A set of telephone poles is stacked in a pile, 8 layers high. The top layer consists of 20 telephone
poles. The next layer down consists of 24 telephone poles. The third layer consists of 28
telephone poles. If this pattern continues for the remaining 5 layers, how many telephone poles
are in the pile?
A. 224
B. 244
C. 252
D. 272

Answer:

[tex](x-y)^4=x^4-x^3y+6x^2y^2-4xy^3+y^4[/tex].

Step-by-step explanation:

We want to find the polynomial that will result from expanding:

[tex](x-y)^4[/tex].

Recall that we can use the Pascal's triangle to obtain the coefficient as:

1     4    6   4   1

Also note how the negative sign is going to alternate.

The power of x will decrease from left to right while the power of y increases from left to right

The expansion then becomes:

[tex](x-y)^4=x^4-x^3y+6x^2y^2-4xy^3+y^4[/tex].

Answer:

The Answer is A!!!!

Step-by-step explanation:

Answer:

100 in²

Step-by-step explanation:

Since the figures are similar

the linear ratio of sides = a : b , then

ratio of areas = a² : b²

ratio of sides = 15 : 21 = 5 : 7

ratio of areas = 5² : 7² = 25 : 49

let the area of the smaller figure be x then by proportion

[tex]\frac{25}{x}[/tex] = [tex]\frac{49}{196}[/tex] ( cross- multiply )

49x = 4900 ( divide both sides by 49 )

x = 100

Area of smaller figure is 100 in²

Answer:

d. :)

Step-by-step explanation:

Answer:

D. The average rate of change is greater for interval D than for interval C because the line is increasing more quickly at interval D than at interval C.

Step-by-step explanation:

The difference between C and D interval is the lowest.

This means that line is increasing more quickly at interval D as compared to others.

Therefore, option D is the right answer.

Answer:

see explanation

Step-by-step explanation:

Corresponding angles are associated with parallel lines

L and M would have to be parallel but not so cannot name a corresponding angle.

If they were parallel then ∠7 would correspond to ∠3

Answer: OPTION B

Step-by-step explanation:

You need to remember that, to subtract radicals, the indices and the radicands must be the same.

Given the expression [tex]3\sqrt{2}-\sqrt{2}[/tex], you can identify that both have index 2 and the radicands are 2 (The numbers that are inside of radicals), therefore, you can conclude that the subtraction can be made.

Then, you must subtract the terms in front of the radicals. Therefore, you get:

[tex]3\sqrt{2}-\sqrt{2}=2\sqrt{2}[/tex]

You can observe that this matches with the option B.

Answer:

The correct answer is option B.  2√ 2

Step-by-step explanation:

It is given that, 3√ 2 – √ 2

To find the correct option

3√ 2 – √ 2  can be written as,

3√ 2 – √ 2  = √ 2 (3 - 1)   taking √ 2  as common

 = √ 2  * 2

 = 2√ 2

Therefore the correct answer is 2√ 2 .

The correct option is option b.  2√ 2

Answer:

I believe it would be 40

Step-by-step explanation:

5:3 = x:24

3 times 8 = 24

5 times 8 = 40

There are 40 girls in the chorus.

Answer:

c

Step-by-step explanation:

Here's how this works:

Get everything together into one fraction by finding the LCD and doing the math.  The LCD is sin(x) cos(x).  Multiplying that in to each term looks like this:

[tex][sin(x)cos(x)]\frac{sin(x)}{cos(x)}+[sin(x)cos(x)]\frac{cos(x)}{sin(x)} =?[/tex]

In the first term, the cos(x)'s cancel out, and in the second term the sin(x)'s cancel out, leaving:

[tex]\frac{sin^2(x)}{sin(x)cos(x)}+\frac{cos^2(x)}{sin(x)cos(x)}=?[/tex]

Put everything over the common denominator now:

[tex]\frac{sin^2(x)+cos^2(x)}{sin(x)cos(x)}=?[/tex]

Since [tex]sin^2(x)+cos^2(x)=1[/tex], we will make that substitution:

[tex]\frac{1}{sin(x)cos(x)}[/tex]

We could separate that fraction into 2:

[tex]\frac{1}{sin(x)}[/tex]×[tex]\frac{1}{cos(x)}[/tex]

