Find the sum of the given arithmetic series. 24 + 48 + 72 + 96 +...+ 480

Answer:

A

Step-by-step explanation:

Step-by-step explanation:

Exterior angle of a dodecagon (12-sided regular polygon) is supplementary to its interior angle.

Sum of all interior angles of

N

-sided regular polygon equals to

(

N

−

2

)

⋅

180

o

.

Therefore, sum of interior angles of

12

-sided polygon is

(

12

−

2

)

⋅

180

o

=

1800

o

All 12 interior angles of dodecagon are equal, so each is

180-30

150

A supplementary exterior angle, therefore, equals to

180-150

=30

hopeit helps..

Answer

The measure of each exterior angle of a regular dodecagon is 30 degrees.

A regular dodecagon is a 12-sided regular polygon with each side equal.

We are asked to find the measure of each exterior angle of a regular dodecagon.

We know that measure of each angle of n-sided regular polygon can be found using

= 360/n

Upon substituting n = 12 in above formula, we will get:

= 360 / 12

= 30

Therefore, the measure of each exterior angle of a regular dodecagon is 30 degrees.

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Answer:

[tex]x=-2[/tex] ⇒ [tex]y=2[/tex]

[tex]x=-1[/tex] ⇒ [tex]y=-4[/tex]

[tex]x=0[/tex] ⇒ [tex]y=-6[/tex]

[tex]x=1[/tex] ⇒ [tex]y=-4[/tex]

Step-by-step explanation:

Formula: [tex]y=2x^{2} -6[/tex]

To find the value of [tex]y[/tex] add the value of [tex]x[/tex] given:

Now solve for each:-

For:

[tex]x=-2[/tex]

[tex]y=2(-2)^{2} -6[/tex]

[tex]y=2[/tex]

For:

[tex]x=-1[/tex]

[tex]y=2(-1)^{2} -6[/tex]

[tex]y=-4[/tex]

For:

[tex]x=0[/tex]

[tex]y=2(0)^{2} -6[/tex]

[tex]y=-6[/tex]

For:

[tex]x=1[/tex]

[tex]y=2(1)^{2}-6[/tex]

[tex]y=-4[/tex]

hope this helps.....

Answer:

2/11 x + 70/11

Step-by-step explanation:

Given the coordinate (-2, 6), (9,8), the equation in standard form is of the form y = mx+b

m is the slope = 8-6/9-(-2)

m = 2/11

Get the y-intercept

Substitute m = 2/11 and (-2, 6) into the expression y = mx+b

6 = 2/11(-2)+b

6 = -4/11 + b

b = 6 + 4/11

b = (66+4)/11

b = 70/11

Get the required equation

y = 2/11 x + 70/11

Hence the required equation is 2/11 x + 70/11

Answer:

I've attached the Answer

Step-by-step explanation:

here it is

Answer:

[tex](\sqrt{6}+\sqrt{3})(\sqrt{6}-\sqrt{3})=3[/tex]

[tex](\sqrt{5}-\sqrt{2})(\sqrt{2}+\sqrt{5})=3[/tex]

Step-by-step explanation:

We want to simplify the expression:

[tex](\sqrt{6}+\sqrt{3})(\sqrt{6}-\sqrt{3})[/tex]

Notice that this is the difference of two squares pattern. Namely:

[tex]a^2-b^2=(a+b)(a-b)[/tex]

If we let a = √6 and b  =√3, we acquire:

[tex](a+b)(a-b)[/tex]

Expand accordingly:

[tex]=a^2-b^2[/tex]

Back-substitute:

[tex]=(\sqrt{6})^2-(\sqrt{3})^2[/tex]

Simplify:

[tex]=6-3=3[/tex]

For the second expression, we have a similar pattern:

[tex](\sqrt{5}-\sqrt{2})(\sqrt{2}+\sqrt{5})[/tex]

We can first rewrite the expression (commutative property):

[tex]=(\sqrt{5}-\sqrt{2})(\sqrt{5}+\sqrt{2})[/tex]

And if we let a = √5 and b = √2:

[tex]=(a-b)(a+b)[/tex]

Expand accordingly:

[tex]=a^2-b^2[/tex]

Back-substitute and simplify:

[tex]=(\sqrt{5})^2-(\sqrt{2})^2=5-2=3[/tex]

Answer:

c. 165.6 cm²

Step-by-step explanation:

We are given two sides of a triangle and an included angle. To find the area, we would apply the following formula:

Area = ½*b*c*Sin(A)

b = 25 cm

c = 25 cm

A = 32°

Area = ½*25*25*Sin(32)

Area = 165.59977

Area ≈ 165.6 cm² (nearest tenth)

Answer:

See in details.

