How many sides does a regular n-gon have if one interior angle measures 150°? Show all work!

Answer:

-1.25

Step-by-step explanation:

Equation: y = -1.25x - 3.

Answer: 1/6

Step-by-step explanation: I think you multiply 3 times 3 because the other circle circle has an option the first doesn't have have.

The conversion of angles to radians

To convert an angle from degrees to radians, we can use the conversion factor of π/180, where π is approximately 3.14159.

(a) Converting θ = 120° to radians:

θ_radians = 120° * (π/180)

= 2π/3 radians

≈ 2.094 radians

Therefore, θ = 120° is approximately equal to 2.094 radians.

(b) Converting θ = 90° to radians:

θ_radians = 90° * (π/180)

= π/2 radians

≈ 1.571 radians

Therefore, θ = 90° is approximately equal to 1.571 radians.

(c) Converting θ = 45° to radians:

θ_radians = 45° * (π/180)

= π/4 radians

≈ 0.785 radians

Therefore, θ = 45° is approximately equal to 0.785 radians.

In summary, θ = 120° is approximately 2.094 radians, θ = 90° is approximately 1.571 radians, and θ = 45° is approximately 0.785 radians.

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Answer:

y = 4

Step-by-step explanation:

Using the tangent ratio in the right triangle and the exact value

tan30° = \(\frac{1}{\sqrt{3} }\) , then

tan30° = \(\frac{opposite}{adjacent}\) = \(\frac{y}{4\sqrt{3} }\) = \(\frac{1}{\sqrt{3} }\) ( cross-  multiply )

y × \(\sqrt{3}\) = 4\(\sqrt{3}\) ( divide both sides by \(\sqrt{3}\) )

y = 4

Answer:

y=4

Step-by-step explanation:

If we have a triangle with angles A, B, and C. The law of sines says that the proportion between the sin of angle A and its opposite side is equal to the proportion between the sin of angle B and its opposite side and it is equal to the proportion between the sin of angle C and its opposite side.

So, by the law of sines we can say that:

\(\frac{sen(60)}{4\sqrt{3} } =\frac{sen(30)}{y}\)

Solving for y, we get:

\(sin(60)*y=4\sqrt{3}*sin(30)\\\frac{\sqrt{3} }{2}y=4\sqrt{3}*0.5\\ \frac{1}{2} y=4*0.5\\y = 4\)

a) The populations of the city (in thousands) in the years 2000, 2003, 2010, 2015, and 2019 are 2424.103, 2225.170, 2393.106, 2304.452 and 2155.096.

b) The year in which the population reached 2.2 million is 2015.

c) The given population is 2.2 million (in thousands), we can see that it matches the value we obtained when we substituted t=15 in the model equation.

(a) Using the model, the populations (in thousands) of the city in the years 2000, 2003, 2010, 2015, and 2019 can be found by substituting the corresponding value of t in the model equation.

For 2000 (t=0), P = 2424.103

For 2003 (t=3), P = 2225.170

For 2010 (t=10), P = 2393.106

For 2015 (t=15),P = 2304.452

For 2019 (t=19), P = 2155.096

(b) Using a graphing utility to graph the function (with proper domain and range values), we can observe that the population reaches 2.2 million in the year 2015 (t=15).

(c) To confirm this answer algebraically, we can substitute the value of t=15 in the model equation-

P = 2635 + 0.08706507(15) = 2304.452

Since the given population is 2.2 million (in thousands), we can see that it matches the value we obtained when we substituted t=15 in the model equation, thus confirming our answer.

Therefore,

a) The populations of the city (in thousands) in the years 2000, 2003, 2010, 2015, and 2019 are 2424.103, 2225.170, 2393.106, 2304.452 and 2155.096.

b) The year in which the population reached 2.2 million is 2015.

c) The given population is 2.2 million (in thousands), we can see that it matches the value we obtained when we substituted t=15 in the model equation.

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Answer:

The answer is (4,36)

Step-by-step explanation:

Not sure if you have A switched around but it is 4,36.

Answer:

on the final exam its 2,24

Step-by-step explanation:

The total number of comic books Jill had in the start is x = 28 books

Given data:

Let's represent the number of comic books Jill started with as "x".

Jill sold half of her comic books, which would be (1/2)x.

After selling half, Jill had (x - (1/2)x) = (1/2)x remaining.

Jill then bought eight more comic books, which increased the number to (1/2)x + 8.

Now, we know that Jill has a total of 22 comic books, so we can set up the equation

(1/2)x + 8 = 22

To solve for x, we can subtract 8 from both sides of the equation:

(1/2)x = 22 - 8

(1/2)x = 14

To isolate x, we can multiply both sides by 2:

x = 14 * 2

x = 28

Hence, Jill started with 28 comic books.

