The sum of two numbers is thirty one. The first is five less than the second. Find the numbers

The regular polygon with an interior angle of measure 135 is an octagon.

A regular polygon is a polygon that has equal side lengths and equal interior angle measures.

Interior angle of a polygon is the angle inside it that is formed by two adjacent sides. The number of interior angles formed inside a polygon is the same as the number of its sides. Meanwhile, the sum of all the interior angles of any polygon is constant to that polygon and depends on the number of sides.

sum = 180(n - 2)

Let n = number of sides of the polygon = number of interior angles

sum = measure of interior angle x n

Using the formula,

sum = 180(n - 2)

135n = 180(n - 2)

135n = 180n - 360

180n - 135n = 360

45n = 360

n = 8

If the polygon has 8 sides and 8 interior angles, then the regular polygon is an octagon.

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Answer:

Common difference = x - 2.

Step-by-step explanation:

Differences:

-2x - 9 - (-3x - 7)

= -2x - 9 + 3x + 7

= x - 2

-x - 11 - (-2x - 9)

= - x - 11 +2x + 9

= x - 2

So, it is Arithmetic.

Answer:

Arithmetic sequence.

Common difference = -x - 11

Step-by-step explanation:

This is an arithmetic sequence.

-3x - 7, -2x - 9,  -x - 11, ...

Find the common difference.

Common difference =second term - first term.

                                 = -2x - 9 - (-3x - 7)

                                = -2x -  9 + 3x  +7

                                = -2x + 3x - 9 + 7      {Combine like terms}

                                = x - 2

If we add the common difference to the second term, we will get the third term.

Third term = second term + common difference

                  = -2x - 9 + x - 2

                  = -2x + x - 9 - 2

                  = -x - 11.

Hence this is an arithmetic sequence.

The solution of the given equation /x + x/2 = x+ 4/2x for x is i√2.

According to the given question.

We have an equation 1/x + x/2 = x+ 4/2x.

Since, we have to solve th egiven equation 1/x + x/2 = x+ 4/2x, for x.

Therefore, the solution of the given equation 1/x + x/2 = x+ 4/2x for x is given by

1/x + x/2 = x+ 4/2x

⇒ 1/x - 4/2x = x - x/2

⇒ 1/x -2/x  = x - x/2

⇒ (1-2)/x    = (2x -x)/2

⇒ -1/x  = x/2

⇒ -2 = x^2

⇒ x = √(-2)

⇒ x = i√2   (√-1 = i)

Hence, the solution of the given equation /x + x/2 = x+ 4/2x for x is i√2.

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Answer:

$56/7 = 8 She spent $8 on each marker, (that's a lot).

Step-by-step explanation:

Hope it helps

Answer:

So per $8 per marker

Step-by-step explanation:

$56 ÷ 7 =$8

Answer: Lord Farquaad

Step-by-step explanation: E

Answer:

x>18

Step-by-step explanation:

45+0.45x>50.40+0.15x

-0.15 -0.15

45+0.3>50.40

-45 -45

5.4>0.3

X>18

Using algebraic expression and equation, an executive assistant invested $14,000 and $7,000 at the rate of 8% and 5% annual interest, respectively.

An algebraic expression is a number, variable, or the combination of both and operational symbols. On the other hand, an equation is the equality of two expressions separated by "=".

Given that an executive invest a total of $21,000, we can express this as:

x + y = 21,000     ⇒     x = 21,000 - y     (equation 1)

where x = amount invested at 8% annual interest

y = amount invested at 5% annual interest

If the annual return is $1,470, then the sum of the product of the rate and the amount is equal to the annual return.

8%x + 5%y = $1,470

0.08x + 0.05y = 1,470     (equation 2)

Substitute equation 1 to equation 2 and solve for y.

0.08(21,000 - y) + 0.05y = 1,470

1680 - 0.08y + 0.05y = 1470

-0.03y = -210

y = 7000

amount invested at 5% annual interest = $7000

x = 21,000 - y

x = 21,000 - 7000

x = 14,000

amount invested at 8% annual interest = $14000

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Answer: $2

Step-by-step explanation:

p=cost of pens

23-8p=7

23-23-8p=7-23

-8p=-16

p=$2

The side of the square inscribed in a square be a units then the required ratio is π : 2.

A square is inscribed in a circle or a polygon if its four vertices are on the circle's circumference or the polygon's sides.

Inscribed in the circle is a square that fits snugly inside a circle. The square's corners will touch but not intersect the circle's boundary, and the diagonal of the square will equal the diameter of the circle. Furthermore, as with any square's diagonal, it equals the hypotenuse of a 45°-45°-90° triangle.

Let the side of the square inscribed in a square be a units.

Hence, the required ratio is 2 : 1.

Let ABCD be a square inscribed in a circle of radius 'r'.

