A plane which passes through three edges of a cube produces a triangular cross section as shown.


In two or more complete sentences, explain how the plane should pass through the cube in order to produce a cross section that is a regular hexagon.

ANSWER

129

EXPLANATION

The given expression is:

[tex]4^2×2^3- (14-16)÷2[/tex]

Deal with the parenthesis first.

[tex]4^2×2^3- ( - 2)÷2[/tex]

[tex]4^2×2^3 + 2÷2[/tex]

Deal with exponents,

[tex]16×8+ 2÷2[/tex]

Divide now

[tex]16×8 + 1[/tex]

Multiply

[tex]128 + 1 [/tex]

You can now add to get

[tex]129[/tex]

The order of operations is PEDMAS

Answer:

The correct answer is first option  6 units

Step-by-step explanation:

From the figure we can see a rectangle was mediated to crerate A'B'C'D'

To find the value of AB

AB = ?

A'B' = 15 units

BC = 3.8 units

B'C' = 9.5 units

From the figure we can write,

A'B'/AB = B'C'/BC

15/AB = 9.5/3.8

AB = (15 * 3.8)/9.5 = 6 units

Therefore the correct answer is first option 6 units

Answer:

3 ft, 5ft, 6ft

Step-by-step explanation:

To build a kennel of my dog, I would try to make it the largest possible with what I have.

So, I would go with the 3 longest planks: 3ft, 5ft and 6ft.

By looking at the length, I see I could make something very close to a right triangle since I could use the 6ft as an hypotenuse, and have the two other sides as 3ft and 5 ft  (6² is almost 3²+5², which equal 34).

That means my corner angle would be slightly over 90 degrees.

Answer:

3,5,6

Step-by-step explanation:

because i said so

Answer:

B

Step-by-step explanation:

Margin of Error is simply a range, an amount that is allowed for in case of miscalculation or change of circumstances. The margin of error is 5%.

1. Find the 5% of 3.20 = .16

2. Subtract and add .16 to 3.20 to get rid of that margin of error

    3.20 + .16 = 3.36 and 3.20 - .16 = 3.04

3. 3.04 and 3.36

Answer:

b 3.04 to 3.36

Step-by-step explanation:

First we need to find 5% of 3.20

.05*3.20 = .16

To find the lower value, subtract 16 cents from 3.20

3.20-.16 = 3.04

To find the upper value, add 16 cent to 3.20

3.20 + .16 = 3.36

The range is 3.04 to 3.36

32

1024/2=528(~512)/2=256/2=128/2=64/2=32

Answer:

1/5

Step-by-step explanation:

Since there are 2 red marbles and since there are a total of 10 marbles, the probability is 2/10. This simplifies to 1/5. So the probability of picking a red marble is 1/5.

The probability of randomly picking out a red marble is 1/5

To determine the probability of randomly picking out a marble and it being red, we need to consider the total number of marbles and the number of red marbles.

Total marbles = 5 green + 3 blue + 2 red = 10 marbles

Red marbles = 2

So, we have

Probability = (Number of favorable outcomes) / (Total possible outcomes)

This gives

Probability = (Number of red marbles) / (Total marbles)

By subsituition

Probability = 2/10 = 1/5

Hence, the probability of randomly picking out a marble and it being red is 1/5

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Answer:

2/3 is the slope and

-1 is the y intercept

Step-by-step explanation:

y = 2/3 x -1

This is in the form y = mx+b where m is the slope and b is the y intercept

2/3 is the slope and

-1 is the y intercept

Answer:

2/3 slope, -1 y intercept.

Step-by-step explanation:

Equations in y=mx+b forms follow these rule- y is the dependent variable, and x is the independent variable; m is the slope and b is the y intercept.

This means that the m, or slope is 2/3, and the y intercept is -1.

Answer:

A: [tex]y=-3sin(2(x+\pi))+2[/tex]

Step-by-step explanation:

As all of the functions are sin functions, the option must be negative due to the shape of the graph.

This narrows down the options to A and B

When looking at b, it has a period of [tex]2\pi[/tex] which is not equivalent to the given graph that has a period of [tex]\pi[/tex]

Function A has a period of [tex]\pi[/tex] and is negative, so it is the correct option

Answer:

[tex]y=-3\sin(2(x+\pi)+2[/tex]

Step-by-step explanation:

The graph completes two cycles on the interval [tex][-\pi,\pi][/tex].

