Given the regular decagon (10-sided polygon), which statements are true?


Choose all that apply
A. The polygon has 90° rotational symmetry
B. The polygon has 36° rotational symmetry
C. The polygon has 144° rotational symmetry
D. The polygon has point symmetry

The pair of points on the inverse function g, given that (-3,4) and (5,-2) are on function f, are (4,-3) and (-2,5), obtained by swapping the x and y coordinates of the original points.

To determine which pair of points are on function g, which is the inverse of function f, we swap the x and y coordinates of the given points on function f. The points (-3,4) and (5,-2) are on function f, so the corresponding points on the inverse function g would be (4,-3) and (-2,5), respectively. In the context of functions and their inverses, the dependence of y on x in one function becomes the dependence of x on y in the inverse function. This flipping of coordinates is an essential property of inverse functions and can be visualized by reflecting across the line y = x on a graph.

Let us simplify each Expression Separately :

✿  [tex]\mathsf{(\frac{cot\theta.cos\theta}{sin\theta}).tan\theta}[/tex]

[tex]\mathsf{\implies (\frac{cot\theta.tan\theta.cos\theta}{sin\theta})}[/tex]

[tex]\mathsf{We\;know\;that : tan\theta.cot\theta = 1}[/tex]

[tex]\mathsf{\implies (\frac{cos\theta}{sin\theta})}[/tex]

[tex]\mathsf{We\;know\;that : cot\theta = \frac{cos\theta}{sin\theta} }[/tex]

[tex]\mathsf{\implies (\frac{cot\theta.cos\theta}{sin\theta}).tan\theta = cot\theta }[/tex]

✿  [tex]\mathsf{(\frac{sin\theta}{cos\theta.tan\theta})}[/tex]

[tex]\implies \mathsf{(\frac{\frac{sin\theta}{cos\theta}}{tan\theta})}[/tex]

[tex]\mathsf{We\;know\;that : tan\theta = \frac{sin\theta}{cos\theta} }[/tex]

[tex]\implies \mathsf{(\frac{tan\theta}{tan\theta})}[/tex]

[tex]\implies \mathsf{1}[/tex]

[tex]\mathsf{\implies (\frac{sin\theta}{cos\theta.tan\theta}) = 1}[/tex]

[tex]\mathsf{The\;Simplest\;form\;of\;the\;Given\;Expression\;is : cot\theta}[/tex]

The simplifying form of expression by using the trigonometry formula is,

⇒ [tex]\frac{cot (\theta) cos (\theta) }{sin (\theta) } \times tan(\theta) \div \frac{sin (\theta)}{cos(\theta)tan(\theta)}[/tex] = cot θ

The used formula is,

[tex]\frac{sin \theta }{cos \theta } = tan \theta[/tex]

And, [tex]\frac{cos \theta }{sin \theta } = cot \theta[/tex]

Given that,

The expression is,

[tex]\frac{cot (\theta) cos (\theta) }{sin (\theta) } \times tan(\theta) \div \frac{sin (\theta)}{cos(\theta)tan(\theta)}[/tex]

Now, by using the trigonometry formula, simplify the expression as,

⇒ [tex]\frac{cot (\theta) cos (\theta) }{sin (\theta) } \times tan(\theta) \div \frac{sin (\theta)}{cos(\theta)tan(\theta)}[/tex]

Substitute [tex]\frac{sin \theta }{cos \theta } = tan \theta[/tex] And, [tex]\frac{cos \theta }{sin \theta } = cot \theta[/tex],

⇒ [tex]\frac{cot(\theta)}{tan\theta} \times tan\theta \div \frac{tan\theta}{tan\theta}[/tex]

⇒ [tex]cot \theta \div 1[/tex]

Therefore, the solution of expression is,

⇒ cot θ

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Answer:

y = 3x - 18

Step-by-step explanation:

The given line, y = -3x + 9, has slope -3.  Any new line perpendicular to this has slope +3/1, or just 3.

Start with the general slope-intercept form of the equation of a straight line:

y = mx + b.  Now substitute 9 for y, 9 for x and 3 for m:

9 = 3(9) + b.  Then b = -18, and the desired equation is y = 3x - 18.