[tex]\frac{1}{sin(x)}=csc(x)[/tex]  and  [tex]\frac{1}{cos(x)}=sec(x)[/tex]

Therefore, the simplification is

sec(x)csc(x)

Answer:

Y-intercept;

(0, 1)

Asymptote;

Horizontal asymptote: y = -2

Step-by-step explanation:

We have been given the following exponential function;

[tex]f(x) = 3^{x+1}-2[/tex]

The y-intercept of a function is the point where the graph of the function intersects the y-axis. At this point, the value of x is usually 0. Therefore, to establish the y-intercept of the given function we substitute x with 0 in the given equation and simplify;

[tex]y=3^{0+1}-2\\ \\y=3-2=1[/tex]

The y-intercept of the given function is thus (0, 1).

Exponential function of the form;

[tex]f(x)=c.n^{ax+b}+k[/tex]

has a horizontal asymptote y = k. In the function given, k = -2 implying that

y = -2 is a horizontal asymptote of the given exponential function

Answer:

Option B is correct.

Step-by-step explanation:

300 cm^3 of snow melts into 33 cm^3 water. We need to find how much water is produced if 600 cm^3 of snow is melt.

Solving using unitary method:

300 cm^3 of snow melts into water = 33 cm^3

1 cm^3 of snow melts into water = 33/300

600 cm^3 of snow melts into water = 33/300 *600

                                                           = 66 cm^3

So, Option B is correct.

The answer is:

The correct option is:

C) [tex](9^{3})^{3}=9^{9}[/tex]

To solve the problem, we need to remember the power of a power property, it's defined by the following way:

[tex](a^{m})^{n}=a^{m*n}[/tex]

When we have a power of a power, we need to keep the base and then, the new exponent will be the product between the two original exponents.

So, we are given the expression:

[tex](9^{3})^{3}[/tex]

Then, calculating we have:

[tex](9^{3})^{3}=9^{3*3}=9^{9}[/tex]

Hence, we have that the correct option is:

C) [tex](9^{3})^{3}=9^{9}[/tex]

Have a nice day!

Answer:

The correct answer is option C)  9^9

Step-by-step explanation:

Points to remember

Identities

(xᵃ)ᵇ = xᵃᵇ

xᵃ * xᵇ = x⁽ᵃ ⁺ ᵇ⁾

xᵃ/xᵇ = x⁽ᵃ ⁻ ᵇ⁾

It is given that (9^3)^3

To find the correct option

(9^3)^3 can be written as, (9³)³

By using above identities,

(9³)³ = 9³ ˣ³

 = 9⁹

Therefore the correct answer is option C).  9^9

7,4 is the answer to the question

Answer:

[tex]x=7/4[/tex]

Step-by-step explanation:

the equation is:

[tex]xy=k[/tex]

To find the value of [tex]x[/tex], we need to substitute the values that we know for [tex]y[/tex] and [tex]k[/tex]:

[tex]y=4[/tex]

and

[tex]k=7[/tex]

so, we substitute this values into the equation

[tex]xy=k[/tex]

[tex]x(4)=7[/tex]

and we clear for [tex]x[/tex], for this we move the 4 to the right dividing:

[tex]x=7/4[/tex]

Answer: rotation

Step-by-step explanation:

Rotation is required to map DEF onto D'EF'

Each point in a figure is transformed into a rotation by rotating it a specific amount of degrees around another point.

Rotation exists as the operation or act of turning or circling something.

Rotation exists in the circular movement of an object around an axis of rotation. A three-dimensional object may include an infinite numeral of rotation axes.

To know more about rotation refer to :

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Answer:

B. A hamburger sells for $5 but costs $0.15 to make, giving a net income of $3.35.

Step-by-step explanation:

It's the right answer, for many wrong reasons:

- The units aren't the same... since the 5 is expressed in dollars and the the costs would be expressed in cents.

- There could only have one production cost per burger... so it's not a second variable.  

- Of course, the calculation in the statement is also wrong ($5.00 - $0.15 doesn't equal $3.35)

So, for all these three reasons, that statement cannot be expressed in the given equation.

Answer:

8.75 cubic feet

Step-by-step explanation:

Your new dresser will be [tex]\frac{2}{5}^{ths}[/tex] larger than your old dresser.

This means that your new dresser wil be

[tex]1+\dfrac{2}{5}=\dfrac{5+2}{5}=\dfrac{7}{5}[/tex]

of your old dresser.

