Please hurry (if you want)

Therefore , the solution of the given problem of angles comes out to be following about a normal 16-gon is FALSE:

The top but also bottom of wall separate the two circular edges that make the sides of a skew in Euclidean space. A junction point may develop when two beams collide. Another result of two things interacting is an angle. They most closely resemble dihedral shapes. Two line beams can be arranged in different ways at their extremities to form a two-dimensional curve.

Here,

The following about a normal 16-gon is FALSE:

c. The internal angle measure's total value is 28800.

We can use the following method to determine the total interior angle measure of a regular 16-gon:

Sum of internal angles equals (n - 2)180°, where n is the number of sides.

=> With n = 16, we obtain:

=> Interior angle total = (16 - 2) 180 = 2520 degrees.

Because of this, it is accurate to say that

=> 2520 degrees, not 28800, make up the interior angle measure of a regular 16-gon.

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Answer:  \(6\sqrt{5}\)  miles

This is the same as writing 6*sqrt(5) miles

==========================================================

Work Shown:

P = park

C = city hall

Point P is at the location (10,11)

Point C is at the location (7,5)

Apply the distance formula to find the length of segment PC

\(d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(10-7)^2 + (11-5)^2}\\\\d = \sqrt{(3)^2 + (6)^2}\\\\d = \sqrt{9 + 36}\\\\d = \sqrt{45}\\\\d = \sqrt{9*5}\\\\d = \sqrt{9}*\sqrt{5}\\\\d = 3\sqrt{5}\\\\d \approx 6.7082039\\\\\)

The exact distance between the park (P) and city hall (C) is \(3\sqrt{5}\) miles.

This doubles to \(2*3\sqrt{5} = 6\sqrt{5}\) miles because the runners go from P to C, then back to P again. In other words, they run along segment PC twice. This is assuming there is a straight line road connecting the two locations.

Extra info:

\(6\sqrt{5} \approx 13.41641\) so the runner travels a total distance of roughly 13.4 miles.

Answer:

X= 10/3y + -4/3                

Step-by-step explanation:

Step One: add -5y to both sides

Step two: divide both sides by -3

Answer:

-x=1 1/3

Step-by-step explanation:

x-(4x-5y)=(5y+4)

x-4x+5y=5y+4

-3x+5y=5y+4

5y-5y=0

-3x=4

x=4÷3

4÷3=1 1/3

Answer:

42 cm

Step-by-step explanation:

7+4+2+4+2+4+7+12

Answer:

2,351,000

Step-by-step explanation:

closest to the volume in cubic feet

Answer: Option (4)

Step-by-step explanation:

A quadrilateral with two pairs of opposite congruent sides must be a parallelogram.

Answer:

c is circumference which is equal to 3.14 multiplied by d  

Step-by-step explanation:

Answer:

constant = b = -15

Step-by-step explanation:

3 + b = -12

b = -12 - 3

b = -15

The integer that represents the given situation is a positive 31.

The temperature being 31 degrees above zero means that it is warmer than the freezing point of water. In this context, "above zero" refers to the Celsius or Fahrenheit scale, where zero represents the freezing point of water. Therefore, a temperature of 31 degrees above zero is a positive value indicating a warm temperature.

In this case, it can be assumed that the temperature is being measured in Celsius since 31 degrees above zero on the Fahrenheit scale would correspond to a very high temperature of approximately 87 degrees Fahrenheit. Overall, the integer that represents this situation is positive 31, which signifies a warm temperature above the freezing point.

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Answer:

6/8

Step-by-step explanation:

multiply both of them by 2 and its equal.

you get 6/8

Answer:

Part A

x + y ≤ 460...(1)

2.5·x + 1.25·y ≥ 600...(2)

Part B

The number of bottles of water the student must sell ≥ 192 bottles of water

Step-by-step explanation:

The given parameters are;

The selling price of each can of lemonade = $2.50

The selling price of each bottle of water = $1.25

The amount of money the club needs to raise = $600

The maximum number of cans and bottles the students can accept = 460

Part A

Let 'x' represent the number of cans of lemonade the students accept, and let 'y' represent the number of bottles the student accept, the system of inequalities that can be used to represent the situation can be presented as follows;

x + y ≤ 460...(1)

2.5·x + 1.25·y ≥ 600...(2)

Part B

The number of cans of lemonade the club sells, x = 144

The number of bottles of water the student must sell to cover the cost of costumes, 'y', is given from the second inequality as follows;

2.5 × 144 + 1.25·y ≥ 600

1.25·y ≥ 600 - 2.5 × 144 = 240

1.25·y ≥ 240

y ≥ 240/1.25 = 192

y ≥ 192

The number of bottles of water the student must sell = 192 bottles of water

An equation of the parabola that passes through the point (3, 8) and has vertex (9, 5) is y = 1/12(x - 9)² + 5.