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Answer:

1. z=140

2. z=130

3. z=145

4. z=180

5. z=155

6. z=120

Step-by-step explanation:

1. z+40=180 so you should subtract 40 from both sides of the equation to get 180-40=140, meaning that z=140

2. 50+z=180 so you should subtract 50 from both sides of the equation to get 180-50=130, meaning that z=130

3. subtract 35 from both sides of the equation to get 180-35=145, meaning that z=145

4. You can just solve this equation as 90+90=180, meaning that z=180

5. subtract 25 from both sides of the equation to get 180-25=155, meaning that z=155

6. subtract 60 from both sides of the equation to get 180-60=120, meaning that z=120

Answer:

x = 2, x = -6

Step-by-step explanation:

Given quadratic function in vertex form:

\(f(x)=(x+2)^2-16\)

The zeros of a function occur when f(x) = 0:

\(\implies (x + 2)^2 - 16 = 0\)

Add 16 to both sides:

\(\implies (x + 2)^2 - 16+16 = 0+16\)

\(\implies (x + 2)^2 =16\)

Square root both sides:

\(\implies \sqrt{ (x + 2)^2} =\sqrt{16}\)

\(\implies x+2= \pm 4\)

Subtract 2 from both sides:

\(\implies x+2-2= -2 \pm 4\)

\(\implies x= -2 \pm 4\)

Therefore:

\(\implies x=-2+4=2\)

\(\implies x=-2-4=-6\)

The zeros of the given quadratic function are x = 2, x = -6.

Answer:

x = 39

y = 129

Step-by-step explanation:

to find x you do

x +51 = 90

subtract 51 from both sides

x = 39

to find y

we already know part of y is a right angle (90 degrees)

so we need to find the tiny other part

this tiny other part is equal to x

so

90 +39 = 129

Answer:

D

Step-by-step explanation:

40 + 20 = 60 lol

Answer:

the answers and working is in the photo above

Answer:

43

Step-by-step explanation:

52-9=43

The same circle's radii. parallelogram, rectangle, square, and rhombus opposite sides, sides of a triangle with equal sides.

What is congruent segments?

Segments of the same length are said to be congruent. Collinear points are those that share a line. A mathematical assertion that can be validated is known as a theorem. A point that divides a segment into two congruent segments is the segment's midpoint.

Congruent line segments are geometrical figures in one dimension with identical dimensions. In terms of congruent lines, the word "congruent" refers to the equality of the two line segments.

When two lines are the same length, they are said to be congruent. Superimposable figures that entirely enclose each other when stacked one atop the other are congruent segments.

The congruent segments continue to be congruent even after being turned, flipped, or rotated. Congruence between any two congruent line segments is represented by the symbol.

Look at the illustration below that shows congruent line segments:

Here, the double vertical bars on each line segment, PQ and XY, represent their equality, resulting in the line segment PQ ≅ XY.

We shall examine the congruent line segments' qualities in order to learn more about them. Congruent lines in geometry possess the following characteristics:

(i) Reflexive

(ii) Symmetric

(iii) Transitive

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Answer:

1=27

2=34

Step-by-step explanation:

1)9y power 2÷3

or, y=9 power 2÷3

or, y=9×9÷3

or, y=81÷3

or, y=27

2) (8x power 2+4x)÷2

=(8x×8+4x)÷2

=(64x+4x)÷2

=68x÷2

or, x=68÷2

or, x=34

Answer:

\(n=-2\)

Step-by-step explanation:

\(-4(8+6n)=-2(n-6)\\ -32-24n=-2n+12\\-32-12=-2n+24n\\-44=22n\\n=-2\)

Answer:

-3 to the power of x

-2 to the power of x

-1 to the power of x

0 to the power of x

1 to the power of x

2 to the power of x

3 to the power of x

Step-by-step explanation:

Answer:

1 minute and 15 seconds

Step-by-step explanation:

Let's start by finding how long it takes Mike to play one full song.

If Mike plays 1/5 of a song in 1/4 of a minute, then he plays 1/5 x 4/1 = 4/5 of a song in one minute (by multiplying the numerator and denominator of 1/5 by 4/1).

To find how long it takes to play one full song, we can set up a proportion:

4/5 of a song is played in 1 minute

1 full song is played in x minutes

We can cross-multiply to solve for x:

4/5 = 1/x

Multiplying both sides by x:

4/5 * x = 1

Dividing both sides by 4/5:

x = 5/4 = 1.25

Therefore, it takes Mike 1.25 minutes, or 1 minute and 15 seconds, to play one full song.

A normal probability distribution becomes a standard normal distribution when it has two requirements: a mean (µ) of 0 and a standard deviation (σ) of 1.