This implies that, the graph has a period of [tex]\pi[/tex].

The functions is a sine function that is reflected in the x-axis and shifted up by 2 units.

The range of the graph is -1 to 5.

This means that the amplitude is 6/2=3

The graph is also shifted to the right [tex]\pi[/tex] units

The function is

[tex]y=-3\sin(2(x+\pi)+2[/tex]

Answer:

0 and -4

Step-by-step explanation:

We have been given the following functions;

f(x) = 1/x

g(x) = x^2 + 4x

The first step would be to evaluate the composite function fºg.

fºg = f[g(x)]. We substitute g(x) in place of x in f(x)

fºg = [tex]\frac{1}{g(x)}=\frac{1}{x^{2}+4x}[/tex]

This is clearly a rational function which will be defined everywhere except where the expression in the denominator will be equal to 0.

We solve for x;

[tex]x^{2}+4x=0\\\\x(x+4)=0\\x=0\\x=-4[/tex]

Therefore, the two numbers that are not in the domain of fºg are 0 and -4

For this case we have the following equations:

[tex]f (x) = \frac {1} {x}\\g (x) = x ^ 2 + 4x[/tex]

We must find (f_ {o} g) (x):

By definition of composition of functions we have to:

[tex](f_ {o} g) (x) = f (g (x))[/tex]

So:

[tex](f_ {o} g) (x) = \frac {1} {x ^ 2 + 4x}[/tex]

We must find the domain of [tex]f (g (x)).[/tex] The domain will be given by the values for which the function is defined, that is, when the denominator is nonzero.

[tex]x ^ 2 + 4x = 0\\x (x + 4) = 0[/tex]

So, the roots are:

[tex]x_ {1} = 0\\x_ {2} = - 4[/tex]

The domain is given by all real numbers except 0 and -4

Answer:

x other than 0 and -4

Answer: it should be 3 units down

Think if it on a graph in your mind and plot points then use every choice to see which makes sense

For this case we have:

Let k> 0:

To graph [tex]y = f (x) + k,[/tex] the graph k units is moved up.

To graph [tex]y = f (x) -k[/tex], the graph moves k units down.

Let h> 0:

To graph [tex]y = f (x-h)[/tex], the graph moves h units to the right.

To graph [tex]y = f (x + h)[/tex], the graph moves h units to the left.

So, we have:

[tex]y = f (x) = \sqrt {x}\\h = 3\\y = f (x) = \sqrt {x + 3}[/tex]

It means that it was shifted 3 units to the left

Answer:

Option A

Answer:

x^2 + y^2 = 32

Step-by-step explanation:

The fact that the circle's center is at (0,0) tells you that the circles equation is of the form x^2 + y^2 = radius^2

radius = 4*sqrt(2)       Given

r^2 = (4sqrt(2) )^2

r^2 = 16 * 2

r^2 = 32

So the entire equation is

x^2 + y^2 = 32

Answer:

A- control group

Since group A is tested under normal condition, it is the control group. Control group is separated from other groups so that the independent variable being tested cannot influence the result.

Answer:

24 and 8

Step-by-step explanation:

The formula for the perimeter of the rect. is P = 2W + 2L.

Here, L = 2W + 8, so the area formula becomes:

P = 2W + 2(2W + 8) = 64

Dividing all terms by 2 reduces this to:

         W + 2W + 8 = 32, or 3W = 24, or W = 8.

Then:  L = 2W + 8 = 2(8) + 8 = 24

Check:  does 2W + 2L = 64 when these values for W and L are substituted?

              Is 2(8) + 2(24) = 64   true?  Yes

The length and width are 24 and 8 respectively.

The length of rectangle will be 8 units.

The width of rectangle will be 24 units.

What is mean by Rectangle?

A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.

Given that;

The length of a rectangle is eight more than twice the width.

The perimeter is 64.

Now,

Let the width of rectangle = x

Then, The length of rectangle = 2x + 8

Here, The perimeter is 64.

So, We get;

2 (length + width) = 64

2 (2x + 8 + x) = 64

2 (3x + 8) = 64

3x + 8 = 64/2

3x + 8 = 32

3x = 32 - 8

3x = 24

x = 8

Thus, The width of rectangle = x

                                            = 8

Then, The length of rectangle = 2x + 8

                                              = 2 × 8 + 8

                                              = 24

Therefore, The length of rectangle will be 8 units.

