Find the measure of each interior and exterior angle of a regular 30-gon

For this case we have the following expression given:

We can use the following property:

And for this case we got:

Now we can apply the following property:

Using this we have for our resut:

And the best answer for this case would be:

C) 2(log6 + logx)

on solving the provided question, we can say that by equation we Consequently, he will sell 16 automobiles at this price.

A number, a variable, or a mix of both, combined with certain operation symbols, make up an expression. An equal sign is used to denote the separation of two expressions in an equation.

Here,

Given: Number of cars sell in a day = 12

Price of a car =\($23,000\)

For each $300 price reduction dealer can sell two more cars per day.

Solution: Let there be x unit 300 price reduction

2x unit increase in sale of car

\(|R(x)=(15000-300x)(12+2x)\)

Cost

\(|C(x)=1000+12000 (12+2x)\)

Profit

\(|P(x)=(15000-300x)(12+2x)-1000+12000 (12+2x)\\15000(12+2x)–12000 (12+2x)-300x(12+2x)-1000\\=180000-144000+30000x-24000x -3600x -600-1000\\=36000+2400x-600 = P'(x)=-1200x +2400 = P"(x)=-1200\)

For critical points

\(P'(x)=0= -1200x + 2400=0= x=2\)

Since P"(x) <0at x = 2it is max profit 12+2x=12+2(2)=16

16cars per day he will sell

\(Price = 15000-300*16 = $10200\)

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Answer:

Step-by-step explanation:

-3≤ x = graph 6

-3 > x = graph 3

x≥ 3 = graph 2

x ≤ 3 = graph 4

3 > x = graph 1

x > 3 = graph 5

the closed circles means greater/less than or equal to

the open circle means greater/less than

the direction of the arrow tells you if the number is greater than x or less than x

Answer:

7, 10, 13, 16 and 34

Step-by-step explanation:

\(let \: t_{n} = 3n + 4 \\ when \: n = 1 \\ t_{1} = 3.1 + 4 = 3 + 4 = 7 \\ \\ when \: n = 2 \\ t_{2} = 3.2 + 4 = 6 + 4 = 10 \\ \\ \ when \: n = 3 \\ t_{3} = 3.3 + 4 = 9+ 4 = 13 \\ \\ when \: n = 4 \\ t_{4} = 3.4 + 4 = 12+ 4 = 16 \\ \\ when \: n = 10 \\ t_{10} = 3.10 + 4 = 30+ 4 = 34 \\ \\ \)

Thus the 1st, 2nd, 3rd, 4th and 10th terms are 7, 10, 13, 16 and 34 respectively

Answer:

40 cm²

Step-by-step explanation:

[] We can break this shape up into a rectangle and a triangle.

-> See attached

[] First, we know that the sides of the rectangle will be 5 cm and 7 cm because they give us the sides.

-> Area of a rectangle is A = L * W where L is the length and W is the width

-> 5 cm * 7 cm = 35 cm²

[] Second, we know that the total length of the shape is 9 cm and the rectangle portion is 7 cm. Using subtract, we can find the height of the triangle to solve for the area

-> 9 cm - 7 cm = 2 cm (this is the height of our triangle)

-> The area of a triangle can be found by using \(\frac{base*height}{2}\)

-> \(\frac{2*5}{2} =\frac{10}{2}=5^{2}\)

[] Last, we can add the area of the rectangle and the triangle together to find the total area.

-> 35 cm² + 5 cm² = 40 cm²

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     I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)

- Heather

Answer:

-------------------------------------

We can see AB and AC are perpendicular.

Verify it by comparing slopes:

Since the product of the slopes is - 1, the segments are perpendicular.

Find the length of AB and AC:

Find the area:

Answer: B: 12 square units

Step-by-step explanation:

I took the test and got it right. 100% correct.