Your old dresser can hold 6.25 cubic feet, so your new dresser can hold

[tex]\dfrac{7}{5}\cdot 6.25=7\cdot 1.25=8.75\ ft^3[/tex]

Final answer:

To find the volume of the new dresser, find 2/5ths of the old dresser's volume (6.25 cubic feet) and add it to the original volume, resulting in a new dresser's volume of 8.75 cubic feet.

Explanation:

To calculate the volume of the new dresser, which will be 2/5ths larger than the old dresser, we will first determine what 2/5ths of the old dresser's volume is, and then add that to the original volume. The old dresser has a volume of 6.25 cubic feet.

Calculate 2/5ths of 6.25 cubic feet: (2/5) × 6.25 = 2.5 cubic feet

Add the additional volume to the original volume to get the new dresser's volume: 6.25 + 2.5 = 8.75 cubic feet

So, the new dresser will hold 8.75 cubic feet of items.

Minimum: 35

First quartile: 6, 13, 14, 18, 19, 29 (avg. is 16.5)

Median: ≈41.08 (41.0769230769)

Third quartile: 44, 53, 55, 71, 84, 93 (avg. is 66.67)

Maximum: 93

Interquartile range: 50.17

Final answer:

The minimum is 6, the first quartile is 16, the median is 29, the third quartile is 54, the maximum is 93, and the interquartile range is 38.

Explanation:

To find the minimum, first quartile (Q1), median, third quartile (Q3), maximum, and interquartile range (IQR) of the given data set, we first need to organize the data in ascending order, which is already done. Then, we apply the appropriate statistical methods to determine each required value.

For this case we have by definition, that a hemisphere represents half of a sphere.

Its volume is given by:

[tex]V = \frac {2} {3} \pi * r ^ 3[/tex]

Where "r" represents the radius.

Substituting the data and clearing the radio we have:

[tex]\frac {2} {3} \pi * r ^ 3 = 18 \pi\\\frac {2} {3} * r ^ 3 = 18\\r ^ 3 = 18 * \frac {3} {2}\\r ^ 3 = 27\\r = \sqrt [3] {27}\\r = 3[/tex]

Thus, the radius of the hemisphere is 3 inches.

Answer:

[tex]3 \ in[/tex]

Answer: these nats

Step-by-step explanation:verry carefully

Answer:

True

Step-by-step explanation:

we know that

sin(90°)=1

sin(270°)=-1

sin(-90°)=-sin(90°)=-1

sin(-90°)=sin(270°)

therefore

For sin(x)=-1

the values of x are x=-90° and x=270° ------> is true

Answer:

1

Step-by-step explanation:

The production cost of company 1 never gets below 340 (at x=20), found e.g., by equating the derived function to 0.

You can figure out that g(x) = 0.05x^2 -7x + 300, but you already know that company 1 has higher cost based on the example values for g(x).

Answer:

Hi!

The answer is:

Based on the given information, the minimum production cost for company __1__ is greater.

Step-by-step explanation:

You have to find the minimum value of a f(x), so you need to differentiate it, set it to zero and solve for x. Then differentiate the function again and calculate the value of the second derivative at the maximum or minimum points to find out whether it is a maximum or a minimum.

[tex]f(x) = 0.15x^2 - 6x + 400[/tex]

[tex]\frac{df}{dx}=2 * 0.15x - 6 = 0.30x - 6 [/tex] First derivative.

[tex][tex]\frac{d^2f}{dx^2} = 2 [/tex][/tex] Second derivative. Confirm it's a minimum point.

Minimum occurs at:

0.30x − 6 = 0

0.30x = 6

x = 6/0.30

x = 20

Replace x on equation f(x):

f(20) = 0.15 * 20² - 6 * 20 + 400 = 340.

For g(x), the value of minimum cost is:

g(70) = 55.

Answer:

The correct option is D

Step-by-step explanation:

The correct option is D.

They both have the same height, assuming that each coin has same volume, then how can coins in 1 stack have different volume than coins in another stack no matter how you stack them.

Like two cylinders with same base area and height have same volume. Like wise rectangle and parallelogram with same base and same perpendicular height having same area....

D) they have the same volume

Answer:

The second photo.

Step-by-step explanation:

If you use a graphing calculator, you can easily find the answer.