Normal distributions have key characteristics that are easy to spot in graphs:

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There are 6 pairwise comparisons that need to be made in order to gain a complete understanding of which treatment effects differ significantly from others.

In order to determine which treatment effects differ significantly from others, we need to make pairwise comparisons between all possible pairs of treatment groups. Let's consider an example with four treatment groups labeled A, B, C, and D.

To determine which treatment effects differ significantly from others, we need to compare the mean scores of each treatment group with the mean scores of every other treatment group. This means we need to make the following pairwise comparisons:

A vs B

A vs C

A vs D

B vs C

B vs D

C vs D

Therefore, there are 6 pairwise comparisons that need to be made in order to gain a complete understanding of which treatment effects differ significantly from others.

It's worth noting that when making multiple pairwise comparisons, there is an increased risk of making a Type I error (i.e., rejecting the null hypothesis when it is actually true) due to the multiple testing problem. To control for this, researchers may choose to adjust the significance level or use methods such as the Bonferroni correction to adjust the p-values of the individual tests.

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Answer:b

Step-by-step explanation:

Answer:

< DGB = 101

Step-by-step explanation:

< CGB is equal to 79

< CGB is another name for < 1

We want to find < DGB which is another name for <2

< 1 and < 2 are a linear pair

<1 + <2 = 180

79 + <2 = 180

<2 = 180-79

<2 = 101

< DGB = 101

Answer:

The answer is 101

Step-by-step explanation:

Since a line has an angle of 180°

To know DGB we will just subtract 79 from 180

hence DGB=180°-79°

=101°

Answer:

Point Slope Form:  y - 0=2 (x - 0)

Simplified Form:  y=2x

Step-by-step explanation:

The point-slope form of line is given by:

y - y1=m(x - x1)

Where

m is the slope

 is the first x-coordinate

 is the first y-coordinate

Given slope is 2, thus we can say:

m = 2

Also, it says the line goes through the point (0,0), so:

and

Now, substituting, we get the point slope form to be:

y-y1=m(x - x1)

y-0=2(r-0)

y=2(x)

y=2x

The equation of line will be y = 2x

The slope of the equation m = 2 and the point P ( x₁ , y₁ ) = P ( 0 , 0 )

What is an Equation of a line?

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation be represented as A

Let the point be represented as P

The value of P = P ( 0 , 0 )

The slope of the equation m = 2

Slope m = 2

Now , the equation of line in the slope intercept form is

y - y₁ = m ( x - x₁ )

Substituting the values in the equation , we get

y - 0 = 2 ( x - 0 )

On simplifying the equation , we get

y = 2x

Therefore , the value of A is y = 2x

Hence , the equation of line is y = 2x

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Answer:

Negative

Step-by-step explanation:

A positive divided by a negative will always be negative.

Answer:

if they are both positive its positive

if ones positive and ones negitive its negative

if they are both negative its positive

Step-by-step explanation:

11 years is the sum of Joey's two digits the next time his age is a multiple of Zoe's age.

Assume Chloe is c years old today, and Joey is c+1 years old today. Chloe and Zoe will be n+c and n+1 years old after n years.

Given,

(n + c) ÷ (n + 1) = 1 + ((c - 1) ÷ (n + 1))

For 9 non-negative integers, n is an integer. As a result, c - 1 has 9 positive divisors. c-1's prime factorization is either \(p^8\) or p²q². Because c - 1 < 100, the only possible solution is c - 1 = 2² × 3² = 36, from which c = 37. We may deduce that Joey is 38 years old today.

Assume Joey's age is a multiplier of Zoe's age after k years, resulting in Joey and Zoe being k + 38 and k + 1 years old, correspondingly.

Given,

(k + 38) ÷ (k + 1) = 1 + ((38 - 1) ÷ (k + 1))

For some positive integers, k is an integer. As 37 is divisible by k + 1, the only possible solution is k = 36. Infer that Joey will be k + 38 = 74 years old at that time, yielding the value 7 + 4 = 11.

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Answer:

18.8 years

Step-by-step explanation:

8% of $2000 = $160

To be worth $5000, the painting need to rise by $3000
And every year it rise by $160, so it will need 3000 : 160 = 18.75 (round to 18.8) years.

By Interception of a point f(x) = 3.75b + 25 and this we get the Value 3.75.

Examples :

f(x) = 3.75b + 25

Axis interception points of 3.75b + 25:

X intercepts:(-20 / 3,0),

Y intercepts : (0.25)

Slope of 3.75b + 25: 3.75.

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Answer:

Width = 12

Length = 16

Step-by-step explanation:

Width = x

Length = x + 4

2x + 2(x+4) = 56

2x + 2x + 8 = 56

4x = 56 - 8

x = 48/4

x = 12