A clock is constructed using a regular polygon with 60 sides. The polygon rotates each minute, making one full revolution each hour. How much has the polygon rotated after 7 minutes?

Answer:

[tex] \boxed{\sf y = 6 \ cm} [/tex]

[tex] \boxed{\sf x = 25 \degree} [/tex]

Step-by-step explanation:

It is given that JKLMN [tex] \sim [/tex] VWXYZ

So, from this we can say that:

JK [tex] \sim [/tex] VW & ∠LMN [tex] \sim [/tex] ∠XYZ

i.e.

(2y - 8) cm = 4 cm & 4x° = 5(x - 5)°

Solving for y:

⇒2y - 8 = 4

Adding 8 to both sides:

⇒2y - 8 + 8 = 4 + 8

-8 + 8 = 0:

⇒2y = 4 + 8

4 + 8 = 12:

⇒2y = 12

Dividing both sides by 2:

⇒[tex] \sf \dfrac{2y}{2} = \dfrac{12}{2} [/tex]

[tex] \sf \dfrac{2}{2} = 1: [/tex]

⇒y = [tex] \sf \dfrac{12}{2} [/tex]

[tex] \sf \dfrac{12}{2} = 6: [/tex]

⇒y = 6 cm

Solving for x:

⇒4x° = 5(x - 5)°

Expanding right hand ride expression:

⇒4x° = 5x° - 25°

Adding 25° to both sides:

⇒4x° + 25° = 5x° - 25° + 25°

25° - 25° = 0°:

⇒4x° + 25° = 5x°

⇒5x° = 4x° + 25°

Substracting 4x° from both sides:

⇒5x° - 4x° = 4x° - 4x° + 25°

4x° - 4x° = 0°:

⇒5x° - 4x° = 25°

5x° - 4x° = x°:

⇒x° = 25°

Answer:

The correct option is;

[tex]The \ domain \ restriction \ x \geq \dfrac{17}{2} \ results \ in \ m^{-1}(x) = \dfrac{17}{2} \pm \sqrt{x + \dfrac{289}{4} }}[/tex]

Step-by-step explanation:

The given information is that m(x) = x² - 17·x

The above equation can be written in the form;

y = x² - 17·x

Therefore;

0 = x² - 17·x - y

From the general solution of a quadratic equation, 0 = a·x² + b·x + c we have;

[tex]x = \dfrac{-b\pm \sqrt{b^{2}-4\cdot a\cdot c}}{2\cdot a}[/tex]

By comparison to the equation,0 = x² - 17·x - y, we have;

a = 1, b = -17, and c = -y

Substituting the values of a, b and c into the formula for the general solution of a quadratic equation, we have;

[tex]x = \dfrac{-(-17)\pm \sqrt{(-17)^{2}-4\times (1) \times (-y)}}{2\times (1)} = \dfrac{17\pm \sqrt{289+4\cdot y}}{2}[/tex]

Which can be simplified as follows;

[tex]x = \dfrac{17\pm \sqrt{289+4\cdot y}}{2}= \dfrac{17}{2} \pm \dfrac{1}{2} \times \sqrt{289+4\cdot y}} = \dfrac{17}{2} \pm \sqrt{\dfrac{289}{4} +\dfrac{4\cdot y}{4} }}[/tex]

And further simplified as follows;

[tex]x = \dfrac{17}{2} \pm \sqrt{\dfrac{289}{4} +y }} = \dfrac{17}{2} \pm \sqrt{y + \dfrac{289}{4} }}[/tex]

Interchanging x and y in the function of the inverse, m⁻¹(x), we have;

[tex]m^{-1}(x) = \dfrac{17}{2} \pm \sqrt{x + \dfrac{289}{4} }}[/tex]

We note that the maximum or minimum point of the function, m(x) = x² - 17·x found by differentiating the function and equating the result to zero, gives;

m'(x) = 2·x - 17 = 0

x = 17/2

Similarly, the second derivative is taken to determine if the given point is a maximum or minimum point as follows;

m''(x) = 2 > 0, therefore, the point is a minimum point on the graph

Therefore, as x increases past the minimum point of 17/2, m⁻¹(x) increases to give;

[tex]The \ domain \ restriction \ x \geq \dfrac{17}{2} \ results \ in \ m^{-1}(x) = \dfrac{17}{2} \pm \sqrt{x + \dfrac{289}{4} }}[/tex] to increase m⁻¹(x) above the minimum.

Answer:

b

Step-by-step explanation:

edge 2021

Answer:

4.322

Step-by-step explanation:

You would round up because of 8.

Hope this helps!! :D

Answer:

4.322

Since 8 is greater than 5, you round upwards.

Answer:

a=8

Step-by-step explanation:

Answer:

6x - 7 = 6(x + 4)

Step-by-step explanation:

The value of the number (n) is -7.

Let a number we want to find be n.

Hence, according to the given condition, the equation will be:

⇒ 6n - 7 = -49

⇒ 6n = -42

Dividing both sides by 6, we get:

⇒ n = -7

Therefore, the number that satisfy the algebraic expression is n = -7.