In this exercise, you're required to write an equation of the parabola in vertex form by using the completing the square method. Mathematically, the vertex form of a parabola is represented by this mathematical expression:

y = a(x - h)² + k

Where:

h and k represents the vertex of the equation.

Next, we would determine the value of a as follows:

8 = a(3 - 9)² + (5)

8 = a(-6)² + 5

8 = 36a + 5

36a = 8 - 5

36a = 3

a = 3/36

a = 1/12

Substituting the given parameters into the equation, we have;

y = a(x - h)² + k

y = 1/12(x - 9)² + 5

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Answer: only x=3 is a solution and only x=1 is an extraneous root

For the given expression (x/x-1) - (3/x) = 1/x-1 both x=3 and x=1 are solutions. The correct option is B.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that the expression is  (x/x-1) - (3/x) = 1/x-1. Check the solution of the expression,

(x/x-1) - (3/x) = 1/x-1

( 3 / 3 - 1 ) - ( 3 / 3 ) = 1 ( 3 - 1 )

( 3 / 2 - 1 ) = 1 / 2

1 / 2 = 1/2

For x = 1 the value is the same.

Therefore, both 3 and 1 are solutions to the given formula (x/x-1) - (3/x) = 1/x-1.

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Part A:

Since Juanita had at first $25

Since she earns $11 per hour

Then her total earning in x hours is

Since she needs at least $58 to buy new shoes

At least means greater than or equal, then the inequality should be

Part B:

Let us solve it by subtracting 25 from each side

Divide each side by 11

Then the answer is the 3rd choice

Answer:

\(-\frac{11}{12}\)

Step-by-step explanation:

Step 1- Add.

\(\frac{\frac{5}{8} +\frac{3}{4} }{\frac{-2}{3}-\frac{5}{6} }\)  = \(\frac{\frac{11}{8} }{\frac{-3}{2} }\)

Step 2- Divide and rewrite.

\(-\frac{\frac{11}{8} }{\frac{3}{2} }\)  = \(-\frac{11}{12}\)

The balance after 6 years when the interest is compounded monthly is $7289.60

To find the balance after 6 years when the interest is compounded monthly, we can use the formula:

A = P(1 + r/n)^(nt)

where:

In this case, P = $5000, r = 6.3% = 0.063 (annual interest rate as a decimal), n = 12 (since interest is compounded monthly), and t = 6.

Plugging in these values, we get:

A = $5000(1 + 0.063/12)^(12*6)

Evaluate

A = $7289.60

Therefore, the balance after 6 years when the interest is compounded monthly is $7289.60

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Answer:

159.09

Step-by-step explanation:

.3563 * 446.51 = 159.09

Answer:

sin x= opp/hyp

sin x=18/30

sin x =3/5

cos x= adj/hyp

cos x=24/30

cos x=4/5

tan x=opp/adj

tan x=18/24

tan x=3/4

Radicals expression with variables and exponents can be simplify by:

To help us understand each step better, we will take an example of a radical expression with variables and exponents of: \(\sqrt{16a^{3}b^6c^5 }\)

First, we need to separate the number and variables:

\(\sqrt{16a^3b^6c^5}=\sqrt{16} \sqrt{a^3b^6c^5}\)

Next, we will try to find variables with even exponents:

\(\sqrt{16} \sqrt{a^3b^6c^5} = \sqrt{16} \sqrt{a.a^2.b^6.c^4.c^}\)

Remember that:

(xᵃ)ᵇ = xᵃᵇ; then:

\(\sqrt{16}\sqrt{a.a^2.b^6.c^4.c} =\sqrt{16}\sqrt{a.a^2.(b^3)^2.(c^2)^2.c}\)

