The point 0 is the center of a regular octagon ABCDEFGH. The point X is the mid-point of the side AB.

The inequality graphed on the given image is the one in option B, the inequality is:

x > -2.

On the graph, we can see an inequality. We can see a vertical line and all the region to the right of that line is shaded.

The vertical line is x = -2

If the right side of that is shaded, then all the points (x, y) with a value of x larger than -2 are solutions, then the inequality is just:

x > -2

Then the correct option is B.

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The birthday polynomial with 10-12-2247 is given as follows:

f(x) = x^7 - x^5 - 2x^4 + 2x³ + 2x² - 4x + 7.

A birthday polynomial is created attributing each digit of the birthday as a coefficient of the polynomial.

The birthday in this problem is given as follows:

10-12-2247.

Thus the coefficients of each term of the polynomial, in order, are given as follows:

There are eight coefficients, hence the polynomial is of the seventh degree.

The signs of each coefficient is not important, they can be chosen at random, and thus the birthday polynomial for the date of 10-12-2247 can be defined as follows:

f(x) = x^7 - x^5 - 2x^4 + 2x³ + 2x² - 4x + 7.

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The equation of the line that passes through the points (2, 1 ) and (4,5) in the Cartesian coordinate plane is y = (2/3)(x - 4) + 5.

By subtracting the y coordinates [5 - 1] = 4, we get

Subtract the x coordinates in the same order  [4 - (-2)]  = [4 + 2] = 6

The slope is given by  y-coordinate/x-coordinate = 4/6  = 2/3.

Now, just choose one point say (4,5), and substitute the coordinates in this formula-

y - [y-coordinate of our point] - (slope)* [ x - ( the  x-coordinate of our point)]

y - 5  = (2/3)(x - 4)      ...........(adding 5 to both sides)

y = (2/3)(x - 4) + 5    

Hence, the equation of the line in the "slope-intercept" form is y = (2/3)(x - 4) + 5.

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The complete question is -

what is the equation of the line that passes through the points (-2,1) and (4,5) in the cartesian coordinate plane?

The end behavior for this polynomial function is like;

f(x)--> +∞, as x--> −∞

f(x)--> +∞, as x--?>+∞

Given,

The polynomial function; y = 7x12 – 3x8 – 9x4

We have to find the nd behavior of the graph of the polynomial function;

End behavior of polynomial function;

The behavior of the function graph at the "ends" of the x-axis is known as the end behavior of a function, or f. In other words, if we look at the right end of the x-axis (as x approaches +) and the left end of the x-axis (as x approaches ), the end behavior of a function represents the trend of the graph.

Here,

We examine the polynomial's degree and the sign of the coefficient of the variable with the highest exponent to determine the graph's final behavior.

That is,

The end behavior for this polynomial function is like;

f(x)--> +∞, as x--> −∞

f(x)--> +∞, as x--?>+∞

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Answer:

The slope of the line is 1

Step-by-step explanation:

gradient = difference of y-coordinates / difference of x-coordinates

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

gradient = 50-30 / 5-(-15)

gradient = 20/20

gradient = 1

Answer:

1,728 small cubes are needed to completely fill a larger cube with side lengths of 30 cm.

Step-by-step explanation:

Answer: B

Step-by-step explanation:

Answer:

[tex]\boxed{\boxed{\tt x=\frac{1}{5}}\: \bf Or\:\boxed{\tt x=0.2}}[/tex]

Step-by-step explanation:

[tex]\tt 50x=10[/tex]

Divide both sides by 50:-

[tex]\tt \cfrac{50x}{50}=\cfrac{10}{50}[/tex]

Simplify:-

[tex]\tt x=\cfrac{1}{5}[/tex]

_____________________

Hope this helps!

Have a great day!

Diameter is 25.46 feet as circumference is 2πr and 2r is d so we just simply divide the circumference with π and get the value as 25.46

Step-by-step explanation:

Answer:

26.727feet

Step-by-step explanation:

Circumference = 22 x diameter

7

7x 84= 22d

d= 588

22

= 26.727feet

With one third of a serving remaining, there are 17 servings are there in a box that holds 13 cups.

Given that:

Each cup holds a bit more than 1 serving, so we know there are at least 13 servings in a box.

We need to know how many servings of 3/4 cup can be obtained from 13 cups.

now we need to divide 13 by 3/4

=13 ÷ 3/4  

= 13 × 4/3

= 52/3

= 17[tex]\frac{1}{3}[/tex]

With one third of a serving remaining, there are 17 servings total.

