What is the sum of the first 30 terms of this arithmetic sequence?

6, 13, 20, 27, 34, …

Hm, it seems like his answer is off. The image is what I got.

Answers:

X+3

Step-by-step explanation:

I got it right

Answer: 118.3 m^2

Step-by-step explanation:

Use Heron's formula: √s(s-a)(s-b)(s-c)

s= a+b+c/2

13+18.2+22.3/2 = 26.75

√26.75(26.75-13)(26.75-18.2)(26.75-22.3)

√26.75(13.75)(8.55)(4.45)

√13994.34609

118.297701 = 118.3 m^2

Answer:

Final answer in simplified form is [tex]3x^2-17x-30[/tex]

Step-by-step explanation:

Given expression is [tex](3x^2-8x-24)-(9x+6)[/tex]

Now we need to find an equivalent expression for [tex](3x^2-8x-24)-(9x+6)[/tex]

First we can distribute the negative sign and remove the parenthesis the combine like terms

[tex](3x^2-8x-24)-(9x+6)[/tex]

[tex]=3x^2-8x-24-9x-6[/tex]

[tex]=3x^2-17x-30[/tex]

Hence final answer in simplified form is [tex]3x^2-17x-30[/tex]

Explanation:

1. In order for the idea of "perpendicular distance" to make any sense in this context, the number of sides of the polygon must be even. Then the "diameter" is the diameter of the inscribed circle. As the number of sides increases, the polygon differs less and less from a circle, so the relationship of perimeter and "diameter" becomes closer to the relationship in a circle.

"As the number of sides in a regular polygon increases, the ratio of perimeter to diameter for that polygon approaches pi."

__

2. We know from the first question that ...

circumference/diameter = π

And we know that ...

diameter = 2·radius

Then the following are true:

A. circumference = π · diameter

B. circumference = (2·radius) · π

__

3. The expressions in order evaluate to approximately ...

4.0, 3.45, 3.31, 3.24

Of these, the last is closest to pi (3.14....). The appropriate choice is ...

D. (10·5)/15.4

__

4. Pi cannot be expressed as a rational number, because pi is irrational. A number of lengthy proofs have been offered to demonstrate this fact. One of them makes use of the fact that the tangent of any rational number is irrational, and the tangent of π/4 is 1. Since 1 is a rational number, π/4 cannot be, so π cannot be expressed as a rational number.

Answer:

Step-by-step explanation:

l - length

w - width

The formula of a perimeter of a rectangle: P = 2(l + w)

The formula of an area of a rectangle: A = lw

We have P = 46in and A = 76in² Substitute:

(1)     2(l + w) = 46

(2)    lw = 76

2(l + w) = 46     divide both sides by 2

l + w = 23          subtract w from both sides

l = 23 - w

subtitute it to (2):

(23 - w)w = 76              use the distributive property

23w - w² = 76              subtract 76 from both sides

-w² + 23w - 76 = 0           change the signs

w² - 23w + 76 = 0

w² - 4w - 19w + 76 = 0

w(w - 4) - 19(w - 4) = 0

(w - 4)(w - 19) = 0 ⇔ w - 4 = 0 or w - 19 = 0

w - 4 = 0           add 4 to both sides

w = 4

w - 19 = 0           add 19 to both sides

w = 19

Put the values of w to (1):

l = 23 - 4 = 19 or l = 23 - 19 = 4

Answer: 5 Vertices

Step-by-step explanation: I believe if it had 4 faces and 8 edges it would have 5 vertices.

Answer:

see explanation

Step-by-step explanation:

1

The cosine function in standard form is

y = acos(bx + c)

where a is the amplitude, period = [tex]\frac{2\pi }{b}[/tex] and

phase shift = - [tex]\frac{c}{b}[/tex]

here b = 2 and c = [tex]\frac{\pi }{2}[/tex], thus

phase shift = - [tex]\frac{\frac{\pi }{2} }{2}[/tex] = - [tex]\frac{\pi }{4}[/tex]

2

the amplitude = | a |

which has a maximum of a and a minimum of - a

y = 4cosx ← has a maximum value of 4

Final answer:

The phase shift of the function y = 5cos(2x + π/2) is -π/4 radians. The functions y = 4cosx and y = cosx + 4 both have a maximum y value of 4.