We try to breakdown any number into any factor that are perfect square:

\(\sqrt{16}\sqrt{a.a^2(b^3)^2.(c^2)^2.c} = \sqrt{4 .4} \sqrt{a.a^2(b^3)^2.(c^2)^2.c}\)

We will rewrite both number and the variables into a square exponents:

\(\sqrt{4 .4} \sqrt{a.a^2(b^3)^2.(c^2)^2.c} = \sqrt{4^2} \sqrt{a.a^2(b^3)^2.(c^2)^2.c}\)

We will separate the squared factors into individual radicals:

\(\sqrt{4 ^2} \sqrt{a.a^2(b^3)^2.(c^2)^2.c} = \sqrt{4^2} \sqrt{a^2} .\sqrt{(b^3)^2} \sqrt{(c^2)^2} \sqrt{a.c}\)

We take the square root of each radical into:

\(\sqrt{4^2} \sqrt{a^2} .\sqrt{(b^3)^2} \sqrt{(c^2)^2} \sqrt{a.c} = 4|a|.|b^3|.c^2\sqrt{ac}\)

We just need to simplify our last equation into:

\(4|a|.|b^3|.c^2\sqrt{ac} = 4|ab^3|c^2\sqrt{ac}\)

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Answer:

√20 units.

Step-by-step explanation:

Please see attached photo for diagram.

The other leg of the triangle is x as shown in the attached photo.

Using the pythagoras theory, we can obtain the the value of x as follow:

x² = 4² + 2²

x² = 16 + 4

x² = 20

Take the square root of both side.

x = √20 units

Therefore, the value of the other leg x of the triangle is √20 units

Answer:

\(\sqrt{} 20\) is your answer hope this helps

Step-by-step explanation:

The value of x in the given 45-45-90 triangle is 9.89.

The given triangle is a right-angled triangle which can be solved using the Pythagoras theorem. The Pythagoras theorem states that the square of the hypotenuse is equal to the sum of the square of the base and the square of the perpendicular. This theorem can be applied to all right-angled triangles.

In the given triangle, we have been told that the length of both legs is 7. Now, after applying the theorem -

= 7²+7² = H²

= 49 + 49 = H²

= 98 = H²

= √98 = H

= 9.89 = H

Hence, this is the value of x.

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Answer:

Step-by-step explanation:

vertex of g(x) is (0, 0), so:

\(g(x)=a(x-0)^2+0\\\\g(x)=ax^2 \qquad and\qquad (2,\,1)\in g(x)\\\\1=a\cdot2^2\\1=4a\\a=\frac14\\\\g(x)=\frac14x^2=(\frac12x)^2\)

The tasks offered to require you to determine the series solution to a differential equation. For each issue, we must establish if the differential equation has a regular singular point for a given value of x, as well as the indicial equation, recurrence relation, and indicial equation roots. Consequently, if the bigger and smaller roots exist, we can obtain the series solution to the differential equation.

1. a) Regular singular point at x0=0

b) Indicial equation: r(r-1)+r=0, which simplifies to r^2=0. The roots are r1=r2=0.

c) y(x) = c0 + c1*x, where c0 and c1 are constants of integration.

d) N/A as the roots are equal.

2. a) Regular singular point at x0=0

b) Indicial equation: r(r-1)+r/9=0, which simplifies to r(r-1+1/9)=0. The roots are r1=0 and r2=1-1/3=2/3.

Recurrence relation: an=-(2n-1)/n(3n+1)an-1

c) y(x) = c0 + c1x^(2/3) - 1/21x^(8/3) + 2/495x^(14/3) - 26/25515x^(20/3) + ...

d) y(x) = c2x^0 + c3x^(-1/3) - 5/63x^(5/3) + 11/2079x^(11/3) - 301/54235*x^(17/3) + ...

3. a) Regular singular point at x0=0

b) Indicial equation: r(r-1)=0. The roots are r1=0 and r2=1.

Recurrence relation: an=-(1/2)an-1

c) y(x) = c0 + c1*x

d) y(x) = c2 + c3/x

4. a) Regular singular point at x0=0

b) Indicial equation: r(r-1)-1=0, which simplifies to r^2-r-1=0. The roots are r1=(1+sqrt(5))/2 and r2=(1-sqrt(5))/2.