The equation of the line perpendicular to y = -3x + 9 that passes through the point (9,9) is y = ([tex]\frac{1}{3}[/tex])x + 6.

The question is asking to find the equation of a line in slope-intercept form that is perpendicular to the given line y = -3x + 9 and passes through the point (9,9). To find the equation of a line that is perpendicular to the given line, we need to determine the slope of the new line. The slope of any line perpendicular to a line with a slope of m is [tex]-\frac{1}{m}[/tex]. Since the given line has a slope of -3, the slope of the perpendicular line will be [tex]\frac{1}{3}[/tex]. Now using the point-slope form of a line, which is y - y₁ = m(x - x₁), where (x₁, y₁) is a point on the line and m is the slope, we can write the equation of the new line through the point (9,9) as y - 9 = ([tex]\frac{1}{3}[/tex])(x - 9). Simplifying this equation gives us y = ([tex]\frac{1}{3}[/tex])x + 6, which is in slope-intercept form y = mx + b where m is the slope and b is the y-intercept of the line.

Answer:

a(n) = 130 + (n-1) 13

13th term = 286

Step-by-step explanation:

We are given a sequence of numbers: 130, 143, 156, 169, ... and we are to write an explicit formula to represent the arithmetic sequence and use it to find the 13th term.

We know that the arithmetic sequence can be defined by:

[tex]a_n=d(n-1)+c[/tex]

where [tex]d[/tex] = the common difference between consecutive terms ; and

[tex]c[/tex]=[tex]a_1[/tex]

13th term:

[tex]a_{13}=130+(12)13 = 286[/tex]

Therefore, the formula for this sequence will be a(n) = 130 + (n-1) 13 and 13th term is 286.

Answer:

I THINK THE ANSWER IS D

TELL ME IF I"M WRONG

Step-by-step explanation:

Answer:

144/3=48 ft per sec

Step-by-step explanation:

Answer:

48 per second

Step-by-step explanation:

if you divide 144 by 3 you get 43

[tex]\left\{\begin{array}{ccc}2x+2y=8\\3x+2y=12&\text{change the signs}\end{array}\right\\\underline{+\left\{\begin{array}{ccc}2x+2y=8\\-3x-2y=-12\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad-x=-4\to\boxed{x=4}\\\\\text{Put the value of x to the first equation:}\\\\2(4)+2y=8\\8+2y=8\qquad\text{subtract 8 from both sides}\\2y=0\qquad\text{divide both sides by 2}\\\boxed{y=0}\\\\Answer:\ \boxed{x=4\ and\ y=0\to(4,\ 0)}[/tex]

Answer:

Boys : girls

5:6

Step-by-step explanation:

Boys : girls

20:24

We can divide each  of these numbers by 4

20/4 =5

24/4 =6

Boys : girls

5:6

Answer:

For every 5 boys there are 6 girls

Step-by-step explanation:

because 20 and 24 both go into the same number and thats four.

20 divided by 4 = 5

24 divided by 4= 6

so for every 5 boys there are 6 girls

Answer:

2/3

Step-by-step explanation:

You flip the second fraction and multiply the fractions.

When we divide (1/2) by (3/4) we have 2/3.

A fraction is written in the form of p/q, where q ≠ 0.

Fractions are of two types they are proper fractions in which the numerator is smaller than the denominator and improper fractions where the numerator is greater than the denominator.

Given, The fraction (1/2) is divided by another fraction (3/4).

Now, we know (a/b)/(c/d) = (a/b)×(d/c).

Therefore, (1/2) is divided by (3/4) is,

= (1/2)×(4/3).

= 4/6.

= 2/3.

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Final answer:

A formula to determine Seth's weekly lunch expense is Weekly Spending = n × 5, where n represents the new price of lunch and the multiplication by 5 accounts for each day of the school week.

Explanation:

To help Seth determine how much he'll now spend on lunch every week, we need to create a formula that takes into account the new price of a lunch and the frequency of his purchases. Let's assume the new price of a lunch is represented by the variable n. Since Seth buys lunch 5 days a week, the formula to calculate his weekly spending will be Weekly Spending = n × 5. This formula can be used to multiply the new price of a lunch (n) by 5, giving Seth the total amount he will spend each week on school lunches.