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Answer:

26,705

Step-by-step explanation:

First find 9% of 24500

24500 x 0.09 = 2205

Second add 2205 + 24500

2205 + 24500 = 26,705

the area of the triangle is 7.5

By using tangent chord angle formula, the measure of angle FGH is 50°.

What is tangent chord angle?
The angle formed by the chord in the alternate segment is equal to the angle formed by the tangent through the point of contact of the tangent for any circle, according to the theorem.

Another name for the tangent-chord theorem is the alternate segment theorem.
We have to find the m ∠FGH.
Since, by tangent - chord angle theorem, the measure of a tangent-chord angle is twice the measure of the intercepted arc inside the angle.
GH = 2(m ∠FGH)⇒ m ∠FGH = 1/2(GH)
Here GH = 100° ⇒ m ∠FGH = 1/2(100°) m ∠FGH = 50°
Hence, by using tangent chord angle formula, the measure of angle FGH is 50°.

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The equation used to represent the distance between two points A and B is AB  =  x Cos 28°

The equation can be defined as a mathematical statement made up of expressions. The length of the line that connects two points is known as the distance between the two points. A triangle is a closed shape with 3 sides, 3 angles and 3 vertices. Triangle is a 2- dimensional figure.

As per the given question,

Let the hypotenuse be x

The two points A and B are on the base of the triangle so,

Base - length = AB

The distance between the two points is

⇒   cos Θ   =   base / hypotenuse

where,      base = AB

                hypotenuse = x

⇒   cos Θ   =   AB / x

⇒   AB   =   x cos Θ      →   1

Substitute Θ  =  28 in 1,

⇒   AB = x cos 28°

Therefore, AB = x cos 28° is the equation used to represent the distance between two points A and B.

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The complete question is

When θ = 28° , which equation can be used to find the distance from point a to point b?

Yes , Dilation do changes the position

Dilation is the process of changing the size or shape of an object. With the aid of the specified scale factor, it is a transformation that makes the objects smaller or larger.

The pre-image is the original figure before dilation, while the new figure is referred to as the image.

Dilation can be of two types:

Dilation does not change the shape of the object from preimage to image only size and position are changed.

The shape can be a point, a line segment, a polygon, etc. It should be noted that the shape can be enlarged or shrunk but the proportion of each dimension of the shape and the angles remain the same.

Hence , It is true that dilation changes the position

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Step-by-step explanation:

convert, Keep Change Flip, convert back

[tex]\frac{23}{4} * \frac{2}{7}[/tex]

[tex]\frac{46}{28} \\[/tex]

[tex]1\frac{18}{28}[/tex]

Answer:

325.6g

Step-by-step explanation:

weight of phone + weight of case

= 310 + 15.6

= 325.6g

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Answer: A C and D

Step-by-step explanation:

The coordinate of the circumcenter of a triangle is (1,3).

Here we have to find the coordinates of the circumcenter of a triangle.

Given data:

The vertices of the triangle are:

A = (0,1)

B = ( 2,1)

C= ( 2,5)

The formula to find the distance between the two points:

Distance = [tex]\sqrt{(x2 - x1)^{2} + (y2-y1)^{2} }[/tex]

In the same manner distance between AB, BC, and AC are:

AB = [tex]\sqrt{(2-0)^{2} + (1-1)^{2} }[/tex]

    = 2

BC = [tex]\sqrt{(2-2)^{2} + (5-1)^{2} }[/tex]

      = 4

AC = [tex]\sqrt{(2-0)^{2} + (5-1)^{2} }[/tex]

     = 2√5

So by the Pythagoras, we get to know that the triangle is a right-angle triangle.

The circumcenter of a right-angle triangle is the midpoint of the hypotenuse.

Midpoint of AC = (0+2)/2 , (1+5)/2

                         = 2/2, 6/2

                         = 1,3

Therefore the coordinate of the circumcenter is (1,3).

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Answer: the answer is  -1

Answer:

Figure 1 (The Star)

Step-by-step explanation:

Line symmetry is symmetry created by a line that divides a shape. Only the "star" (Figure 1) and the "A" (Figure 2) can be split through the center into two identical halves, therefore we can rule out Figures 3 & 4. Rotational symmetry is when a shape looks the same after a partial turn. Rotational symmetry is only true for the "star" (Figure 1) which will be symmetric every 72-degree (360/5) turn. However, the "A" (Figure 2) can only be flipped 180 degrees to remain symmetric.