Answer:

  see below

Step-by-step explanation:

Comparing the given equation to the standard-form equation of a circle ...

  (x -h)^2 +(y -k)^2 = r^2 . . . . . circle centered at (h, k) with radius r

we find that ...

  h = 2, k = -5, r = 2

So, the circle you're looking for is centered at (2, -5) and has a radius of 2.

To express the given information in a linear equation, the setup time and hourly rate per square foot should be considered in the equation y = 4 + (1/1000)x.

To express the information in a linear equation:

For this case we have that by definition, the equation of a line in the slope-intersection form is given by:

[tex]y = mx + b[/tex]

Where:

m: It's the slope

b: It is the cut point with the y axis.

We look for two points through which the line passes to find the slope:

[tex](x1, y1) = (2,2)\\(x2, y2) = (0, -4)[/tex]

[tex]m = \frac {y2-y1} {x2-x1} = \frac {-4-2} {0-2} = \frac {-6} {- 2} = 3[/tex]

So, the line is:

[tex]y = 3x + b[/tex]

We have "b" replacing any of the points:

[tex]-4 = 3 (0) + b\\-4 = b[/tex]

Finally, the equation is:

[tex]y = 3x-4[/tex]

Answer:

[tex]y = 3x-4[/tex]

The area of the triangle will be 14 square units. Then the correct option is C.

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.

The triangle ABC with vertices A(2, 3), B(1, -3), and C(-3, 1).

Then the area of the triangle is given as,

A = 1/2 | {[2 x (-3) + 1 x 1 + (-3) x 3] - [3 x 1 + (-3) x (-3) + 2 x 1]} |

A = 1/2 | {[-6 + 1 - 9] - [3 + 9 + 2]} |

A = 1/2 | {-14 - 14} |

A = 1/2 x 28

A = 14 square units  

The area of the triangle will be 14 square units. Then the correct option is C.

More about the triangle link is given below.

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Answer:

7, 5

Step-by-step explanation:

_________________________________________________

Answer:

7 and 5

Step-by-step explanation:

So we can start with 1 and 4. We can see they added 3 to 1. Ok, that's the first part.

Then, they took 4 and subtracted 2. We can see they subtracted 2. Ok, that's the second part.

We can see they keep doing this:

Add 3, subtract 2. Add 3, subtract 2. and so on, until we get to 4. They just subtracted 2, so we can add 3. So, our first unknown number would be 7. We can then subtract 2, making the second unknown number 5.

Hope I helped, soz if I'm wrong ouo.

~Potato.

Copyright Potato 2019.

Answer:

10.4 cm

Step-by-step explanation:

The volume (V) of a pyramid is calculated using

V = [tex]\frac{1}{3}[/tex] area of base × height (h)

area of square base = 6² = 36, thus

[tex]\frac{1}{3}[/tex] × 36h = 120

12h = 120 ( divide both sides by 12 )

h = 10 cm

To find the slant height (s) consider the right triangle from the vertex to the midpoint of the base and from the midpoint of base to the side.

That is a right triangle with hypotenuse s and legs 10(h) and 3 (midpoint of the base )

Using Pythagoras' identity then

s² = 10² + 3² = 100 + 9 = 109

Take the square root of both sides

s = [tex]\sqrt{109}[/tex] ≈ 10.4 cm

Answer:

its the second one

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

the answer is B, is this a lesson or a quiz?

Answer:

1. The correct answer option is B.

2. The correct answer option is C.

4. The correct answer option is D.

Step-by-step explanation:

1. [tex]\frac{3}{x^2+14x+48}[/tex] ÷ [tex]\frac{3}{10x+60}[/tex]

Changing division to multiplication by taking the reciprocal of the latter fraction:

[tex]\frac{3}{x^2+14x+48} \times \frac{10x+60}{3}[/tex]

[tex]\frac{3}{(x+6)(x+8)} \times \frac{10(x+6)}{3}[/tex]

Cancelling the like terms to get:

[tex]\frac{10}{(x+8)}[/tex]

The correct answer option is B. [tex]\frac{10}{(x+8)}[/tex]

2. [tex]\frac{4x^2+36}{4x} \times \frac{1}{5x}[/tex]

Factorizing the terms and then cancelling the like terms to get:

[tex]\frac{4(x^2+9)}{4x} \times \frac{1}{5x}[/tex]

[tex]\frac{x^2+9}{5x^2}[/tex]

The correct answer option is C. [tex]\frac{x^2+9}{5x^2}[/tex].

