Find the nth term rule for the arithmetic sequence with
a7 = -17 and a25=-71

The measurement of angle ∠2 is 67.50°.

So,

Therefore, ∠2 is 67.50°.

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The correct question is given below:

Given the regular polygon, find the measure of each numbered angle.

m ∠ 2

These are the description of the real numbers.

According to the statement

We have to explain all about the real numbers.

So, For this purpose, we know that the

Positive or negative, large or small, whole numbers, fractions or decimal numbers are all Real Numbers.

From the given information:

Real numbers are composed of the subsequent set of numbers : Whole numbers, natural numbers, integers, rational numbers and irrational numbers.

• Natural numbers include all positive numbers which can be used for ordering or counting. They include numbers from 1, till infinity.

• Whole numbers include all positive integer values including 0.

• Integer numbers are the set of all positive and negative integer values including 0. Examples are : (-1, 0, 8)

• Irrational numbers are non-integer values which can't be expressed within the form a/b. like (√5, 1.7171...)

Using the definitions above :

• 12 = Natural, integer , integer and rational (12/1)

• -15 = Integer, rational (-15/1)

• 1 1/2 = 3/2 = Rational

• 3.18 = rational (terminating decimal)

• root 48 = √48 = 6.928... = irrational(non-terminating and non-repeating)

• 9.3 = rational (terminating decimal)

• -2 7/9 = -25/9 = rational (a/b)

• root 25 = √25 = ±5 = integer, rational (5/1)

• root 3 = √3 = 1.732... real (non-terminating and non-repeating) .

• negative root 64 = - √64 = - 8 = integer, rational (-8/1)

• negative root 12 = - √12 = - 3.464... = irrational (non - terminating)

• 8/4 = 2 = natural, number, rational, integer

So, These are the description of the real numbers.

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The simplified expression for (16-12 / 15-11) is 1 .

The given expression is,

( 16-12 / 15-11 )

First we need to solve the numerator which is (16-12) and on simplifying the numerator we can write,

Numerator = ( 16 - 12 ) = 4                         equation 1

Similarly, now we can proceed to solve the denominator which is (15 - 11) and on simplifying the denominator we write,

Denominator  = (15 - 11) = 4                       equation 2

Now we can substitute the value of numerator and the denominator from equation 1 and equation 2 in the given expression ( 16-12 / 15-11 ) as,

(Numerator / Denominator) = (16-12 / 15-11) = (4/4) = 1

The simplified expression for (16-12 / 15-11) is 1 .

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The most commonly used explicit of an arithmetic sequence is given as,

an = a + (n - 1) d

Each term in the sequence can easily be solved/computed without knowing the other terms in the sequence. Now by using the given information, we can say that,

2nd row seat = 12+ 1x2

3rd row seat = 12 + 2 x2

nth seat = 12 + (n-1) x 2

16th row seat = 12 + (16–1) x2 = 42

Since the number of seats is increasing at a constant rate, we can calculate the average number of seats in each row by taking the average of the first and last rows

Average number of seats per row = (12 +42)/2= 27

So total seats = average per row x number of rows

= 27 x 16 = 432.

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The statement given is true.

If the sum of tine acute angles of a triangle is greater than 90 , then the triangle is acute.

The acute angle can be defined as the angle  less than 90°. Or we can say that the angle which is between 0° and 90° is called as an acute angle of a triangle. In the triangle all the angles gives the sum of 180 degree, that means, at least two angles in every triangle are always acute angles.

According to statement given in the question. This statement is absolutely true. If the sum of two acute angle is greater than 90 then the third angle of that polygon i.e. triangle must be less than 90 which makes the whole triangle a acute . Since, all the angles are now acute angles that means less than 90 thus this made the triangle as a acute triangle.

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Answer:

6561

Step-by-step explanation:

You multiply by 3 each time.

The summation notation for given arithmetic series is ∑21-2n , where n starts from 0.

The given series is 21+19+17+ . . .

On looking at the series we can easily notice that there is an decrease of 2 from one term to the next successive term.

So the formula will be (-2n +/- something).

Our first term is 21 and then decrease of 2, So we can say that the formula will be (21 - 2n) and n starts from 0.

So if n=0, our first term is 21

If n=1, our second term is 19

If n=2, our third term is 17

and so on.