Explanation:

To find the phase shift of the function y = 5cos(2x + π/2), we need to look at the argument of the cosine function. The general form is y = Acos(Bx - C) where C/B is the phase shift. In this case, the argument of the cosine is 2x + π/2, thus the phase shift is -π/2 divided by the coefficient of x, which is 2, giving us a phase shift of -π/4 or -0.785 radians.

To determine which of the provided functions has a maximum y value of 4, consider the amplitude of the cosine functions. For the functions y = 4cosx, y = cos4x, and y = cos(x + 4), the amplitude is 1, and thus the maximum y value is 1 for the latter two, and 4 for the first one. However, y = cosx + 4 is a cosine function shifted upward by 4 units, and hence its maximum y value is also 5. So, the functions with a maximum y value of 4 are y = 4cosx and y = cosx + 4.

The yellow and orange triangle is AA

It is AA because the orange triangle has two angles listed and, the yellow triangle has two angle listed.

Answer:

AA

Step-by-step explanation:

For the 2 triangles to be similar we require 2 corresponding angles to be congruent.

There are 2 angles of measure 30°

If we consider the yellow triangle the the third angle is

180° - ( 41 + 30)° = 180° - 71 = 109°

The 2 triangles have therefore 2 corresponding congruent angles

Hence the triangles are similar by the postulate AA

20% off, means that 20% of the regular price is how much you would save.

Multiply the original price by 20%

18 x 0.20 = 3.6

The discount is $3.60

Answer: Option a.

Domain: (-∞, ∞)

Range: (-∞, ∞)

Step-by-step explanation:

We have the function [tex]f(x) = 2x + cosx[/tex]

Note that f(x) is the sum of two continuous functions [tex]h(x) = 2x[/tex] and [tex]g(x) = cosx[/tex]

The domain and range of h(x) are all real numbers

The domain of g(x) is all real numbers. The range of g(x) is [-1, 1]

Then the domain of [tex]f(x) = h(x) + g(x)[/tex] will be the intersection of the domains of the function [tex]h(x) = 2x[/tex] and the function [tex]g(x) = cosx[/tex].

Therefore the domain of f(x) are all real numbers.  x ∈ (-∞, ∞)

The range of f(x) will be equal to the union of the range of g(x) and h(x)

Therefore the range will be all real numbers f(x) ∈ (-∞, ∞)

Answer:

[tex]y=\sqrt{x} -5[/tex]

Answer:

The function [tex]f(x)=\sqrt{x-5}[/tex]

Step-by-step explanation:

The Range of any function is complete set of all possible resulting values of the dependent variable , after substituting the domain.

so, the function [tex]f(x)=\sqrt{x-5}[/tex] has range [tex]f(x)$\geq$ -5[/tex]

This includes - 4 .

Hence, the function is [tex]f(x)=\sqrt{x-5}[/tex] .

Answer:

60

Step-by-step explanation:

(This is not how teachers usually teach you)

First i divided 36 by 2 to get 30% = 18 then i multiplied 30% by 3.3333etc. to get 100% and i multiplied 18 by the same number (18*3.3333 = 60) and i got 60.

Answer:

Step-by-step explanation:

Givens

To find the regular price for tickets, we can use the rule of three.

If $36 represents 60%, how much would represents 100%?

[tex]x=100\% \frac{\$36}{60\%} = \$60[/tex]

Therefore, the cost of a regular price ticket is $60.

Answer:

V = 115.3 ft³

Step-by-step explanation:

The left part of the figure shows a cube of side length 4.2 ft.  The volume of a cube is V = s³, where s is the side length.  Hence, the volume of this particular cube is V = (4.2 ft)³ = 74.088.

The volume of a pyramid is V = (1/3)(base area)(height).

Here V = (1/3)(4.2 ft)²(7 ft) = 41.16 ft³.

Summing up the two distinct areas, we get V = 41.16 ft³ + 74.088 ft³, or

V = 115.3 ft³ after rounding up to the nearest tenth.

The volume of the composite figure is 115.2 cu.ft. , Option A is the correct answer.

Those figures that required x,y and z axis for their representation are three dimensional figures.

They have length , breadth and height.

All the object that we see around us can be categorized into Three Dimensional Figure.

In the given figure

It can be seen that it consists of a cube and a square pyramid

To determine the volume we have to determine the volume of each figure and then add

Volume of a cube =  side * side * side

Side of the cube = 4.2 ft.

