MATHEMATICS MIDDLE SCHOOL

A cube with 3-inch edges is to be constructed from 27 smaller cubes with 1-inch edges. Twenty-one of the cubes are colored red and 6 are colored white. If the 3-inch cube is constructed to have the smallest possible white surface area showing, what fraction of the surface area is white?

Answers

Answer 1

Answer:

The fraction of the surfacearea that is white is 2/9.

What is a cube?

It is a polygon having six faces.

The volume of a cube is Side³.

We have,

Cube:

Volume = Side³
Side = 3 inch

Volume = 3³ = 27 inches³

Now,

Redcubes = 21

White cubes = 6

Now,

The total surfacearea of the cube.

= 6 x side²

= 6 x 3²

= 6 x 9

= 54 inches²

Now,

27 cubes make the total surface area 54 inches².

27 cubes = 54 inches²

Multiply 6/27 on both sides.

6 white cubes = 6/27 x 54

6 white cubes = 12 inches²

Now,

White surfacearea = 12/54 inches²

12/54 = 2/9

Thus,

2/9 fraction of the surfacearea is white.

Learn more about cubes here:

brainly.com/question/11168779

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Answer 2

Answer: The volume of the larger cube is 3*3*3, which is 27.
The volume of the smaller cubes is 1*1*1, which is 1.
27/1=27
That means all cubes will be used, so only the placement of the cubes matter.
The center of the cube will show no sides,
The center of the face will show 1 side, which has a surface area of 1sq.in.
Since there are 6 white cubes and 6 faces with 6 face centers, and only one cube center, there will be 5 cubes on the center of the faces and 1 in the cube center.

This means there will be 0 faces of 1 cube and 1 faces shown for the rest of the cubes. Since each face is 1sq.un., the rest is math

(0*1)+((1*1)5)
(0)+(1*5)
0+5
5sq.un. of the cube is white.

a=The fraction of surface area showing
b=Surface area of large cube

b=3*3*number of sides on cube(6)

5*a=b
5*a=54
a=54/5

Your answer is 54/5.

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For the function f(x)=x2-4, fins the value of f(x) when x=6

Complete the equation of the line through (-9,-7) and (-6,-3)

Answers

The equation of the line through (-9, -7) and (-6, -3) is $y+3=(4)/(3)(x+6)$

Solution:

Given, two points are (-9, -7) and (-6, -3)

We have to find that a line that passes through the given two points.

First let us find the slope of the line that passes through given two points.

The slope of the line "m" is given as:

$\mathrm{m}=(y_(2)-y_(1))/(x_(2)-x_(1))$

$\text { where, }\left(x_(1), y_(1)\right) \text { and }\left(x_(2), y_(2)\right) \text { are two points on line. }$

So slope of our line $=(-3-(-7))/(-6-(-9))=(-3+7)/(-6+9)=(4)/(3)$

Now, let us find the line equation using point slope form:

$\mathrm{y}-\mathrm{y}_(1)=\mathrm{m}\left(\mathrm{x}-\mathrm{x}_(1)\right) \text { where } \mathrm{m} \text { is slope and }\left(\mathrm{x}_(1), \mathrm{y}_(1)\right) \text { is point on the line. }$

By substituting the values we get,

$\text { Then, line equation } \rightarrow y-(-3)=(4)/(3)(x-(-6))$

$y+3=(4)/(3)(x+6)$

Hence, the line equation is $y+3=(4)/(3)(x+6)$

Which represents a quadratic function? f(x) = 2x3 + 2x2 – 4 f(x) = –7x2 – x + 2 f(x) = –3x + 2 f(x) = 0x2 + 3x – 3

Answers

Answer:

Second option: $f(x) =-7x^2 -x + 2$

Step-by-step explanation:

A quadratic function has the form:

$f(x)=ax^2+bx+c$

(Where $a\neq0$ )

You can observe that the highest exponent of a quadratic function is 2.

Then, let's check which of the options shows a quadratic function:

1) $f(x) = 2x^3 + 2x^2 - 4$

Its highest exponent is 3, then this is not a quadratic function.

2) $f(x) =-7x^2 -x + 2$

Its highest exponent is 2 and $a\neq0$ , then this is a quadratic function.

3) $f(x) = -3x + 2$

Its highest exponent is 1, then this is not a quadratic function.

4) $f(x) =0x^2+3x-3$

You can observe that $a=0$ , then this is not a quadratic function.

Answer:

B. f(x) = –7x2 – x + 2

Step-by-step explanation:

the answer above me is right so I'm just shortening it so the answer is easy to find, have a great day !

Kareem saves his coins in a jar. 30% of the coins are pennies. if there are 24 pennies in the jar, how many coins does Kareem have?

Answers

30%=30/100=3/10

3/10 of all=pennies=24
divide by 3
1/10 of all=8
times 10
10/10 of all=80
80 coins she has

PLEASE HELP!! WILL MARK BRAINLIEST AND THANK YOU!!!Determine whether the figure has line, point, and/or rotational symmetry.

(you can choose multiple)

line

point

rotational

none

Answers

The figure has the following symmetry:

A. line

B. point.

What is the order of rotational symmetry?

In Mathematics and Geometry, the order of rotational symmetry of any geometrical figure can be defined as the number of times in which the geometrical figure can be rotated around a full (complete) circle and still look the same.

As a general rule in geometry, a geometrical figure with number of sides (n) has "n" lines of symmetry and its order of rotational symmetry is equal to "n."

Based on the above rule, we can reasonably infer and logically deduce that the figure has both line symmetry and point symmetry.

Read more on order of rotational symmetry here: brainly.com/question/24279623

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Answer:

line and point

Step-by-step explanation:

there are 3 points and 5 lines

When is it helpful to use simpler numbers to solve a problem