Answer:

Step-by-step explanation:  Pru, Piper, Phoebe their ratio 5:3:4 added = 12

What this would mean is that Pru has 5/12 of the total amount, Piper has 3/12 of the total, and Phoebe has 4/12 of the total amount of spices all together.

pru = piper + 24

5/12x = 3/12x + 24

5/12x - 3/12x = 24

2/12x = 24

x = 24 / (1/6)

x = 24 * 6

x = 144 spices in all.

Pru has : 5/12(144) = 720/12 = 60 spices

Piper has : 3/12(144) = 432/12 = 36 spices

Phoebe has : 4/12(144) = 576/12 = 48 spices <====

Answer:

48 spices

Step-by-step explanation:

The number of spices each has is a multiple of 5, 3, and 4.

The number of spices each has is 5x, 3x, and 4x.

Pru has 5x spices.

Piper has 3x spices.

Pru has 24 more spices than Piper, so

5x = 3x + 24

2x = 24

x = 12

Phoebe has 4x spices, so Phoebe has

4(12) = 48

Answer:

16.5 inches

Step-by-step explanation:

WE have arc length formula for a circle as

Arc length = [tex]\frac{x}{360} (2\pi r)[/tex]

where x is the central angle the arc subtends at the centre.

Here x = 135

r= 7 inches

Hence arc length

=[tex]\frac{135}{360} (2\pi )(7) =16.5"[/tex]

Hence option B

16.5 inches is right answer for arc length for a circle of radius 7 inches.

The measure of length of arc AB is 16.5 inches. Therefore, option B is the correct answer.

An arc of a circle is a section of the circumference of the circle between two radii. A central angle of a circle is an angle between two radii with the vertex at the centre. The central angle of an arc is the central angle subtended by the arc. The measure of an arc is the measure of its central angle.

Given that, the radius of the circle is 7 inches and measure of arc AB is 135°.

Let O be the center of circle.

So, ∠AOB=135°

We know that, arc length of circle is θ/360° ×2πr

= 135°/360° ×2×3.14×7

= 0.375×2×3.14×7

= 16.485

≈ 16.5 inches

Therefore, the approximate length of AB is 16.5 inches.

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Answer:

what he said

Step-by-step explanation:

Answer:

YES

Step-by-step explanation:

First, let's find the total number of seats int he airplane.

14 + 64 + 4 * 108 = 510

The airplane has a total or 510 seats.

Half of the number of seats is 510/2 = 255.

Now let's calculate the number of seats being used and compare with 255.

5/7 * 14 + 5/16 * 64 + 5/9 * 4 * 108 =

= 2 * 5 + 4 * 5 + 12 * 4 * 5

= 10 + 20 + 240

= 270

270 seats are being used.

270 is greater than 255, so more than half of the seats are being used.

Answer: YES

Answer:

the ansnwer is 56

mark as brainlest please!!

Step-by-step explanation:

Answer:

56

Step-by-step explanation:

Add 7, 8 times and you'd get 56

The simple interest after three years is ₹2625 and the total amount is ₹14,375.

To find the simple interest and total amount after three years, we can use the formula:

Simple Interest = Principal × Rate × Time

Total Amount = Principal + Simple Interest

Given that the Principal is ₹11,750 and the Annual Rate of Interest is 7.5%, we can calculate the Simple Interest by substituting these values into the formula:

Simple Interest = ₹11,750 × 0.075 × 3

After calculating, we find that the Simple Interest is ₹2625.

To find the Total Amount, we can use the formula:

Total Amount = Principal + Simple Interest

Substituting the values into the formula, we get:

Total Amount = ₹11,750 + ₹2625

After calculation, the Total Amount is ₹14,375.

The expression 2x²+ 5x - 12 has infinite many solutions

From the question, we have the following parameters that can be used in our computation:

2x²+ 5x - 12

The above is an expression and not an equation

This means that it has infinite many solutions

Hence, the expression 2x²+ 5x - 12 has infinite many solutions

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Answer:

A. W-2 form

Step-by-step explanation:

Answer:

Step-by-step explanation:

Y=cos(x+r/2)

Answer:

[tex]y=cos(x+\pi )[/tex]

Step-by-step explanation:

From the graph, we can see that y = -1 when x  = 0.