Give Brainliest please

Answer: I love how people are posting cod stuff on brainly

Step-by-step explanation: What’s ur fav gun

Answer:

sin theta = 15/17

Step-by-step explanation:

Let theta be A

sin^2 A = 1 - cos^2 A

sin^2 A = 1 - ( 8/17 )^2

sin^2 A = 1 - 64/289

sin^2 A = 289 - 64 /289

sin^2 A = 225 / 289

sin A = root 225/289

sin A = 15/17

so sin theta = 15/17

Answer:

32

Step-by-step explanation:

p=x+y , P=22+10 , P=32

Answer:

0.7704 = 77.04% probability that he is through grading before the 11:00 P.M. TV news begins

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:

\(Z = \frac{X - \mu}{\sigma}\)

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Distribution of n values from a normal distribution:

If we take n values from a normally distributed variable, the mean is \(\mu*n\), and the standard deviation is \(s = \sigma\sqrt{n}\)

There are 46 students in an elementary statistics class. For each student, the mean is of 5 min and a standard deviation of 4 min.

This means that

\(\mu = 46*5 = 230\)

\(s = 4\sqrt{46} = 27.13\)

(a) If grading times are independent and the instructor begins grading at 6:50 P.M. and grades continuously, what is the (approximate) probability that he is through grading before the 11:00 P.M. TV news begins?

This is the probability that he finishes grading in 4 hours and 10 minutes, that is, 4*60 + 10 = 250 minutes, which is the pvalue of Z when X = 250.

\(Z = \frac{X - \mu}{\sigma}\)

In this distribution

\(Z = \frac{X - \mu}{s}\)

\(Z = \frac{250 - 230}{27.13}\)

\(Z = 0.74\)

\(Z = 0.74\) has a pvalue of 0.7704

0.7704 = 77.04% probability that he is through grading before the 11:00 P.M. TV news begins

As a result, the usual professional basketball player makes 125000 times more than the typical American worker.

Mathematicians use the unitary method to tackle proportionality-related issues. Finding the value of one unit of a quantity and then using that value to determine the value of another quantity is what this process entails. The unitary technique, for instance, can be used to calculate how far a car will travel on 5 gallons of gas if it travels 40 miles on 2 gallons. We start by determining the price of one unit of gasoline: 2 gallons of fuel equals 20 miles per gallon, while 1 gallon of gasoline travels 40 miles. The distance the car will drive on 5 gallons of gasoline can then be calculated using this value:

given

The query does not include information on the typical wage of a professional basketball player. Let's say the average wage for a professional basketball player in the NBA is $5x106 per year.

We divide the salary of the basketball player by the salary of the worker to determine how many times higher the typical professional basketball player's salary is than the average American worker's salary:

$5x10^6 / $4x10^4 = $125000 / $1 = 125000

As a result, the usual professional basketball player makes 125000 times more than the typical American worker.

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Given:

The line is perpendicular to the line whose equation is

It passes through the point (6, -5)

A line with a slope (m) is perpendicular with another line with a slope (m*) if:

The slope of the line would thus be:

In point-slope form:

In slope-intercept form:

Answer:

30. i. dftjtuutuldrudtuftuftuftuftjxtuxtul who j t x t j x f h x g xg

Step-by-step explanation:

\(11.6\pi × \dfrac{180°}{\pi} = 2088°\)

Answer:

11.6 z × 180° / z = 2088°

\(11.6\pi \: \: \: \times \: \: \frac{180}{\pi} = 2088\pi \\ \\ \\ \\ i \: hope \: it \: is \: helpfull\)

9514 1404 393

Answer:

  B. (3/2x, 3/2y)

Step-by-step explanation:

It is perhaps easiest to see that B' is 3 grid squares from the origin while B is 2 grid squares from the origin. The scale factor is the ratio of these distances:

  3/2

Dilation about the origin multiplies each coordinate value by the scale factor:

  (x, y) ⇒ (3/2x, 3/2y)

Answer:

12 hours

Step-by-step explanation:

4 / 2

2/2

1

4 = 2²

2² x 3 = 4 x 3 = 12

Answer:

(3,-2)

Step-by-step explanation:

Answer:

Step-by-step explanation:

I'm ASSUMING you want to find n where g(n) = 8

g(n) = a/n

g(4) = 9 = a/4

          a = 36

g(n) = 8 = 36/n

         n = 36/8 = 4.5

Answer:

\((\frac{1}{2}+\frac{\sqrt{3}}{2}i)^5=\frac{1}{2}-\frac{\sqrt{3}}{2}i\)

Step-by-step explanation:

Convert 1/2 + i√3/2 to rectangular form

\(\displaystyle z=a+bi=\frac{1}{2}+\frac{\sqrt{3}}{2}i\\\\r=\sqrt{a^2+b^2}=\sqrt{\biggr(\frac{1}{2}\biggr)^2+\biggr(\frac{\sqrt{3}}{2}\biggr)^2}=\sqrt{\frac{1}{4}+\frac{3}{4}}=\sqrt{1}=1\\\\\theta=\tan^{-1}\biggr(\frac{b}{a}\biggr)=\tan^{-1}\biggr(\frac{\frac{\sqrt{3}}{2}}{\frac{1}{2}}\biggr)=\tan^{-1}(\sqrt{3})=\frac{\pi}{3}\\\\z=\cos\frac{\pi}{3}+i\sin\frac{\pi}{3}\)

Use DeMoivre's Theorem

\(\displaystyle z^n=r^n(\cos(n\theta)+i\sin(n\theta))\\\\z^5=1^5\biggr(\cos\biggr(\frac{5\pi}{3}\biggr)+i\sin\biggr(\frac{5\pi}{3}\biggr)\biggr)\\\\z^5=\frac{1}{2}-\frac{\sqrt{3}}{2}i\)

The rays and lines in the picture are as follows;

rays: BD, AC and AB

lines: AC

A ray is a part of a line that has one endpoint and goes on infinitely in only one direction.

A ray is named using its endpoint first, and then any other point on the ray

A line segment has two endpoints.

Therefore, the rays and lines are as follows:

rays: BD, AC and AB

lines: AC

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When csc(\(\theta\)) = 13/9 and 0 < theta < 90, the exact value of sin(\(\theta\)) is 9/13.

To find the exact value of sin(\(\theta\)) given that csc(\(\theta\)) = 13/9 and 0 < \(\theta\) < 90 degrees, we can use the reciprocal relationship between csc(\(\theta\)) and sin(\(\theta\)).

The reciprocal of csc(\(\theta\)) is sin(\(\theta\)), so sin(\(\theta\)) = 1 / csc(\(\theta\)). Therefore, sin(\(\theta\)) = 1 / (13/9).

To simplify the expression, we can multiply the numerator and denominator of 1 / (13/9) by the reciprocal of 13/9, which is 9/13:

sin(\(\theta\)) = (1 / (13/9)) * (9/13)

Multiplying the fractions, we get:

sin(\(\theta\)) = 9 / 13

Hence, the exact value of sin(\(\theta\)) is 9/13.

Since the value of csc(\(\theta\)) is positive (13/9) and \(\theta\) is in the first quadrant (0 < \(\theta\) < 90), we know that sin(\(\theta\)) is also positive. This confirms that sin(\(\theta\)) = 9/13 is the correct value.

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Answer:

a)

\(4ydy = xdx\)

\(2 {y}^{2} = \frac{1}{2} {x}^{2} + c\)

\( {y}^{2} = \frac{1}{4} {x}^{2} + c \)

\( {y}^{2} - \frac{1}{4} {x}^{2} = c \)

b)

c = 4, so

\( {y}^{2} = \frac{1}{4} {x}^{2} + 4\)

\(y = - \sqrt{ \frac{1}{4} {x}^{2} + 4} \)

\(y = - \frac{ \sqrt{ {x}^{2} + 16} }{2} \)

Integrate by parts with

\(u = f(\phi) \implies du = f'(\phi) \, d\phi = (2\phi - 1) \, d\phi\)

\(dv = d\phi \implies v = \phi\)

to evaluate the integral in the definition of \(f\).

\(\displaystyle \int_0^1 f(\phi) \, d\phi = \phi\,f(\phi) \bigg|_0^1 - \int_0^1 \phi(2\phi-1) \, d\phi = f(1) - \frac16\)

Now if \(\phi=1\), we have

\(f(1) = 1^2 - 1 - \left(f(1) - \dfrac16\right) \implies 2f(1) = \dfrac16 \implies f(1) = \dfrac1{12}\)

and so

\(\displaystyle \frac1{12} = 1^2 - 1 - \int_0^1 f(\phi) \, d\phi \implies \int_0^1 f(\phi) \, d\phi = -\frac1{12}\)

