The figure shown is composed of a rectangle
and a hexagon. The length of each side of the
hexagon is 2 centimeters. Determine the area
of the shaded region.

The coordinates of midpoint M is (3,-4)

It is given that AB is a line segment whose end points A ( 4,6) and B (2.-14) and M is the midpoint

We need to find out the coordinates of midpoint  M which can be found out using the mid point formula  which is (x1 + x2/2 , y1 +y2/2)

the x coordinate of the midpoint M of line segment AB = 4 + 2/2

                                                                                               = 6/2

                                                                                                = 3

the y coordinate of the midpoint M of line segment AB = 6+ (-14) /2

                                                                                               = -8/2

                                                                                               = -4

Hence the coordinates of the midpoint M of line segment AB is (3,-4)

In geometry, the midpoint is the center point of a line section. it's far equidistant from each endpoints, and it's far the centroid each of the segment and of the endpoints. It bisects the section.

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Based on the annual gross income to John, the FICA amount that is deducted and the salary withheld for 23%, John's monthly take-home pay is $5,537.67

First, find the cost of the per-year health insurance plan that John pays:

= (1 - 60%) x 2,500

= 40% x 2,500

= $1,000

The annual take home pay is:
= 87,600 - 1,000 - (87,600 * 23%)

= 87,600 - 1,000 - 20,148

= $66,452

The monthly take-home pay is:

= 66,452 / 12

= $5,537.67

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The component form of the resultant vector is  X1 = -5 and Y1 = -3

The course of vector rotation is counterclockwise if θ is positive (e.g., 90°) and clockwise if θ is bad (e.g., 90°). Consequently, the clockwise rotation matrix is located as

Let's say we have got a factor (x1, y1). The point also defines the vector (x1, y1).

The vector (x1, y1) has a length of L.

We rotate this vector anticlockwise around the starting place by using β Degree.

The turned-around vector has coordinates (x2, y2)

The turned-around vector also has to have period L.

Theorem

x2=cosβx1−sinβy1

y2=sinβx1+cosβy1

By using the above information, we can say that X1 = -3 and Y1 = 5

So now we have the rotate the vector by 270 Degree

After Rotation New coordinates are X1 = -5 and Y1 = -3

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Answer:

I'm pretty sure the answer is A

Step-by-step explanation:

Hope this helps:).......if not then sorry for wasting your time and may God bless you<3

Answer:   x = 8

The diagram is shown below.

==================================================

Explanation:

Use the SAS triangle area formula to get the following equation.

area = 0.5*side1*side2*sin( angle between those sides)

area = 0.5*AB*AC*sin( angle BAC )

area = 0.5*(x+1)*x*sin(30)

area = 0.5x(x+1)*0.5

area = 0.25x^2+0.25x

Set this equal to the stated area of 18 square cm and solve for x.

0.25x^2+0.25x = 18

4*(0.25x^2+0.25x) = 4*18

x^2+x = 72

x^2+x-72 = 0

(x-8)(x+9) = 0

x-8 = 0 or x+9 = 0

x = 8 or x = -9

Ignore the negative value since we cannot have a negative side length.

The only possible outcome is that x = 8 which leads to x+1 = 8+1 = 9.

The diagram is below.

Answer:

c = (y + bd) / b

Step-by-step explanation:

Use the distributive property to open the parentheses.

b(c - d) = y

bc - bd = y

Move the bd to the other side

bc = y + bd

Move the b to the other side

c = (y + bd) / b

Hope this helped! Have a great day!

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

Hello! Explanation below!

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

Ideally, we should break apart the number for this problem. So, here goes nothing. :)

500 / 8 = 62.5

20 / 8 = 2.5

8 / 8 = 1

Now, add your products.

62.5 + 2.5 + 1 = 66

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

Good luck!

~pinetreee

Answer:

Step-by-step explanation:

ANSWER:  

about 2.085

The dimensions of the rectangular figure is width of 34.5 meters and length of 141 meters.