Step-by-step explanation:

Categorical data don't have any logical order and it can't be translated into a numerical value.

Numerical data are numbers and they represent some order and value.

Answer:

Step-by-step explanation:

[tex] = > 12 \times 2[/tex]

[tex] = 24[/tex]

Answer:Decreasing

Step-by-step explanation:

The line is going down.

The given graph is decreasing. The correct option is A.

Increasing graph: A graph is considered increasing if it moves upwards as you move from left to right along the x-axis. In other words, the y-values increase as the x-values increase. This is often represented by a positive slope, where the line or curve ascends as it extends to the right.

Decreasing graph: A graph is considered decreasing if it moves downwards as you move from left to right along the x-axis. In this case, the y-values decrease as the x-values increase. It is represented by a negative slope, where the line or curve descends as it extends to the right.

Constant graph: A graph is considered constant if it remains flat and does not rise or fall as you move along the x-axis. The y-values do not change with increasing x-values, and this is represented by a horizontal line.

In given figure the line goes to downwards and the vales of y is decreasing  for the increasing values of x.

Hence, the given graph is decreasing. The correct option is A.

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The criteria that is excluded from national benchmark test is Qualitative literacy. That is option C.

National Benchmark Test is an academic assessment test usually written by students that are about entering the university.

The National Benchmark Tests comprise three multiple choice tests, written as:

Qualitative literacy is the ability to understand and interpret qualitative evidence. It is not included in the national benchmark test criteria.

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Answer:

6

Step-by-step explanation:

4+x-3=2x-5

1+x=2×-5

2x-x=6

x=6

Answer:

66 in^2

Step-by-step explanation:

Imagine that the figure is a whole square, where the space between is filled in.

Find the area of the imaginary square (l x w):

9 in. x 9 in. = 81 in^2

Lets make that whole square the original figure it used to be (take away the space we “filled in”)

Lets find the area of the space we filled in:

5 in x 3 in= 15 in^2

Subtract the imaginary square’s area by the area of the space that was originally blank:

81 in^2 - 15 in^2 = 66 in^2

66 in^2 IS YOUR FINAL ANSWER, that is the real area of the composite figure you have.

Hope this helps!

Answer: -1410

Step-by-step explanation:

Let's start by subbing in -4 for x

[tex]-4x^4 - 3x^3 - 29x^2 - 114\\-4(-4)^4-3(-4)^3-29(-4)^2-114[/tex]

Now we can solve

[tex]-4(256)-3(-64)-29(16)-114\\-1024--192-464-114\\-832-464-114\\-1296-114\\-1410[/tex]

Answer:

[tex]-1440[/tex]

Step-by-step explanation:

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

Given:

[tex]-4x^4-3x^3-29x^2-114=[/tex]

[tex]x=-4[/tex]

--------------->>>>

Let's substitute [tex]-4[/tex] for [tex]x[/tex] and solve

[tex]-4(-4)^4-3(-4)^3-29(-4)^2-144=[/tex]

Multiply the exponents

[tex]-4(256)-3(-64)-29(16)-144=[/tex]

Multiply the parenthesis

[tex]-1024+192-464-144=[/tex]

[tex]-832-464-144=[/tex]

[tex]-1296-144=[/tex]

[tex]=-1440[/tex]

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

Hope this helps.