The width of rectangle will be 24 units.

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Answer:

x = 4, y = 2

Step-by-step explanation:

Given the 2 equations

5x + 2y = 24 → (1)

5y = x + 6 → (2)

Rearrange (2) expressing x in terms of y by subtracting 6 from both sides

x = 5y - 6 → (3)

Substitute x = 5y - 6 into (1)

5(5y - 6) + 2y = 24 ← distribute and simplify left side

25y - 30 + 2y = 24

27y - 30 = 24 ( add 30 to both sides )

27y = 54 ( divide both sides by 27 )

y = 2

Substitute y = 2 into (3) for corresponding value of x

x = (5 × 2) - 6 = 10 - 6 = 4

Answer:

Step-by-step explanation:

Z score is the number of standard devations above the mean.

For example if z=1, the data value is 1 st. dev. above the mean.

So, z=1.95, so the player's heigh is 1.95 st. dev. above the mean.

Answer:

If sine theta = .3090 then arc sine theta =

18 degrees

Then we look up csc 18 degrees which = 3.2361

Step-by-step explanation:

Answer:

cscΘ ≈ 3.2362

Step-by-step explanation:

Using the trigonometric identity

• cscx = [tex]\frac{1}{sinx}[/tex] , then

cscΘ  = [tex]\frac{1}{0.3090}[/tex] ≈ 3.2362

Answer:

The value of x is 6 and -6. The smallest value of x is -6

Step-by-step explanation:

2/3 x² = 24

solving this equation for finding the value of x.

Multiply both sides by 3/2

x² = 24 * 3/2

x² = 72/2

x² = 36

Now, to find the value of x taking square root on both sides

√x² = √36

x= ±6

So, the value of x is 6 and -6. The smallest value of x is -6

Answer:

x = - 5

Step-by-step explanation:

A line with an undefined slope indicates that the line is vertical and parallel to the y- axis.

The equation of a vertical line is

x = c where c is the value of the x- coordinates the line passes through.

The line passes through (- 5, 2) with x- coordinate -5, hence

x = - 5 ← equation of line

The equation of a line that passes through the point (-5, 2) and has an undefined slope is x = -5.

i.e y-axis.

The equation of a line is given by:

y = mx + c

where m is the slope of the line and c is the y-intercept.

We have,

The equation of a line passes through the point (-5, 2)

The equation of a line has an undefined slope.

Now,

An undefined slope means,

The line is parallel to the y-axis.

There is only one point on the x-axis.

Slope = Change in y-axis / Change in the x-axis

Slope= Change in y-axis / 0

Slope = undefined

If the slope of a line is undefined there is no y-intercept.

The equation of  the line is:

y = mx + c

y = (1/0)x + 0

0 = x

x = 0

This means the y-axis.

The equation of the line passes through the point (-5, 2) so,

x = -5

Thus,

The equation of a line that passes through the point (-5, 2) and has an undefined slope is x = -5.

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(–1,4)

Shapes are congruent if you can turn one into the other by moving, rotating or flipping. We can use this symbol [tex]\cong[/tex] to show that two things are congruent. Two triangles are congruent if and only if all the corresponding legs are congruent. The only point that makes the corresponding legs to be congruent is [tex](-1,4)[/tex]. Why? because we can match these two triangles by flipping the red one two times and moving it into the blue one.

Answer:

(–1,4)

Step-by-step explanation:

Answer:

2 13/15

Step-by-step explanation:

2.26/ 1 X 100/100 = 226/100

226/100 Dived by 2 ( both top and bottom ) = 113/50

113/50 = 2 13/50

2.26 = 2 13/50

Answer:

See step-by-step

Step-by-step explanation:

A prism is named by the shape of its bases.  That makes this an octagonal prism

The shape of the bases are octagons.

The vertices are all the letters

The lateral edges are all the vertical lines connected by the vertices.  RQ, WN, VM, are all examples.

The rectangles making up the sides are called lateral faces.

The altitudes are the same as the lateral edges.  They all represent the height of the prism.

Answer:

Miguel

Step-by-step explanation:

Since the pie is round it is a circle, and all circles have 360 degrees in total. Miguel cut 1/4 of the pie and 1/4 x 360 = 90. 90 is greater than 60.