So, we have the expression (21 - 2n).

The summation notation for given arithmetic series is ∑21-2n , where n starts from 0.

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The piecewise function that best models her weekly pay h(t) is given by:

A piecewise-defined function is a function that has different definitions, depending on the input of the function.

For this problem, we have that:

Her weekly pay is calculated differently according to the number of hours worked, divided into two cases as follows:

For up to 40 hours, she receives the standard wage of $12, hence:

h(t) = 12t, 0 ≤  t ≤ 40.

For more than 40 hours, she receives $12 x 40 = $480 plus 1.5 x $12 = $18 per hour worked, hence:

h(t) = 480 + 18t.

Hence the piecewise function that best models her weekly pay h(t) is given by the following definition, from the equations that we found prior in this problem:

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Answer:16

Step-by-step explanation:

since the increase is 2 units for purple counters

8 ÷ 2 = 4

4×4=16

The number of books published by a small publishing company is 3240.

Given that, a small publishing company is planning to publish a new book. The production costs will include one-time fixed costs and variable costs.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

Let the number of books be x.

With one method, the one-time fixed costs will total $44,714, and the variable costs will be $11.50 per book.

That is, 44,714+11.50x

With the other method, the one-time fixed costs will total $17,174, and the variable costs will be $20 per book.

That is, 17,174+20x

Now, the number of books produced will the costs from the two methods be the same.

So, 44,714+11.50x=17,174+20x

⇒ 44,714-17,174=20x-11.50x

⇒ 8.5x = 27540

⇒ x=3,240

Therefore, the number of books published by a small publishing company is 3240.

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Answer:

answer 2

Step-by-step explanation:

3*4=12

Answer:

B.  5^6 x 3^12

Step-by-step explanation:

(5^2 x 3^4)^3 =

5 x 5 x 3 x 3 x 3 x 3 =

25 x 81 =

2025

2025^3 =

8,303,765,625

Option B is correct because,

5^6 x 3^12 =

5 x 5 x 5 x 5 x 5 x 5 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 =

15,625 x 531,441 =

8,303,765,625

Answer:9

Step-by-step explanation:

The diver take her at a distance of 9.2 meters.

A resultant displacement can be used to quantify distance. It involves measuring the coordinate values of the beginning and ending positions. The distance is measured in quantities like meters, centimeters, kilometers, etc.

A diver descends 1.7 meters below the surface of the water while suspended 7.5 meters above it, according to the question.

According to fundamental mathematics, values that are less than zero can be represented as negative values.

She will thus descend (-1.7) meters as she dives below the surface.

The formula may now be expressed as follows: Total Distance = 7.5 - (-1.7) = 9.2 meters.

As a result, the diver descends 9.2 meters below the surface with her.

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Answer:

C polyatomic atoms

Step-by-step explanation:

The slope of the line segment joining the two points given (-6,-3) and (0, -1.5) expressed in fraction form as required in the task content is; m = 1/4.

It follows from the task content that the slope of the line segment joining the two points given (-6,-3) and (0, -1.5) be determined.

On this note, it follows from the slope formula that slope;

m = (y2 - y1)/(x2 - x1)

Therefore, the slope of the line segment joining the two points is;

m = (-1.5 - (-3))/(0 - (-6))

m = 1.5/6

m = 1/4.

Ultimately, the slope of the line segment joining the two points given (-6,-3) and (0, -1.5) expressed in fraction form as required in the task content is; m = 1/4.

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The given inequality can be graphed by solving the inequation first.

What is an inequality?

Inequality is defined as an equation that lacks an equal sign. Inequality is a phrase that defines the relative magnitude of a statement and may be used to compare these two statements.

The given inequality can be solved as

[tex]5y\geq -x-32[/tex]

[tex]for, x=1, 5y\geq -1-32[/tex]

[tex]or, 5y\geq -33[/tex]

[tex]or, y=\frac{33}{5}[/tex]

Solve for two more values of x and then plot the inequality on the graph

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Answer:7

Step-by-step explanation:

3-1= 2

5+2=7

Answer:

They are easier to compare because you don't have to simplify in your head or change denominators to make two fractions comparable.