An equation is an expression that shows the relationship between two or more numbers and variables.

Let x represents the width (in meters) of the figure, and y represents the length (in meters). Hence:

y = 4x + 3

4x - y = -3    (1)

Also:

2x + 2y = 351    (2)

From both equations:

x = 34.5, y = 141

The dimensions of the rectangular figure is width of 34.5 meters and length of 141 meters.

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Using the Laws of Detachment and Syllogism, the conclusions can be described as follows:

1. Invalid.

2. Law of Syllogism.

3. Law of Detachment.

4. Invalid.

For item 1, the events are given as follows:

Neither of the laws are reached in the conclusion, hence we have an invalid conclusion.

For item 2, the transitive property was applied correctly, hence the Law of Syllogism was used.

For item 3, p and p -> q are true, then we concluded that q is true, hence the Law of Detachment was used.

For item 4, we have an invalid conclusion, as we have p -> q and q, but no conclusion can be reached regarding p.

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Answer/Step-by-step explanation:

8x - 6y = 6

-8x -8x

-6y = -8x + 6

÷-6 ÷-6 ÷-6

y = (4/3)x - 1

Point 1: (0, -1)

Point 2: (3, 3)

Point 3: (6, 7)

I hope this helps!

The volume of the shred is 777.6 cubic feet

The volume of a shape is the amount of space inside the shape.

For most regular shapes, the formula of the volume is the product of the base area and the height

The given parameters are

Length = 20.25 ft

Width = 12 ft

Height = 3 1/5 feet

The volume of the shred is calculated using the following volume formula i.e. the volume of a cuboid or rectangular prism

Volume = Length x Width x Height

Substitute the known values in the above equation

So, we have

Volume = 20.25 x 12 x 3 1/5

Evaluate the product in the above equation

So, we have

Volume = 777.6 cubic feet

So, the required volume of the shred is 777.6 cubic feet

Hence, the volume of the shred is 777.6 cubic feet

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After solving the equation ln x-1/2=4, the value of x is equal to  [tex]e^{4.5}[/tex]

To solve linear equations, utilize the steps that are provided below.

Lets take an example of solve z for 7z – (3z – 4) = 12

Here is no multiplication or division, so this will be easy to solve

⇒ 7z – (3z – 4) = 12

⇒ 7z – 3z + 4 = 12

⇒ 4z = 12 – 4

⇒ 4z = 8

⇒ z = 8/4

⇒ z = 2

See, that was so simple, using the mentioned methods, every linear equation can be solved easily.

We have been asked to find x in ln x-1/2=4

⇒ ln x-1/2=4

⇒ ln x = 4 + 1/2

⇒ ln x = 4.5

⇒ x = [tex]e^{4.5}[/tex]

Thus x = [tex]e^{4.5}[/tex], in the equation ln x-1/2=4

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Answer:

[tex] \sf \huge \fbox{{No}}[/tex]

Step-by-step explanation:

Consider an event or an competition is going on. two competetors (let A & B) are racing with each other to win something. Let's see what are the possible events that can occur,

Event 1- Competetor A wins the race against B

Event 2- Competetor B wins the race against B

Event 3- Match draw, either both of them are winner or none of them are winner.

So there are three possible events that can occur & we know that total probability always equals one, let's calculate the probability for each event individually.

The probability of occuring each event is equal, hence,

[tex] \sf Probability \: of \: winning \: p(w)= \frac{1}{3} [/tex]

[tex] \sf Probability \: of \: losing \: p(l)= \frac{1}{3}[/tex]

[tex] \sf Probability \: of \: match \: draw \: p(d)= \frac{1}{3}[/tex]

Now,

the sum of probability of winning & probability of losing,

[tex]p(w) +p(l) = \frac{1}{3} + \frac{1}{3} = \frac{2}{3} ≠1[/tex]

Hence, the result is contradiction to the statement the probability of winning plus the probability of losing always equal 1.