Answer:

Miguel

Explanation:

Think of the 1/4 as 90 degrees.

An entire circle is 360 degrees. A quarter of that is 90 or 1/4.

Hope this picture helps.

Answer: 10

Step-by-step explanation:

15 - 5 is 10.

Answer: 10

Step-by-step explanation:

From the given box plot in the picture, we can see that the least observation  from the data = 4.5

The largest observation from the data = 14.5

We know that the range of data tells the difference between the largest observation and the lowest observation.

[tex]\text{ i.e. Range=Largest observation - Least observation}\\\\=14.5-4.5=10[/tex]

Therefore, the range of the data = 10

Answer:

[tex]x^3+x^2-5x+28[/tex]

Step-by-step explanation:

since a=lw, the area is (x^2-3x+7)(x+4)

1. distribute parentheses [tex]\left(x^2-3x+7\right)\left(x+4\right)=x^2x+x^2\cdot \:4+\left(-3x\right)x+\left(-3x\right)\cdot \:4+7x+7\cdot \:4[/tex]

2. apply +(-a)=-a rule [tex]x^2x+4x^2-3xx-3\cdot \:4x+7x+7\cdot \:4[/tex]

3. Simplify

    Steps to simplify:

[tex]x^2x=x^3[/tex]

[tex]3xx=3x^2[/tex]

[tex]3\cdot \:4x=12x[/tex]

[tex]7\cdot \:4=28[/tex]

[tex]x^3+4x^2-3x^2-12x+7x+28[/tex]

4. Add like terms [tex]=x^3+4x^2-3x^2-5x+28[/tex]

5. Add like terms [tex]=x^3+x^2-5x+28[/tex]

the area of the rectangle as a single polynomial in simplest form is  x³+x²-5x+28.

Area is the space occupied by a plane object.

To calculate the area of a rectangle, we use the formula below.

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1

Hence, the area of the rectangle as a single polynomial in simplest form is  x³+x²-5x+28.

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ANSWER

Converges

[tex]S_{ \infty } = 68[/tex]

EXPLANATION

The guy sequence is

17 + 12.75 + 9.5625 + ...

The common ratio is:

[tex] \frac{9.5625}{12.75} = \frac{12.75}{17} = \frac{3}{4} = r[/tex]

Since

[tex] |r| < 1[/tex]

the series converges.

The sum to infinity of this sequence is :

[tex]S_{ \infty } = \frac{a}{1 - r} [/tex]

where a=17 is the first term of the series.

[tex]S_{ \infty } = \frac{17}{1 - \frac{3}{4} } [/tex]

[tex]S_{ \infty } = \frac{17}{ \frac{1}{4} } = 68[/tex]

Answer:

414

Step-by-step explanation:

12 times 7, 12 times 15, 7 times 15

Answer:

$2,239.66

Step-by-step explanation:

To find the amount of reimbursement, convert miles to km by multiplying 1564 by 1.609 since 1 mile = 1.609 km.

He drive 1564(1.609)=2,516.476 km.

Multiply this distance by $0.89 per km.

2516.476(0.89)=$2,239.66

Answer:

[tex]0.056\ \frac{miles}{second}[/tex]

Step-by-step explanation:

we know that

The rate is equal to

[tex]200\ \frac{miles}{hour}[/tex]

Remember that

[tex]1\ hour=3,600\ seconds[/tex]

substitute

[tex]200\ \frac{miles}{hour}=(200/3,600)\ \frac{miles}{seconds}=0.056\ \frac{miles}{second}[/tex]

Side length of cube = 9 feet

The side length of the cube is 9 feet. Thus, the third option is correct.

To find the side length of a cube when given its volume, we can use the formula for the volume of a cube:

Volume = side length³

In this case, we know that the volume of the cube is 729 cubic feet.

Let's substitute this value into the formula:

729 = side length³

To find the side length, we need to take the cube root of both sides of the equation:

∛729 = ∛(side length³)

Simplifying:

9 = side length

Therefore, the side length of the cube is 9 feet.

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3n -10 ≥ 2

Add 10 to each side:

3n ≥ 12

Divide both sides by 3:

n ≥12/3

n≥4

The dot would be solid and located on the number 4, with the line and arrow moving/ pointing to the right.

1. n >2

2. n≤3

3. n<4

4. n≥5