So to check whether which of the given options is the equation of the given graph, we will set our calculator to the radian mode and then plug the value of x as 0.

1. y = cos(x + pi/2) = cos(0 + pi/2) = 0

2. y = cos(x+2pi) = cos(0+2pi) = 1

3. y = cos(x+pi/3) = cos(0+pi/3) = 1/2 = 0.5

4. y = cos(x+pi) = cos(0+pi) = -1

Therefore, the equation of this graph is y = cos(x+pi) = cos(0+pi) = -1.

Answer:

see explanation

Step-by-step explanation:

(1)

to calculate the slope m use the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (- 2, - 5) and (x₂, y₂ ) = (18, - 5)

m = [tex]\frac{-5+5}{18+2}[/tex] = [tex]\frac{0}{20}[/tex] = 0

(2)

divide number of miles travelled by number of gallons used

= [tex]\frac{132}{6}[/tex] = 22 miles per gallon

Answer:

Option a is the correct choice.

Step-by-step explanation:

Let n be number of hours studied by Nikki.

We are told that Cindy studied seven more hours than Nikki studied. This means that number of hours studied by Nikki plus 7 hours equals to the number of hours studied by Cindy.    

We can represent this information in an expression as :

[tex]\text{The number of hours studied by Cindy}=n+7[/tex]

We can see from our given choices that expression given in option a represents the number of hours studied by Cindy in terms of hours studied by Nikki.

Therefore, option a is the correct choice.

Answer:

Yes it is proportional.

Step-by-step explanation:

35/1 is the same thing as 70/2, as well as 105/3, because they all simplify to 35/1.

Answer:

k = 25

Step-by-step explanation:

(2x  - sqrt(k) )^2              Expand this as a binomial                          

4x^2 - 4x*sqrt(k) + k      The middle term must be -20x Solve for k so it is

-4xsqrt(k) = - 20x            Divide by -4x

sqrt(k) = -20x/-4x             Do the division

sqrt(k) = 5                         Square both sides

k = 25

Multiply by the inverse of 3/4 which is 4/3. -6 times 4/3 (or 1 1/3) which is -8 because 1/3 of -6 is -2 and -2 plus -6 is -8.

x=-8

Answer:

Multiply by 4/3

Step-by-step explanation:

To solve for x, we need to isolate x.

We can isolate x in one step by multiplying by the reciprocal of 3/4, which is 4/3

3/4x = -6

Multiplying by 4/3

4/3* 3/4 x = -6 * 4/3

x = -8

Hi There!

Answer:

B) 28

Step-by-step explanation:

y = 12 and x = 14 are both proportional.

y = 24 and x = ? are both proportional.

You notice that 24 is twice as much as 12 so we do the same with x.

14 * 2 = 28

They are both proportional when y = 24 and x = 28.

Hope This Helps :)

Answer:

B) 28

Step-by-step explanation:

The equation for direct proportion is

y= kx

If y =12 and x =14

12 = k * 14

Divide each side by 14

12/14 = k

Simplifying

6/7 =k

y =6/7 x

Now if y =24

24 = 6/7 x

Multiply each side by 7/6 to isolate x

24 * 7/6 = 7/6 * 6/7 x

28 =x

The problem where one number is 7 more than another and their squares differ by 217 can be solved by creating a system of equations and simplifying to find the numbers are 12 and 19.

To solve the problem where one number is 7 more than another and the difference between their squares is 217, we can create a system of equations. Let's assume the first number is x and the second number is x+7. The problem then translates to the equation (x+7)² - x² = 217.

Step-by-step solution:

After computing the solution, we find that the two numbers are 12 and 19.

Answer:

Tim read for 42 minutes

Step-by-step explanation:

You have to subtract 6:47 by 6:05 to find how long he read for.

   6:47

-   6:05

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

   0:42

Answer:

Tim read for 42 minutes

Step-by-step explanation:

Since the hours are the same, we only need to subtract the minutes.

47-5 = 42 minutes