Now, the diameter of the circle is the diagonal of the square.

Therefore, BD = 2r.

In △BDC, using Pythagoras theorem

[tex]BC^2+CD^2=BD^2[/tex]

⇒ [tex]a^2+a^2=(2r)^2[/tex]

⇒ [tex]2a^2=4r^2[/tex]

⇒ [tex]a^2=2r^2[/tex]

Area of square=[tex]2r^2[/tex]

Area of circle =[tex]$$\pi r^2[/tex]

Required ration = [tex]$\pi r^2:2r^2[/tex] = π : 2

Therefore, the required ration is π : 2.

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Answer:

56.1

Step-by-step explanation:

Answer: A=n(b^2-r)

Step-by-step explanation:

r + A/n = b^2

r-r+A/n = b^2-r

A/n = b^2-r

A*n/n=n(b^2-r)

A=n(b^2-r)

Answer:

X = √2 R , where X is the length of the legs as R is the length of the radius .

Step-by-step explanation:

The opposite sides of two same angled triangle is also same . So in this case we can say two legs are in same length as their opposite angles are same (45°)

Now , suppose the given radius is R (look at the diagram) then total diameter  is 2R ( DIAMETER = 2 × RADIUS )

Now , we will consider the length of the legs are X ( as the are same ).

Now, we will apply Pythagoras theorem ( The squares on the legs of a right triangle is equal to the square on the hypotenuse . )

∵  X² + X² = (2R)²

or , 2X² = 4R²

or, X² = 2R²

We will root both side

X = √2R

So , X is the length of the legs as R is the length of the radius .

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A triangle's centroid is the point through which all of the mass of a triangular plate appears to act.

The centroid of a triangle is the point through which all of the mass of a triangular plate appears to act. Also known as the "center of gravity," "center of mass," or "barycenter." A fascinating fact is that the centroid is the point at which the triangle's medians intersect.

The triangle's centroid is defined as the point of convergence. Three triangle medians intersect at the figure's centroid "G." The center of gravity is another name for a centroid.

The triangle is divided into two equal-area triangles by each median. The centroid is the intersection of the three medians The centroid is the intersection of the three medians. The three medians divide the triangle into six triangles, each with the same area.

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Answer: well they are parallel to each other

Answer:

Step-by-step explanation:

Two lines perpendicular to the same line are ___ to each other.

Two lines perpendicular to the same line are parallel to each other.

ΔJKL has sides that measure 17.07 units.

So,

The formula of perimeter: √(x₂−x₁)²+(y₂−y₁)²

Filling the values in the formula, we obtain:

Then, each side of the triangle will be: 17.07 units

Therefore, ΔJKL has sides that measure 17.07 units.

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The closing price of the stock is 131.82 dollars.

A stock is an equity or share that represents the ownership of a fraction of a issuing corporation.If someone holds a stock more than 50% that person decides or in charge of most of the things in that co-corporation.

According to the given question The value of a stock opens at 130.48 on monday.

Given it change throughout the day as follow: -0.47, +2.89 , +3 .39 , -4. 47.

∴ The closing price of the stock will be

130.40 + ( -0.47 +2.89  +3 .39  -4. 47 )

= 130.48 + 1.34.

= 131.82 dollars.

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Answer:

r = [tex]\sqrt{\frac{3V}{4\pi h} }[/tex]

Step-by-step explanation:

V = [tex]\frac{4}{3}[/tex] πr²h ( multiply both sides by 3 to clear the fraction )

3V = 4πr²h ( isolate r² by dividing both sides by 4πh )

[tex]\frac{3V}{4\pi h}[/tex] = r² ( take square root of both sides )

[tex]\sqrt{\frac{3V}{4\pi h} }[/tex] = r

The coordinates of the midpoint of a segment with the given endpoints will be (-7.5, 3.5).

Let AB be the line segment and C be the mid-point of line segment AB. Let the coordinate of point A (x₁, y₁), the coordinate of point B (x₂, y₂), and the coordinate of the mid-point (x, y).

Then the coordinate of the mid-point of the line segment is given as,

(x, y) = [(x₁ + x₂) / 2, (y₁ + y₂) / 2]

The endpoints are A(-12, 2) and C(-3,5).

Then the coordinates of the midpoint of a segment with the given endpoints will be

(x, y) = [(- 12 - 3) / 2, (2 + 5) / 2]

(x, y) = (-15/2, 7/2)

(x, y) = (-7.5, 3.5)

The coordinates of the midpoint of a segment with the given endpoints will be (-7.5, 3.5).

