The diagram below shows a rectangle inside of a regular hexagon. the apothem of the hexagon is 17.32 units. to the nearest square unit, what is the area of the shaded region?

Given:

[tex]a_1=-4[/tex] and [tex]a_n=a_{n-1}+9[/tex] where [tex]n\geq 2[/tex].

To find:

The explicit formula for the given recursive formula.

Solution:

We know that recursive formula of an AP is:

[tex]a_n=a_{n-1}+d[/tex]

Where, d is the common difference.

We have,

[tex]a_n=a_{n-1}+9[/tex]

Here, d=9.

The first term of the AP is [tex]a_1=-4[/tex].

The explicit formula for an AP is:

[tex]a_n=a_1+(n-1)d[/tex]

Substituting [tex]a_1=-4[/tex] and [tex]d=9[/tex], we get

[tex]a_n=-4+(n-1)9[/tex]

[tex]a_n=-4+9n-9[/tex]

[tex]a_n=-13+9n[/tex]

Therefore, the required explicit formula for the given sequence is [tex]a_n=-13+9n[/tex].

Answer:

sorry if u need help, hope u feel better! :)

Answer:

49

Step-by-step explanation:

x=180-131=49

Given:

A figure of a right angle triangle.

To find:

The value of x to the nearest hundredth.

Solution:

In a right angle triangle,

[tex]\tan \theta=\dfrac{Opposite}{Adjacent}[/tex]

In the given triangle,

[tex]\tan 62^\circ=\dfrac{x}{35}[/tex]

[tex]1.8807=\dfrac{x}{35}[/tex]

[tex]1.88073\times 35=x[/tex]

[tex]65.82555=x[/tex]

Approx the value to the nearest hundredth (two decimal place).

[tex]x\approx 65.83[/tex]

Therefore, the value of x is 65.83 units.

Answer:  son is 12 years old

Step-by-step explanation:

Let m be the age of mother, f be the age of father, and s be the age of son.

m + f + s = 28 x 3 = 84

m + son = 23 x 2 = 46

f + s = 25 x 2 = 50

m = 46 - s

f = 50 - s

we plug in m and f to the functions.

we get 46 - s + 50 - s + s = 84  

96 - s = 84  

-s = -12  

s = 12 years old

Answer:

Hi how are you doing today Jasmine

Answer:

V=lbh=2.4×3×6=43.2cm^3

We are given a candy batband we are given its dimensions

We need to find it's volume

Volume of a cuboid is given by l×b×h

Volume = length × breadth × height

Volume = 2.4 × 3 ×6

The question has missing details. However, general questions that could be asked is as follows:

(1) The number of miles traveled after using (say) 5 gallons

(2) The number of gallons used after traveling for (say) 36 miles

Answer:

See Explanation

Step-by-step explanation:

Given

[tex]s = 120 - 12r[/tex]

A linear equation is represented as:

[tex]y = c + mx[/tex]

Where

[tex]c =y\ intercept[/tex] and

[tex]m = slope.[/tex]

c, in this question represents the initial capacity of the tank.

So, the initial capacity is 120 liters

Solving (a): r = 5

[tex]s = 120 - 12r[/tex]

[tex]s = 120 - 12 * 5[/tex]

[tex]s = 120 - 60[/tex]

[tex]s = 60[/tex]

60 miles traveled

Solving (b): s = 36

[tex]s = 120 - 12r[/tex]

[tex]36 = 120 - 2r[/tex]

Collect like terms

[tex]2r =120 -36[/tex]

[tex]2r =84[/tex]

Solve for r

[tex]r = 42[/tex]

42 gallons used

Answer:

18

Step-by-step explanation:

Answer:

Use substitution to receive: 18

Step-by-step explanation:

6a - 4b when a = 5 and b =  3

6(5) - 4(3)

30 - 12 = 18

Answer:

no

Step-by-step explanation:

The given ratios 3/11 and 17/6 are not proportional.

A ratio is the relation between two numbers as a / b. A proportion is the equality of two ratios as a / b = c / d.

Ratio and proportion can be applied to solve Mathematical problems dealing with unit values of the quantities.

The given ratios are 3/11 and 17/6.

In order to check the proportionality cross multiplication is done as follows,

3/11 and 17/6

Cross multiply the numerators and denominators as follows,

3 × 6 and 17 × 11

=> 18 and 187

Since the cross multiplication of the numerators and denominators are not equal, the given ratios are not proportional.

Hence, the given ratios are not proportional.