Answer:

Step 3

Step-by-step explanation:

Answer:

3.5

Step-by-step explanation:

Answer:

17150 ft²

Step-by-step explanation:

Given the ratio of sides = a : b , then

ratio of areas = a² : b²

Here ratio of sides = 175 : 40 = 35 : 8 , then

ratio of areas = 35² : 8² = 1225 : 64

let x be the area of AT & T Stadium then by proportion

[tex]\frac{x}{1225}[/tex] = [tex]\frac{896}{64}[/tex] ( cross- multiply )

64x = 896 × 1225 = 1097600 ( divide both sides by 64 )

x = 17150

The AT & T screen has an area of 17150 ft²

Answer:

$625.6

Step-by-step explanation:

Information about a holiday:

7 night holiday

$340 per person

8% discount if you book before 31 March

Number of people Naseem booked the holiday for = 2

Date of booking of the holiday = February 15

Total cost of the holiday per person = cost per person - discount before March 31

= $340 - 8% of $340

= 340 - 8/100 * 340

= 340 - 0.08 * 340

= 340 - 27.2

= $312.8

Total cost of the holiday for 2 persons = 2 × Total cost of the holiday per person

= 2 * $312.8

= $625.6

Answer:

9. a) 180 - (55+90) = a

b) a=35 degrees

10. a) 2w + 3w + 40 = 180

b) w=28

c) 2w=56      3w=84

Step-by-step explanation:

Answer:

the person above is 100% right trust me :)

Step-by-step explanation:

Explanation:

You are basically graphing the three horizontal lines y = 6, y = 4 and y = 2; however, there are restrictions to each line.

That's how we get the staircase pattern as shown in graph A. This is considered a piecewise function since we're graphing pieces of various other functions.

Note the use of open holes vs closed circles for the endpoints. The open holes correspond to parts of the inequality that don't have "or equal to", which means we leave that part out of the graph. In contrast, the closed fill in circles do have "or equal to" associated with them, so we do include those endpoints.

Answer:

A

Step-by-step explanation:

Answer:

Draw 8 boxes with 8 cupcakes in each one of them.

Step-by-step explanation:

34+30=64, and 64/8 also equals 64.

1) 7/12= 0.58, 4/7= 0.57

they are about 1/2

2) 7/12 + 4/7 = 97/84= 1.15 approximately 1

which is 1m from the option

Answer:

11,304.0 cm³

Step-by-step explanation:

the volume = π.r².h

= 3.14 × 20² × 9

= 11,304

Answer:

<B = <K

<C = < L

AC= JL

BC= KL

Step-by-step explanation:

The triangles are equel, meaning the letters will be in the same place on a triangle, hope this helps

A fruitseller bought 50kg of the fruits. He sold 30kg of fruits for the cost price of 35kg of fruits and he sold the remaining quantity for the cost Price of 18kg of fruits. calculate his profit or loss percent in the total transaction.

let the cost price be 50x

→he sells 30kg of fruits on it's CP of 35 kg

→CP of 30kg fruits = 30x

→SP of 35kg fruits = 35x

→remaing fruits are 20kg

→he sells 20kg of fruits on CP of 16kg

→CP of 20kg fruits = 20x

→SP of 20kg fruits = 16x

→total CP is = 50x

→total SP is = (35 + 16) = 51x

→SP > CP (it means profit)

→profit = SP-CP

→ 51-50

→ 1

→ Profit% = gain/CP × 100

→ Profit% = 1/50 × 100

→ 2%

Hence the fruit seller had a profit% of 2%.

Answer:

$2,226.20

Step-by-step explanation:

[tex]a_{5}[/tex] = 500e^5(0.03)

Answer:

B is your answer to this question

Answer:

4th Option isn't a function

Step-by-step explanation:

it is because a domain can't have two images in the co domain set

Hope it helps

Please mark as brainliest

Answer:

"D" (the fourth one....(7,1),(6,2)....

a "function" is a very specific relationship in math...

for a relationship to be "a function" every possible INPUT (x-values) has to map (correspond) to a UNIQUE output value (Y-value)

a line is a function (all x's have unique y values.

A circle is NOT ..... at the center (x-value) there are two y values (one above and one below)

in your problem answer "D" the "x-value" "5" has two different "y-values"

3 and 4

Step-by-step explanation:

Answer:

Fewer than 286

Step-by-step explanation:

Average daily guest = visitors per week / number of days in a week

2000 / 7 = 285.7 = 286 guests

Answer:

x is equal to 12 which represents the situation