Substituting the values

Volume of cube = 4.2 * 4.2 * 4.2

Volume of cube = 74.088 cu.ft

Volume of a square pyramid is given by

(1/3) * a² * h

a is the area of the base

area of the base =  area of the square = side * side

Area of the base = 4.2 * 4.2

Area of the base = 17.64 sq.ft

Height of the pyramid  = 7 ft.

Volume of  square pyramid = (1/3)* 17.64 *7

Volume of a square pyramid = 41.16 cu.ft

Total volume = 74.088 + 41.16

Total Volume = 115.2 cu.ft

Therefore , The volume of the composite figure is 115.2 cu.ft. , Option A is the correct answer.

To know more about Three Dimensional Figures

https://brainly.com/question/24303419

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Answer:

No, it is not safe

Answer:

Hello!

The answer is no, he will not be safe. I had a similar problem on a test and got the answer correct. The only difference was they used slightly different numbers, so I am pretty sure this is correct. I hope this helps!

Step-by-step explanation:

Okay, so you are looking for x.

sin x= [tex]\frac{16.5}{17}[/tex]

x=[tex]sin^{-1}[/tex]([tex]\frac{16.5}{17}[/tex])

x≈76.07

76.07>70

Answer:

15 g

Step-by-step explanation:

30% · 50 g = 30/100 · 50 g = 1500/100 g = 15 g

Answer:

15g

Step-by-step explanation:

Answer:8462

Step-by-step explanation:

Answer:

8862 feet

Explanation:

The formula for circumference is C=pi*diameter. So, by substitution we can use 26586=(3)d and solve by dividing 26586 by 3 which gives us d=8862 feet.

Answer:

The radius is r=5 units

Step-by-step explanation:

we know that

The equation of the circle in standard form is equal to

[tex](x-h)^{2}+(y-k)^{2}=r^{2}[/tex]

where

(h,k) is the center and r is the radius

we have

[tex]x^{2}+y^{2}-12x+6y+20=0[/tex]

Convert to standard form

Group terms that contain the same variable, and move the constant to the opposite side of the equation

[tex](x^{2}-12x)+(y^{2}+6y)=-20[/tex]

Complete the square twice. Remember to balance the equation by adding the same constants to each side

[tex](x^{2}-12x+36)+(y^{2}+6y+9)=-20+36+9[/tex]

[tex](x^{2}-12x+36)+(y^{2}+6y+9)=25[/tex]

Rewrite as perfect squares

[tex](x-6)^{2}+(y+3)^{2}=5^{2}[/tex]

therefore

The center is the point (6,-3) and the radius is r=5 units

Answer:

(-5 +/- sqrt(65))/2

Step-by-step explanation:

To solve this, we can use the quadratic formula!

So,

x = (-b +/- sqrt(b^2-4ac))/2a

x = (-5 +/- sqrt(25+40))/2

x = (-5 +/- sqrt(65))/2

So (-5 +/- sqrt(65))/2  is our answer.

Answer:

559.2 yards.

Step-by-step explanation:

Let the height of the mountain be x yards and the distance from the second location to the base of the mountain be y yards.

Then we have the equations:

tan 27 = x/y

tan 23 = x / (220 + y)

From the first equation  y =  x/ tan27 so substituting in the second one we have:

tan 23 =  x / (220 + x / tan 27)

Cross multiply:

x = 220 tan23 +  x tan 23 / tan 27

x =  93.384 + 0.833 x

x - 0.833x = 93.384

x = 93.384 / 0.167

x = 559.2 yards to 1 dec place (answer).

Answer: 1) Quadrant: I, reference angle: [tex]\dfrac{2\pi}{5}[/tex]

              2) Quadrant: III, reference angle: 85°

              3) Quadrant: IV, reference angle: [tex]\dfrac{\pi}{4}[/tex]

Step-by-step explanation:

Reference angle is the angle closest to the x-axis

1) The given angle is (2/5)π. The first quadrantal (π/2) would be (2.5/5)π

Since (2/5)π < (2.5/5)π then it must be in Quadrant 1.

The angle closest to the x-axis is the same as the given angle.

2) The given angle is -95°. It is measured clockwise since it is a negative angle.  Since it is greater than 90°, it is greater than the 270° quadrantal. So it must be in Quadrant III.

The angle closest to the x-axis is 85°.

3) The given angle is (23/4)π.  Since (8/4)π is one rotation, this is greater than one rotation. (23/4)π - (8/4)π - (8/4)π = (7/4)π. So, it rotates two complete rotations and lands at coterminal angle (7/4)π.