4. [tex]\frac{\frac{4t^2-16}{8} }{\frac{t-2}{6} }[/tex]

Changing division to multiplication by taking the reciprocal of the latter fraction:

[tex]\frac{4t^2-16}{8} \times \frac{6}{t-2}[/tex]

[tex]\frac{4(t-2)(t+2)}{8} \times \frac{6}{t-2}[/tex]

Cancelling the like terms to get:

[tex]3(t+2)[/tex]

The correct answer option is D. [tex]3(t+2)[/tex].

Answer:

b) true

c) false

d) true

e) true

Step-by-step explanation:

b) Any line that contains an interior point of a circle is a secant of the circle. The center is an interior point, so a line that contains the circle center is a secant.

__

c) Chords of different lengths intercept arcs of different measures

__

d) Any line perpendicular to a radius at the point where the radius meets the circle is a tangent to the circle. The endpoint of a diameter is the endpoint of a radius, so a line perpendicular there will be a tangent.

__

e) The measure of an inscribed angle is half the measure of the intercepted arc, so all inscribed angles that intercept equal arcs are equal.

The statement 'If a line contains the center of a circle, it is a secant of the circle.' is true. The statement 'If 2 chords intersect a circle, they intercept equal arcs.' is false. Statements 'If a line is perpendicular to a diameter at one of its endpoints, then it is tangent to the circle.' and 'Inscribed angle that intercept equal arcs are equal.' are both true.

b) True. If a line contains the center of a circle, it does pass through the circle at two points, therefore it's a secant of the circle.

c) False. Two chords intersecting inside a circle do not always intercept equal arcs. The length of the arcs they intercept depends on their distance from the center of the circle, not on the mere fact that they intersect.

d) True. If a line is perpendicular to a diameter at one of its endpoints, it does indeed result in a tangent to the circle. This is because the line touches the circle at exactly one point (the endpoint), fulfilling the definition of a tangent line.

e) True. Inscribed angles that intercept (cut off) equal arcs are indeed equal. This is a basic theorem in circle geometry.

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Answer:

C. 6 kg

Step-by-step explanation:

Let m represent the mass of plates on one side of the barbell. Then the total weight of the barbell is ...

2m +24 = 60 . . . . . kilograms

m +12 = 30 . . . . . . . divide by 2

m = 18 . . . . . . . . . . . subtract 12

The mass of plates on one side of the barbell must total 18 kg. If they all have the same mass, then that must be a divisor of 18. In whole numbers, that would include plates of mass 1, 2, 3, 6, 9, 18 kg.

The only one of these on your list of answer choices is ...

6 kg

[tex]\dfrac{\mathrm dy}{\mathrm dx}=\cos(x+y)[/tex]

Let [tex]v=x+y[/tex], so that [tex]\dfrac{\mathrm dv}{\mathrm dx}-1=\dfrac{\mathrm dy}{\mathrm dx}[/tex]:

[tex]\dfrac{\mathrm dv}{\mathrm dx}=\cos v+1[/tex]

Now the ODE is separable, and we have

[tex]\dfrac{\mathrm dv}{1+\cos v}=\mathrm dx[/tex]

Integrating both sides gives

[tex]\displaystyle\int\frac{\mathrm dv}{1+\cos v}=\int\mathrm dx[/tex]

For the integral on the left, rewrite the integrand as

[tex]\dfrac1{1+\cos v}\cdot\dfrac{1-\cos v}{1-\cos v}=\dfrac{1-\cos v}{1-\cos^2v}=\csc^2v-\csc v\cot v[/tex]

Then

[tex]\displaystyle\int\frac{\mathrm dv}{1+\cos v}=-\cot v+\csc v+C[/tex]

and so

[tex]\csc v-\cot v=x+C[/tex]

[tex]\csc(x+y)-\cot(x+y)=x+C[/tex]

Given that [tex]y(0)=\dfrac\pi2[/tex], we find

[tex]\csc\left(0+\dfrac\pi2\right)-\cot\left(0+\dfrac\pi2\right)=0+C\implies C=1[/tex]

so that the particular solution to this IVP is

[tex]\csc(x+y)-\cot(x+y)=x+1[/tex]