To know more about ratio and proportion click on,

brainly.com/question/14279414

#SPJ5

Answer:

our mama

Step-by-step explanation:

Answer:

y=3

Step-by-step explanation:

good luck

Answer:

replace x with number then multiply or divide

Step-by-step explanation:

Answer:

The population size is relatively small In total population sampling, researchers choose to study the entire population because the size of the population that has the particular set of characteristics that we are interest in is typically very small. Therefore, if you failed to include a small number of units (e.g., people) in your research, a significant piece of the puzzle that you are trying to understand may be missing.

x = cos (47) = Pi/3, cos 47 = X/3

Step-by-step explanation:

x = 2.05, 2.05 (2.05)²

Answer:

20% of students picked the vanilla cake.

Step-by-step explanation:

Total number of students: 16 + 64 = 80

Proportion that chose vanilla cake: 16/80 (simplify by dividing by 16) = 1/5 = 0.2 * 100 = 20%

Answer:

10 people didn't answer the servey

Step-by-step explanation:

servey=80 people

70= answered the servey

so we should take the difference:-

80–70= 10

Hope I got the right answer!

Answer:  B, 10.11km

Step-by-step explanation:

If All 6 members swam 1685 meters... you would have 10110 meters in total...

since 1000 meters is one kilometer.., it would be b... 10.11km

Answer:

10 Newtons to the left

Step-by-step explanation:

The overpowering force is the pull that is 30 Newton's left. We subtract this from the smaller force of 20!

[tex]30N-20N=10N[/tex]

Have a Happy April Fool's XD

Answer:

The answer is 48pi

Step-by-step explanation:

Circumference: C=2*pi*radius

The radius of Circle B is 2*12=24

Thus, the circumference of Circle B is: 2*pi*24=48pi

Answer:

Here we don't have the options, so i will answer in a general way.

Every sentence that has the general structure like:

"something is greater than something"

"something is smaller than something"

"Something is no greater than something"

"something is no smaller than something"

There are a lot of other sentences, for example the ones like:

"N is at least equal to M" written as: N ≥ M

"N is at most equal to M" written as: N ≤ M

And there may be other ways to represent inequalities in sentences, but this is the most general way

Then the given sentence:

"One-half + k greater than 18"

This is written as:

1/2 + k > 18

Which is an inequality.

Answer:

ABD

Step-by-step explanation:

took one for the team

Answer:

A

Step-by-step explanation:

sqrt of (x_2 - x_1)^2 + (y_2 - y_1)^2

sqrt of (7 - -5)^2 + (2 - 7)^2

sqrt of (12)^2 + (-5)^2

sqrt of (144 + 25)

sqrt of (169)

13

Answer:

Step-by-step explanation:

A line can be expressed as

y=mx+b, where m=slope and b=y intercept

We are given m=6 and b=-5 so we can just use them in the equation.

y=6x-5

So C is the correct answer.

Answer:

caca

Step-by-step explanation:

caca

Answer:

1) 5x = 25

x = 5

2) y/4 = 7

y = 28

3) n/2 = 19

n = 38

4) 6g = 54

g = 9

5) 8b = 64

b = 8

6) h/6 = 11

h = 66

7) f/4 = 9

f = 36

8) 7s = 49

s = 7

Essay Definition of Citizenship:

In the literal sense a person who lives in a city is said to be a citizen. But in political science we use this terminal different sense. To find the real meaning of the term we are to go back to ancient Greece. Aristotle, the father of political science, called a person a citizen who would take a direct and active part in the administration of the state.

Since the states in ancient Greece were as small as the cities of Greece it was possible for the residents of the city-state to make law, to adjudicate and even enforce the law. These citizens did not include the slaves, women and manual workers. In such a case the number of the citizens was just half of the entire population. The position was not very different in the medieval Europe. There were serfs in the place of the slaves.

The position is quite different in modern nation-states, where all adult people are citizens who need not take an active part in the administration of the country, because it is not possible for the entire population of a vast country to meet together and make law and interpret it or enforce it.

Answer:

(4.5, -0.5)

Step-by-step explanation:

dude just use desmos its so much easier :)

Answer:

Not Perpendicular

Step-by-step explanation:

Answer:

[tex]\huge\boxed{\tt{3}}[/tex]

Step-by-step explanation:

Given the expression:

[tex]\displaystyle \frac{3y+6}{2x}[/tex]

Given that: y = 4 , x = 3

[tex]\displaystyle = \frac{3(4)+6}{2(3)} \\\\= \frac{12+6}{6} \\\\= \frac{18}{6} \\\\= 3\\\\\rule[225]{225}{2}[/tex]

Hope this helped!