Learn more about the Algebraic Expressions here: https://brainly.com/question/4348710?referrer=searchResults

#SPJ2

Answer:

43

Step-by-step explanation:

-2+3×15

45-2

43 is the answer

D

you buy lunch and your teacher asks you how much you brought from home then you divide, simple.

Answer:$9,100.09

Step-by-step explanation:

Answer:

266

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

−√57 is -7.54983443 repeating but rounded is -7.5 which is smack dab in the middle of integers (numbers) of -7 and -8.

Answer:

Answer: The scale factor of the triangle is 4

Step-by-step explanation:

Answer: (x^b)^a

Step-by-step explanation:

the inverse of a monomial with an exponent raised to another power will give the same product if you flip the exponents.

Here we have a general rule for exponents.

We will find that:

[tex](x^a)^b = x^{a*b}[/tex]

To get this, we can first check it with some values for the exponents.

a = 2

b = 3

[tex](x^2)^3 = (x^2)*(x^2)*(x^2) = (x*x)*(x*x)*(x*x) = x^6 = x^{2*3}[/tex]

Similarly, we can prove it for two general values of a and b:

[tex](x^a)^b = (x^a)*(x^a)*...*(x^a)\\b\ times[/tex]

Now each one of these parentheses has a multiplying by itself a times.

So when we write all the x's, we will see that there are a total of b*a x's

Thus we will have:

[tex](x^a)^b = (x^a)*(x^a)*...*(x^a) = x^{a*b}[/tex]

If you want to learn more, you can read:

https://brainly.com/question/5497425

Answer: (b) 7.8 degrees

Step-by-step explanation: You need to pay attention to the number -8.4. It says the temperature changed by +2.7 degrees an hour for 6 HOURS. Therefore, your equation would be -8.4 + (2.7 * 6).

You have to solve whats in the parenthesis first, so your equation would end up being -8.4 + 16.2 making your answer 7.8 degrees.

Answer:

214°

Step-by-step explanation:

The arc subtending an angle at the centre are equal, that is

arc ED = 90° and

arc DF = 360° - (90 + 146)° = 360° - 236° = 124°

Thus

arc EDF = arc ED + arc DF = 90° + 124° = 214°

Answer:

hi rojithapo

Step-by-step explanation:

my name is Naveen I am indian not China

my look like China boy

Answer:

-1.31

Step-by-step explanation:

14x - 11x - 29x = 34

-26x = 34

x = 34/ -26

x= -1.31

Answer:

no . of items = 10

Position of mean = (n+1)/2

                            = 11/2 = 5.5th item

In the data 5.5 item is the average of 5th and 6th item

median = (x+2+x+4)/2

or 25= (2x+6)/2

or 50 = 2x +6

0r 2x = 44

x =22

Answer:

X=23

Step-by-step explanation:

11,13,15,19,_,_,30,39,46

The middle number is the first dash which is represented by x+2 which is equal to 25

25-2=23 which is x

Dash 2 which is represented by x+4 is equal to 23+4=27

Answer:

6p(3q - 2).

Step-by-step explanation:

The GCF ( Greatest Common Factor) of 18pq and 12p is 6p.

So 18pq-12p = 6p(3q - 2).

Answer:

31

Step-by-step explanation:

Answer:

Step-by-step explanation

Answer:

12

Step-by-step explanation:

9 ÷3 =3 ×4 that is how to do the problem

4/5

subtract 1/5 from 5/5.

Answer:

4/5

Step-by-step explanation:

if he has a 1/5 of winning, the left over chances he has has to be towards losing because we already know his chance of winning, and there is no in between, so the left over is 4/5

Answer:

$297.70

Step-by-step explanation:

First, find her hourly wage:

183.20/8

= 22.9

Then, multiply this by 13:

22.9(13)

= 297.7

So, she will make $297.70 next week

Answer:

297.70

Step-by-step explanation:

Read the pdf named "Brain"

Answer:

Not equivalent

Step-by-step explanation:

Given:

We see that

Comparing:

They have same denominator but different numerator, hence they are different

Answer:  No

Step-by-step explanation:

No there are not since 3 times 7 = 21 and 9 times 3 = 27. The numbers that are used to multiply for the answers,  7 and 9, are not the same so therefore both ratios are not equivalent.

Answer:

x = 19

Step-by-step explanation:

-8 + 22 = 13x - 5 - 12x​

switch sides

13x - 5 - 12x = -8 + 22

group like terms

13x - 12x = -8 + 22 + 5

simplify:

x = 19

Answer:

I believe the answer is x=-2, and y=3.

Step-by-step explanation:

Given: x-y=-5

Fill in: -2-3=-5

Calculate: -5=5

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

Given: x+y=1

Fill in: -2+3=1

Calculate: 1=1

Answer:

x = -2.

y = 3.

Step-by-step explanation:

x-y=-5

x+y=1

From the first equation

x = y - 5

Substitute this in the second equation:

y - 5 + y = 1

2y = 1 + 5 = 6

y = 3.

Substitute this into the second equation:

x + 3 = 1

x = -2.

Answer:

3 times 4 minus a number, plus 7

3(4 - x) + 7