Step-by-step explanation:

Answer:

A′(2, −2), B′(−3, 3), C′(5, 2)  (2nd choice)

Step-by-step explanation:

Rotating a point 270° clockwise about the origin is the same as rotating the point counterclockwise by 90°

In either case, the coordinates of any point (x, y) become new coordinates (-y, x)

I will summarize the original and rotated points,.

Original          Rotated
Point(x, y)       Point(-y, x)        Remarks
--------------       --------------         -------------                            
A(-2, -2)          A'(2,  -2)            eliminates 1st and 3rd choices
B( 3,  3)           B'(-3,  3)            no luck, both 2nd and 4th choices have this
C(2, -5)           C'( 5, -2)            only the 2nd choice fits all three

Answer: A′(2, −2), B′(−3, 3), C′(5, 2)

The coordinates of triangle A′B′C′ after rotating triangle ABC 270° clockwise are A′(2, −2), B′(−3, 3), and C′(5, 2).

The correct answer is (A).

The coordinates in a graph indicate the location of a point concerning the x-axis and y-axis.

The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.

We have,

To rotate a point (x,y) 270° clockwise about the origin,

We can use the formulas:

x' = y and y' = -x.

So, to rotate triangle ABC 270° clockwise, we need to apply these formulas to each vertex:

A' = (-2, 2) rotated 270° = (2, -2)

B' = (3, 3) rotated 270° = (-3, 3)

C' = (2, -5) rotated 270° = (5, 2)

Therefore,

The coordinates of triangle A′B′C′ after rotating triangle ABC 270° clockwise are A′(2, −2), B′(−3, 3), and C′(5, 2).

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Answer: Large number: 36

Smaller number: 9

Step-by-step explanation:

Answer:

The 3 integers are 6 8 and 10

Step-by-step explanation:

Comment

Start with the median. That's the middle number of an ordered set of numbers.

a 8 b               is what you have so far.

Now the range between a and b is 4 which means that a and b differ by 4.

a + 4 =  b

The mean will solve this quickly. Put a + 4 for b

[(a + 8  + a + 4)]/3 = 8            Combine like terms

(2a + 12)/3 = 8                       Multiply both sides by 3

3 (2a + 12)/3 = 8 *3              

2a+12 = 24                            Subtract 12 from both sides

2a + 12 - 12 = 24-12               Combine

2a = 12

a = 6

but we know that the range between a (which is 6 ) and b is a + 4 = 10

So b must equal 10

The algebraic expression of the piggy bank contained $25 and $1.50 is added each days is 25+1.50x

Given,

The piggy bank contained = $25

The amount added in each day = $1.50

Consider number of days as x

Then the algebraic expression = 25+1.50x

Hence, the algebraic expression of the piggy bank contained $25 and $1.50 is added each days is 25+1.50x

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The volume of a cone that has a diameter of 10 inches and height of 2 inches in terms of pi 50/3pi cubic inches

The formula for calculating the volume of a cone is expressed according to the formula

V = 1/3 pir²h

where

r is the radius of the cone = 10/2 = 5in

h is the height = 2in

Substitute to have;

V = 1/3pi(5)² × 2

V = 50/3pi

Hence the volume of a cone that has a diameter of 10 inches and height of 2 inches in terms of pi 50/3pi cubic inches

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Answer:

8,052

Step-by-step explanation:

(2,014 - 2,012) x (2,014 +2,012)

2 x 4,026

8,052

According to the question, to calculate the probability of an event which states that flip a coin and not landing on head. That means P = {H,T}

Therefore, the probability can be written as:

Probability of getting tail = [tex]\frac{no of favorable events}{total number of outcomes} = \frac{1}{2}[/tex]

Therefore, the probability of a coin in which head is not landing is [tex]\frac{1}{2}[/tex].

What is Probability?

The term probability means the study of the occurrence or the outcomes of the event. It is the measurement of the events that occurred during events. And many uncertain events cannot be measured.

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3/13 is the probability of following event. The card is a face card.

In statistics, what does a probability mean?

Total no.of cards = 52

Let A be the event of taking face card.

No.of face cards = 4×3 = 12

Now n(S)= 52C1 = 52, n(A) = 12C1 = 12

So P(A) = n(A)/n(S) = 12/52 = 3/13

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