrt2 = a\sqrt2+2\sqrt2$

So, increase of $2\sqrt2$ not 2.

C. diagonals of each face is increased by 2 inches -- False

There are 12 number of edges in a square.

So sum of all 12 edges = 12a

When edge is increased by 2, sum of all edges = 12(a+2) = 12a + 24

An increase of 24.

D. sum of these edges is increased by 24 inches -- True

Answer from: Quest

x= -3 and $x=\frac{-3+/-3i\sqrt{3} }{2}$

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

$(x^3-a^3)=$ $(x-a)(x^2+ax+a^2)$

where a is the cube root of $a^3$ .

here this is 27 and the cube root of 27 is 3. so we write using the form:

$(x-3)(x^2+(3)x+3^2)\\(x-3)(x^2+3x+9)$ .

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

$x=\frac{-b+/-\sqrt{b^2-4ac} }{2a}$

where a = 1, b=3, and c=9

$x=\frac{-3+/-\sqrt{3^2-4(1)(9)} }{2(1)} \\x=\frac{-3+/-\sqrt{9-36)} }{2} \\x=\frac{-3+/-\sqrt{-27)} }{2}\\x=\frac{-3+/-3i\sqrt{3} }{2}$

this cubic has two complex roots.

Answer from: Quest

true

step-by-step explanation:

according to the national european world center, the engineering of the ford company on elon musk's flame throwers proved the globalization of the natural wallabies and therefore, results in the growth product domestication in almonds.

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Help will mark brainlist if it correct If each edge of a cube is increased by 2 inches, the A. volu...