It follows that

\(\displaystyle \int_0^2 f(\phi) \, d\phi = \int_0^2 \left(\phi^2 - \phi + \frac1{12}\right) \, d\phi \\\\ ~~~~~~~~~~~~~~~ = \left(\frac{\phi^3}3 - \frac{\phi^2}2 + \frac\phi{12}\right) \bigg|_0^2 \\\\ ~~~~~~~~~~~~~~~ = \frac{2^3}3 - \frac{2^2}2 + \frac2{12} \\\\ ~~~~~~~~~~~~~~~ = \boxed{\frac56}\)

Answer:

84

Step-by-step explanation:

21x      x=4

plug in numbers for letters

21(4)

multiply

84

Answer: 84

Step-by-step explanation:

The length of the congruent triangles are as follows:

BC = 36

EF = 36

Two triangles are said to be congruent if pairs of their corresponding sides and their corresponding angles are equal.

ΔABC≅ΔDEF

Let's find the length of the given sides as follows:

BC = x + 20

EF = 2x + 4

Therefore,

BC = EF

x + 20 = 2x + 4

x - 2x = 4 - 20

- x = -16

x = 16

Therefore,

BC = x+20 = 16 + 20 = 36

EF = 2x+4 = 2(16) + 4 = 32 + 4 = 36

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Answer:

x = -3

Step-by-step explanation:

The two angles shown are corresponding angles, meaning that they have the same value. Because of this, we can create an equation to solve for the value of x.

2x + 9 = 7x + 24

Remember, those two angles are similar, and that's why we can make the two values equal to each other. First, let's remove 7x from both sides.

2x - 7x + 9 = 7x - 7x + 24

-5x + 9 = 24

Then, we'll remove 9 from both sides.

-5x + 9 - 9 = 24 - 9

-5x = 15

Finally, we'll divide both sides by -5 to isolate x and figure out what it is equivalent to.

-5x/-5 = 15/-5

x = -3

And there it is... the value of x. Hopefully that's helpful! :)

Answer:

A. cos( \(-\frac{\pi}{3}\))

Step-by-step explanation:

Typed the all the expressions into desmos and picked the ones that matched

The expression cos (π/12)cos(5π/12) + sin (π/12)sin(5π/12) is equivalent to expression cos( π/3).

Trigonometric Ratios are ratios of the side of a right angled triangle. These are used to find the missing sides and angles of a right angled triangle.

The trigonometric expression is

⇒cos (π/12)cos(5π/12) + sin (π/12)sin(5π/12)

The trigonometric formula of cos (x-y) =  cosx cosy +sinx siny

Here x = π/12 and y = 5π/12

cos (π/12)cos(5π/12) + sin (π/12)sin(5π/12) = cos ( π/12 - 5π/12)

=cos( -π/3)

= cos( π/3)

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Answer:

x =-48.1

Step-by-step explanation:

-72 + 12 - 2.x = 23 + 13.2

Combine like terms

-60 -2x = 36.2

Add 60 to each side

-2x -60+60 = 36.2+60

-2x = 96.2

divide by -2

-2x/-2 = 96.2/-2

x =-48.1

Answer:

\( = - 48.1\)

Step-by-step explanation:

\( - 72 + 12 - 2x = 23 + 13.2 \\ - 2x = + 72 - 12 + 23 + 13.2 \\ - 2x = 96.2 \\ \frac{ - 2x}{ - 2} = \frac{96.2}{ - 2} \\ x = - 48.1\)

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Using matrices the simultaneous equation is solved to get x = 3 and y = 5

This method required finding determinants in three occasions then dividing

The given equation

\(\left[\begin{array}{cc}3&2&\\1&1\\\end{array}\right] \left[\begin{array}{c}x\\y\\\end{array}\right]= \left[\begin{array}{c}19\\8\\\end{array}\right]\)

the determinant is

\(\left[\begin{array}{cc}3&2&\\1&1\\\end{array}\right]\)

3 * 1 - 2 * 1 = 3 - 2 = 1

Solving for x

determinant while replacing x values

\(\left[\begin{array}{cc}19&2&\\8&1\\\end{array}\right]\)

19 * 1 - 2 * 8 = 19 - 16 = 3

solving for x = 3/1 = 3

Solving for y

determinant while replacing y values

\(\left[\begin{array}{cc}3&19&\\1&8\\\end{array}\right]\)

3 * 8 - 19 * 1 = 24 - 19 = 5

solving for y = 5/1 = 5

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