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Answer:

figurative

Step-by-step explanation:

this is because its using something else to paint a picture as to HOW something is, for ex. HOW bright the moon is.

Answer:

[tex]g(x) = f(x + 5) + 2[/tex], or [tex]g(x) = | x + 5| + 2[/tex]

Step-by-step explanation:

To shift f(x) left 5, we should add 5 to x.
That way, each value of the new function takes the value of 5 tiles right in the original function.

So far, we have [tex]g(x) = f(x + 5)[/tex].

We also need to shift it up 2, therefore, we should add 2 to every y value.

Therefore, we have [tex]g(x) = f(x + 5) + 2[/tex].

Based on the triangle midsegment theorem, the length of HI is: 8 units.

Every triangle has three midsegments. A midsegment of a triangle can be described as the segment that intersects two sides of a triangle at their midpoint.

For example, in the diagram given, the midsegments in triangle GHI are segments JL, KL, and JK.

According to the triangle midsegment theorem:

JL = 1/2(HI)

KL = 1/2(HG)

JK = 1/2(GI)

Given that, JL = 4 units, applying the triangle midsegment theorem, we would have:

JL = 1/2(HI)

4 = 1/2(HI)

Multiply both sides by 2

2(4) = 1/2(HI)(2) [multiplication property]

8 = HI

HI = 8 units

In conclusion, based on the triangle midsegment theorem, the length of HI is: 8 units.

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The nearest whole number 83.92 - 47.23=37(rounding off)

Given,

83.92 - 47.23=36.69

The whole number is 0,1,2,3...

Rounding a number refers to the act of simplifying a number such that its value remains near to what it was. The outcome of rounding off a number is less precise but more convenient to utilize. We consider the place value of digits in a number when rounding it.

Let us look at an example to better grasp the notion of rounding. Susan walked 2.05 miles, which she estimated to be around 2 miles.

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Answer:

(-2, 3)

Step-by-step explanation:

When rotating the preimage 90° counterclockwise about the origin (x, y) becomes (-y, x).

x=3 and y=2

So (3, 2) becomes (-2, 3)

The image of the point (-2,3) after a rotation of 90° counterclockwise about the origin will be (3, 2).

A spatial transformation is each mapping of feature space to itself and it maintains some spatial correlation between figures.

The point (-2, 3) is in the second quadrant. After a rotation of 90° counterclockwise about the origin, the point will be in the first quadrant.

After the rotation, the coordinate of the points will get swapped and in the first quadrant, the value of the coordinate will be positive.

The image of the point (-2,3) after a rotation of 90° counterclockwise about the origin will be (3, 2).

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The scale factor from shape B to shape A is 4.

Step 1: To determine the scale factor, we need to know the dimensions of the shape before scaling and its dimensions after scaling. From the given diagram, figure A has a base length of 36 units and another base of length  28 units. Figure B has a base length of 9 units and another base length is 7 units.

Step 2: To find the scale factor, we divide a particular dimension from figure B with the same dimension in figure A.

The base length of figure B /the base length of figure A = 36 / 9 = 4

Similarly, the length of another base of figure B / another base of figure A = 28 / 7 = 4

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The average number of callers in the call centre is 112.5.

Number of callers received by the call centre per minute = 25

Average time each person spends on hold = 1 minute

Average time each caller spends talking = 3.5 minutes

The total amount of time of spending by each caller in the call centre is,

= Time spend on hold + Time spend on talking

= 1 + 3.5

= 4.5 minutes

The total amount of time spent by each caller in the call centre is 4.5 minutes.

The average number of callers in the call centre is,

= Total time spent in the call centre × Number of callers per minute

= 4.5 × 25

= 112.5

Therefore, the average number of callers in the call centre is 112.5.

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The value of real root 4√1/160,000 is 1.5625e-6.

By considering the given value

4√1/160,000

=(6.25e-6)^1/4

=1.5625e-6

The values of x where the function's graph actually crosses the x-axis are known as real roots. Any roots without a I term are real roots. Imaginary roots are x-values that set the function to zero but do not actually cause the graph to cross the x-axis.