Therefore Figure 1 is the only figure with both rotational and line symmetry.

Answer:

they are equivalent when m = 1

Step-by-step explanation:

-5(3m-7) = -15+35

-5(3m-7) = 20

-15m+35 = 20

-15m+35 = 20

-15m = -15

m = 1

To dilate a rectangle means to either expand or contract the size of rectangle without changing it's shape .

Dilation is where the polygon grows or shrinks but keeps the same overall shape.

To dilate a rectangle means to either expanding or contracting the rectangle without changing it's shape .

For example: Assume that, the origin (0, 0) be the center of dilation in the coordinate plane.

Let ABCD be a Rectangle in the coordinate plane. The points in the coordinate planes are A(-2, 2), B(3, 2), C(3, -2), D(-2, -2)

To dilate this rectangle by factor 3 , then every coordinate point of the original triangle will multiplied by the scale factor

Coordinates of new rectangles : A'(-4,4) , B'( 6, 4) ,C(6, -4) and D'(-4,  -4)

Therefore, When we dilate a rectangle by scale factor 2 ,

The rectangle has enlarge it's size .

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Answer:

101.25

Step-by-step explanation:

To find the number of students, we need to first determine the total amount earned from the students. We can do this by multiplying the number of people by the cost per student: $3/student * 120 people = $<<3*120=360>>360.

Since the total amount earned was $435 and we know that $360 of that came from students, we can find the number of students by subtracting the total earned from students from the total amount earned: $435 total - $360 from students = $75 from adults.

Since the cost per adult was $4, we can divide the total amount earned from adults by the cost per adult to find the number of adults: $75 / $4/adult = <<75/4=18.75>>18.75 adults.

Since there were 120 people in total and 18.75 of them were adults, there must have been 120 people - 18.75 people = <<120-18.75=101.25>>101.25 students

The number of hours taken by Meredith to edit a textbook if she works alone is 20 hours and time taken by Phil alone to edit text book is 60 hours..

Given that, Phil and Meredith work for a book publisher editing mathematics textbooks.

The basic concept of Time and Work is similar to that across all Arithmetic topics, i.e. the concept of Proportionality. Efficiency is inversely proportional to the Time taken when the amount of work done is constant.

Let the time taken by Meredith be x.

Phil has less experience and takes three times​ as long as Meredith to edit a textbook.

So, time taken by Phil be 3x.

Now, 1/x +1/3x =1/15

⇒ (3+1)/3x =1/15

⇒ 4/3x =1/15

⇒ 4/x =1/5

⇒ x=20 hours

So, time taken by Phil =3x =60 hours

Therefore, the number of hours are 60 hours.

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The equation of a line with point (0,5) and gradient 3 in the form of y = mx + c is y = 3x + 5.

The point slope form of the equation to be used for finding the equation is -

y - [tex] y_{1}[/tex] = m (x - [tex] x_{1}[/tex] )

As per the mentioned information, m or slope is 3, [tex] y_{1}[/tex] is 5 and [tex] x_{1}[/tex] is 0. Keep the values in point slope form to find the equation.

y - 5 = 3 (x - 0)

Performing multiplication on Right Hand Side

y - 5 = 3x - 0

Shifting 5 to Right Hand Side

y = 3x + 5

Thus, the answer is y = 3x + 5.

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Answer:

Step-by-step explanation:

Upper right graph meets both of the requirement, the line lays on both (0,9) on the y axis and (3,0) on the x axis

volume of ball = 5421.85[tex]cm^{3}[/tex]

A sphere is a set of points in space that are a given distance r from the center.

The volume of a 3 -dimensional solid is the amount of space it occupies.  Volume is measured in cubic units( in3,ft3,cm3,m3 , et cetera).  Be sure that all of the measurements are in the same unit before computing the volume.

The volume V of a sphere is four-thirds times pi times the radius cubed.

V=4/3πr^3

The volume of a hemisphere is one-half the volume of the related sphere.

Given that

diameter of ball = 21.8 cm

now we need to find the volume of ball

volume of the sphere =[tex]\frac{4}{3}[/tex] [tex]\pi[/tex][tex]r^{3}[/tex]

diameter = 21.8cm

radius = diameter/2

         = 21.8/2

          =10.9

now substitute the value of radius in the volume formula

volume of ball =[tex]\frac{4}{3}[/tex][tex]\pi[/tex][tex](10.9)^{3}[/tex]

volume of ball = 5421.85[tex]cm^{3}[/tex]

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