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According to the question, the given data is as shown below:

A hose with a larger diameter working alone is [tex]9[/tex] hours

A hose with a smaller diameter working alone is [tex]18[/tex] hours

Now, the time taken by the larger hose to fill the pool is [tex]\frac{1}{9}[/tex]

Similarly, the time taken by the smaller hose to fill the pool is [tex]\frac{1}{18}[/tex]

When they are working together, the expression can be written as:

[tex]\frac{1}{9} +\frac{1}{18} =\frac{1}{a}[/tex]

[tex]\frac{1}{a} =\frac{27}{9X18} =\frac{1}{6}[/tex]

The total time taken by the two hoses to fill the swimming pool is [tex]6[/tex] hours.

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Answer:

The rate of the hose with the large diameter is : 1/9

What is the unknown in the problem? : C. The time it takes for the hoses working together to fill the pool

What part of the job does the hose with the large diameter do? : x/9

The second derivative is zero tells us nothing about stability.

What is a solution's equilibrium?

Differential equations can have solutions called equilibrium solutions when the derivative along those solutions equals zero. In other words, at that solution, the slope is a horizontal line.

Consider the following potentials:

U(x) = [tex]x^{4}[/tex]

U(x ) = [tex]x^{6 } - x^{4}[/tex]

U( x ) = [tex]x^{4} + x^{3}[/tex]

All three of these potentials have an equilibrium point at x=0. All three of these potentials are such that the second derivative of U(x) at this equilibrium point is zero.

However, you should convince yourself (perhaps by plotting these potentials) that in the first case the equilibrium is stable, in the second case it is unstable, and in the third case the equilibrium is, as you put it, "stable in one direction but unstable in the other".

The second derivative is zero tells us nothing about stability.

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Answer:

Answers on attached image

Step-by-step explanation:

Answer:

14 1/3

Step-by-step explanation:

You have to divide 86 by 6, which gives you 14 with a remainder of 2. This would result in 14 2/6, or simplified: 14 1/3

Answer:

14 2/6

Step-by-step explanation:

We want to transform 86/6 into a mixed number. We can achieve this by following these steps:

Step 1: Divide the numerator (86) by the denominator (6):

86 / 6 = 14 remainder 2

Step 2: Build your answer using the quotient (14) as the whole number and the remainder (2) as the numerator, keeping the same denominator (6). Thus,

The improper fraction 86/6

is equivalent to 14 2/6

simplest form is 14 1/3

The sequence is in an arithmetic sequence, common difference is 2, next two term is 9 and 11.

The arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant.

Here the sequence is 1, 3, 5, 7....

Here the sequence is in arithmetic sequence, so the common difference(d) is 3-1 = 5-3 = 2

So the common difference is 2

Now we need to find the next two terms, and for this, we have the formula to find the nth term of the sequence,

[tex]a_{n}[/tex] = a + (n-1)d

We have to find the 5th and 6th terms.

[tex]a_{5}[/tex] = 1 + 4×2

   = 1 + 8

   = 9

[tex]a_{6}[/tex] = 1 + 5×2

   = 1 + 10

   = 11

Therefore the sequence is in an arithmetic sequence, the common difference is 2 and the next two terms of the sequence are 9 and 11.

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Just search it up online

Answer:

Asking people at an international airport can be thought of as bias because   there might a lot of people at the airport who are old and who like to travel.

Asking people whether they’d prefer Italy or France could be bias because what if the people are Italian? Then they’d obviously choose Italy. Or maybe they’re French and they’ve lived in France and been to France too many times and they’d rather visit Italy.

If 86% of people asked took a French course, you can assume they want to learn French (obviously) and that they probably want to learn French so they can visit and be able to communicate with others in France.

Step-by-step explanation:

In linear equation, the intersection at coordinate (9, 315).

What in mathematics is a linear equation?

Gym one:

f(x) =80 x + 25

Gym two:

g(x) = 35x (+ 0 [since there was no joining fee])

The first month is easy.

Gym one's cost is just the joining fee plus the one month of membership fee. Or...

105 = 80(1) + 25

Gym two's cost is just that first month's membership fee. Or...

35 = 35(1) + 0

then  second month

[f(x) = 185 = 80(2)+25

g(x) = 70 = 35(2)],

then a tenth month [

f(x) = 825 = 80(10) + 25;

g(x) = 350 = 35(10)]

and  that gym one's cost exceeded the cost of gym two,

back one month and found the answer.

By month nine, both gyms had equalized at $315.

the intersection at coordinate (9, 315).

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The result of the given expression is negative fifth sixth

The interpretation of the statement as a linear function is expressed as;

-1/6(3) - 3(1/3)²

Expand the fraction in parenthesis

-1/6(3) = -1/2

3(1/3)² = 3(1/9) = 1/3

Substitute

-1/6(3) - 3(1/3)²

-1/2 - 1/3

-3-2/6
-5/6

Hence the result of the given expression is negative fifth sixth

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Answer:yes b

Step-by-step explanation:because tou add it