If there are no stationary points on the curve, then f has a single real root. If stationary points are found, you could demonstrate using the geometry of the curve that the curve can only intersect the x axis once due to the configuration of the stationary points.

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Answer:

here Multiply

−

4

by

1

.

x

=

6

±

√

36

−

4

⋅

−

27

2

⋅

1

Multiply

−

4

by

−

27

.

x

=

6

±

√

36

+

108

2

⋅

1

Add

36

and

108

.

x

=

6

±

√

144

2

⋅

1

Rewrite

144

as

12

2

.

x

=

6

±

√

12

2

2

⋅

1

Pull terms out from under the radical, assuming positive real numbers.

x

=

6

±

12

2

⋅

1

Multiply

2

by

1

.

x

=

6

±

12

2

Simplify

6

±

12

2

.

x

=

3

±

6

The final answer is the combination of both solutions.

x

=

9

,

−

3

Step-by-step explanation:

The numeric value at x = 12 for the given piecewise function is:

g(12) = 10.

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

To find the numeric value of a function, we replace each instance of the variable in the function by the desired value. For example, to find f(12), we replace each instance of x by 12.

From the piecewise function given in the problem, the definition for x = 12 is given by the following rule:

g(t) = 5t/6.

Hence the numeric value is:

g(12) = 5 x 12/6 = 5 x 2 = 10.

The numeric value at x = 12 for the given piecewise function is:

g(12) = 10.

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Answer:

[tex]162 \pi[/tex]

Step-by-step explanation:

Volume of a cone is
[tex]V = \dfrac{1}{3}\pi r^2h[/tex]

where r = radius, h = height

So

[tex]v = \dfrac{1}{3} \pi \times 9^2 \times 6\\\\= \dfrac{1}{3} \pi \times 81 \times 6\\\\= 162 \pi[/tex]

All of the statements are true.

- They often will have the independent variable on the x-axis and the dependent variable on the y-axis.

- They can be used for density curves.

- They are often used to indicate continuity in the data. (i.e. no gaps)

- They are always straight lines.

A line graph is a type of chart used to show information that changes over time.

We have,

- They often will have the independent variable on the x-axis and the dependent variable on the y-axis.

This statement is true because the independent variable belongs on the x-axis (horizontal line) of the graph and the dependent variable belongs on the y-axis (vertical line).

- They can be used for density curves.

A density curve is a graph that shows probability.

This statement is true.

- They are often used to indicate continuity in the data. (i.e. no gaps)

Line graphs can be used for continuous data on the y-axis since continuous data are measured on a scale with many possible values.

This statement is true.

- They are always straight lines.​

We plot line graphs using several points connected by straight lines.

This statement is true.

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The complete terms and growth factors are as follows

Given data

a. __,5, 25, __625

-1,__,-36, 216,__

c. 10, 5, __, __0.625

d.__ ,__,36,-108,__

e.__,12,18,27,__

The terms of a geometric sequence is gotten by

a * r = T2

a is the first term

r is the growth factor

T2 is the second term

a. __,5, 25, __625

5 * r = 52

r = 5

growth factor is 5

the complete terms include

1, 5, 25, 125, 625

b. -1,__,-36, 216,__

-36 * r = 216

r = 216 / -36 = -6

r = -6

growth factor is -6

the complete terms include

-1, 6, -36, 216, -1296

c. 10, 5, __, __0.625

10 * r = 5

r = 5 / 10 = 0.5

r = 0.5

growth factor is 0.5

the complete terms include

10, 5, 2.5, 1.25, 0.625

d.__ ,__,36,-108,__

36 * r = -108

r = -108 / 36 = -3

r = -3

growth factor is -3

the complete terms include

6, -18, 36,-108, 324

e.__,12,18,27,__

12 * r = 18

r = 18 / 12 = 1.5

r = 1.5

growth factor is 1.5

the complete terms include

8, 12, 18, 27, 40.5

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