The angle closest to the x-axis is π/4

Answer:

the point r would be located at (4,3)

Step-by-step explanation:

granted that the quadralaterel is a square that would mean that all side lengths are equal and the distance between points x and q is 3 meaning that the same would have to be said about the distance between s and r

Answer:

Option 1.

[tex]P(A) = \frac{1}{8},\ P(A|B) = \frac{1}{3}[/tex]     Dependent

Option 2

[tex]P(A) = \frac{1}{4},\ P(A|B) = \frac{1}{4}[/tex]    Independent

Option 3

[tex]P(B) = \frac{1}{8},\ P(B|A) = \frac{1}{4}[/tex]    Dependent

Option 4

[tex]P(B) = \frac{1}{4},\ P(B|A) = \frac{1}{4}[/tex]     Independent

Step-by-step explanation:

Two events A and B are independent if the occurrence of A does not affect the probability of B.

On the other hand The probability of A given B is defined as:

[tex]P (A | B) = \frac{P (A\ and\ B)}{P (B)}[/tex]

When two events are independent then:

[tex]P (A\ and\ B) = P (A) * P (B)[/tex]

So if the two events A and B are independent this means that:

[tex]P (A | B) = \frac{P (A) * P (B)}{P (B)}[/tex]

[tex]P (A | B) = P (A)[/tex]

Which makes sense because if the events are independent then the probability of A not being affected by B.

So to solve this problem identify in what cases

[tex]P (A | B) = P (A)[/tex] or [tex]P (B | A) = P (B)[/tex]

When this happens those events are independent

Option 1.

[tex]P(A) = \frac{1}{8},\ P(A|B) = \frac{1}{3}[/tex]     Dependent

Option 2

[tex]P(A) = \frac{1}{4},\ P(A|B) = \frac{1}{4}[/tex]    Independent

Option 3

[tex]P(B) = \frac{1}{8},\ P(B|A) = \frac{1}{4}[/tex]    Dependent

Option 4

[tex]P(B) = \frac{1}{4},\ P(B|A) = \frac{1}{4}[/tex]     Independent

Answer:

A = 21.65 cm squared

Step-by-step explanation:

The basic area formula for a triangle is

[tex]A= \frac{1}{2}bh[/tex]

We have our base as 5, so we can find the height using right triangle trig.  Side BC is opposite the given angle, which is the height, and we are given side CD as 5 which is the base.  Using the tangent ratio to find side BC:

[tex]tan(60) = \frac{x}{5}[/tex] which simplifies to

5 tan(60) = x so

x = 8.66

Filling in for the area:

[tex]A= \frac{1}{2}(5)(8.66)[/tex] so

A = 21.65 cm squared

probability of drawing a blue marble is 1/3

Divide 110 by 10 to get a rate if 11 feet per second. Multiply 11 by 12 seconds to get 132 feet

Answer:

4046.56 cm3

Step-by-step explanation:

The base is made by 5 isosceles triangles, with one side of 14 cm, and the opposite angle of [tex] \frac{360} 5 = 72° [/tex]. Each of the other angle is [tex]\frac{180-72} {2} =54°[/tex]. From there, you can calculate the height of each base triangle as in [tex]\frac {h} 7 = tan54[/tex] or 9.634...cm.

Your volume will be [tex]5 * \frac  {(14 * 9.634)} 2 * 12 = 4046.56 cm^3[/tex]

B. Three. It is three because there is one decimal place in each factor.

Answer:

B. Three.

Explanation:

Three because there is one decimal place in each factor and there are 3 factors.

39.4 degrees Celsius

Hope this helps :)

Answer:

39.4°C

Step-by-step explanation:

The equation for fahrenheit to celsius is

(°F − 32) × 5/9 = °C

With our variable of 103 plugged in it is

(103°F − 32) × 5/9 = 39.444°C

Therefore, her fever is 39.4°c

Answer: Estimates vary, but each person uses about 80-100 gallons of water per day

Answer:

The answer is 1/4.

Step-by-step explanation:

5 rock CDs, plus 3 country CDs, plus 4 movie sound track CDs, equal 12 CDs in total. To find the odds of choosing a country CD, you divide the total number of CDs, by the number of what you choose (3/12).

Answer:

The odds that he choose a country CD is 1/3

Step-by-step explanation:

12/12 ÷ 3 = 1/3