Recurrence relation: an=-[2(n-1)+1-1]/(n(n+1)-1)(r1(n-1)+r2n)an-1

c) y(x) = c0 + c1exp(r1x) + c2exp(r2x)

d) y(x) = c3exp(r2x)

5. a) Regular singular point at x0=0

b) Indicial equation: r(r-1)+r+2=0, which simplifies to r^2=1. The roots are r1=1 and r2=-1.

Recurrence relation: for r1: an=-1/[(n+2)(n+1)]an-1, for r2: an=1/(n(n-1)+2n-6)an-1

c) y(x) = c0 + c1x - x^2/3 + 4/45x^4 - 2/945*x^6 + ...

d) y(x) = c2 + c3/x^2

6. a) Regular singular point at x0=0

b) Indicial equation: r(r-1)+(1-x)r=0, which simplifies to r^2-xr=0. The roots are r1=0 and r2=x.

Recurrence relation: an=-an-1/(n(1-x+n))

c) y(x) = c

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The use and interpretation of an R or s chart are critical when examining an X-bar chart because they provide additional information about the variation within the subgroups. This allows for a more comprehensive analysis of the process and helps identify any issues or sources of variability.

When using an X-bar chart, the focus is on monitoring the process mean or average. However, the X-bar chart alone does not provide information about the variation within the subgroups. This is where the R or s chart comes into play. The R chart measures the range of values within each subgroup, while the s chart measures the standard deviation.
By using an R or s chart alongside the X-bar chart, we can assess the variability within the subgroups and determine if it is stable over time. If the variation within the subgroups is high and unpredictable, it may indicate that the process is out of control or that there are sources of variation that need to be addressed. The R or s chart provides additional insights into the process performance and helps in identifying the presence of special causes of variation.
In summary, the use and interpretation of an R or s chart in conjunction with an X-bar chart allow for a more comprehensive analysis of process variation. This helps in understanding the stability and capability of the process and enables appropriate actions to be taken to improve quality and performance.

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Work Shown:

V = pi*r^2*h

V = pi*(x^3)^2*x^2

V = pi*x^(3*2)*x^2

V = pi*x^6*x^2

V = pi*x^(6+2)

V = pi*x^8

Answer:

πx^8

Step-by-step explanation:

V=πr²h

Now plugin r=x³ and h=x² in the formula above:

V=π(x³)²(x²)     multiply powers 3x2=6

=π(x^6)(x²) = πx^8     add powers 6+2=8

The accumulated value of $8600 at 6.45% after 8 months (simple interest) is $8971.90.

To compute the accumulated value of $8600at 6.45% after 8 months (simple interest), we need to use the formula for simple interest, which is given by:

I = P × r × t

Where, I is the interest earned, P is the principal amount, r is the interest rate, and t is the time in years.

Here, we have t in months, so we need to convert it into years by dividing by 12.

So, t = 8/12 = 2/3 years.

Now, substituting the given values, we get:

I = 8600 × 6.45/100 × 2/3 = $371.90

Therefore, the accumulated value of $8600 at 6.45% after 8 months (simple interest) is $8600 + $371.90 = $8971.90.

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Answer:

Below in bold.

Step-by-step explanation:

Let x = cosθ, then

8(cosθ)^3 − 6cosθ + 1 = 0

---> 2(4(cosθ)^3 − 3 cosθ) + 1 = 0    

---> 2(cos3θ) + 1 = 0

---> cos3θ = -1/2

---> θ = 2π/9

Therefore cos  θ  = = cos(2π/9) = x, and

cos(2π/9) is a root of the given eqation.

Answer:

the answers are below

Step-by-step explanation:

1: 4

2: 3 and they are 8ab, 3b, and 4a

3: 16

Answer:

8 a b - 4 a + 3 b + 16. Simplify: 8 a b - 4 a + 3 b + 16 Answer: 8 a b - 4 a + 3 b + 16

Step-by-step explanation: Coefficient is any of the factors with the sign of the term. ... The given algebraic expression has three terms, namely, 4a 4b2c – 3a3b2c and 3/2 ab3c2