A rectangular paperboard measuring 21 in long and 16 in wide has a semicircle cut out of it, as shown below.
Find the area of the paperboard that remains. Use the value 3.14 for pi, and do not round your answer. Be sure to include the correct unit in your answer.

The Incenter of triangle ABC is I =  (ax1+bx2+cx3 / a+b+c , ay1+by2+cy3 / a+b+c).

Given:

Let I be the incenter of triangle ABC.

Let A(x1,y1) ,B(x2,y2) and C(x3,y3) are vertices.

Let a,b and c are lengths of the sides AB,BC and AC.

we know that:

Incenter I = (ax1+bx2+cx3 / a+b+c , ay1+by2+cy3 / a+b+c)

we can find a, b and c values using the distance formula between the vertices.

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

BC = b = [tex]\sqrt{(x3-x2)^2 + (y3-y2)^2}[/tex]

AC = c = [tex]\sqrt{(x3-x1)^2 + (y3-y1)^2}[/tex]

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Answer:

8 + [8 + (-1*(-3)-4)]÷(-7) = 7/1 = 7

                    Hope this helped answer your question!

Answer:

7

Step by Step Explanation:

El espacio que ocupa la casa sería 6/15, el espacio que ocupa el huerto sería 4/15 y el espacio restante del terreno sería 5/15.

Para representar en forma de fracciones el área de los diferentes espacios del terreno de Pedro debemos tener en cuenta que el total tiene 15 metros. Adicionalmente, cuando representamos una fracción estamos informando cuántas unidades de un número x de unidades estamos utilizando. Por ejemplo, en este caso del total (15 metros) del terreno que tiene Pedro, él esta utilizando 6 metros para su casa. Esta fracción se representaría así:

6 / 15

Por otra parte, la fracción para representar el área del huerto de Pedro debe seguir los mismos lineamientos que la anterior, es decir en el numerador (número de la parte de arriba) ponemos el número de unidades que utilizamos y en el denominador (número de la parte de abajo) ponemos el número total de unidades disponibles. Entonces la fracción del huerto sería:

4 / 15

Por ultimo, para saber cuántas unidades quedan disponibles del terreno de Pedro, debemos restarle al total de terreno la cantidad de espacio que usamos:

15 - 4 - 6 = 5

De acuerdo con lo anterior, el espacio disponible serían 5 metros, que expresado en fraccionarios sería:

5 / 15

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Answer:

undefined

Step-by-step explanation:

since all the x are zero it’s undefined and when all y is zero it’s 0

Hopes this helps please mark brainliest

The intersection of these lines is the answer to the given system of equations. → (-1, -2)

Given the system of equations,

y = x - 1

y = 3x + 1

Now, equating both the given equations,

x - 1 = 3x + 1

3x - x = -2

2x = -2

x = -1

From, y = x - 1

          y = -1 - 1

          y = -2

The answer to the given system of equations is located at the intersection of these lines.

⇒ (-1, -2)

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The statement "I have anywhere from $5 to $8 in my pocket." has been represented on the number line shown in the image attached below.

In Mathematics, a number line can be defined as a type of graph with a graduated straight line which comprises both positive and negative numbers that are placed at equal intervals along its length.

This ultimately implies that, a number line primarily increases in numerical value towards the right from zero (0) and decreases in numerical value towards the left from zero (0).

Translating the statement, we have the following inequality:

Let the variable x represent the amount of money in pocket.

From $5 to $8 in my pocket = 5 ≤ x ≤ 8.

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The area of the shaded region is calculated as: 6.88 yd²

The area of the shaded region in the diagram = area of rectangle - area of semicircle.

Given the following:

Area of the semicircle = 1/2(πr²) = 1/2 × 3.14 × 4² = 25.12 yd²

Area of the rectangle = length × width = 8 × 4 = 32 yd²

The area of the shaded region = 32 - 25.12 = 6.88 yd²

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The answer to this question is after solving definite integration 0,1,-4,-10

What is Definite integration?

It is just basically Simple Integration with limits. In other words it is completely same as area under curve

Solution:

We will proceed by finding area under curve

Here we have to consider the area above x axis as positive and area under x axis as negative area

In First part +ve area and -ve area cancels each other hence answer is 0

In second part after cancellation only 1 square block above x axis remains whose area is 1  hence answer is 1

remaining 2 parts graph is completely below x axis hene area is negative therefore definite integeration will be negative

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No, the centroid and Circumcentre are not same but it is same in equilateral triangle.

The intersection of a triangle's perpendicular bisectors is called the circumcenter.A triangle's circumcenter is a location that is equally spaced from each of its vertices.The centroid of a triangle is the location where its medians connect.

Triangle's centroid is always within it. The centroid of a triangle is its center of gravity in physical terms. If the triangle is evenly distributed around the plane's surface and you want to balance it by supporting it at only one point, you must do it near the center of gravity.Are the circumcenter and centroid at the same location? In the case of an equilateral triangle, they will both be.

Therefore, the centroid and Circumcentre are not same but it is same in equilateral triangle.

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It is Growing Exponential function because the base is greater than 1 and the exponent has a positive sign.

What is exponential decay function?

A exponential decay is a function that, as the name implies, decays exponentially. So it decays fast at the beginning and slower as the value of the variable increases.

[tex]y=5^x[/tex]

It is a function called "Exponential function". The base determines the growth or decay of the function.

If  base > 1, then the function grows, otherwise if base is between 0 and 1, the function decays.

Here, the  base is positive and it's not 1 or 0.

If we have

[tex]y=5^{-x}[/tex]

this function can be rewritten in this way:

[tex]y=(1/5)^x[/tex]

Here, base between 0 and 1, the function decays

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Answer: 1.41 meters

Step-by-step explanation:

14.1 decimeters to meters
Decimeters are 10 times smaller than meters, so you divide the value by 10 to get meters
14.1/10 = 1.41
1.41 meters

Answer:

Step-by-step explanation:

27.5 percent of what is 13.75

13.75 : 27.5 * 100 =

(13.75 * 100) : 27.5 =

1375 : 27.5 = 50

Answer:11x

Step-by-step explanation:

The length of 1 on AC is 54.6 cm.

Given:

Let x be the length

we know that,

AC dimensions = 54.6 * 175.7 * 85.6 cm

It is the volume = l * b * h

Volume :

Volume is defined as the space occupied within the boundaries of an object in three-dimensional space.

Length :

Length is defined as the measurement or extent of something from end to end.

Breadth :

The breadth of something is the distance between its two sides.

On comparing both

Length l = 54.6 cm

Breadth b = 175.7 cm

Height h = 85.6 cm

Therefore the length of 1 on AC is 54.6 cm.

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Answer: I hope this is helpful mark me brainlist if this apply to you

Step-by-step explanation:

The square meter, also called the meter squared, is the International System of Units (SI) unit of area. The symbol for square meters is m2. Less formally, square meter is sometimes abbreviated as sq m.A metre square is a square with sides one metre in length – it refers to the shape and the side length, not the area. By contrast, a square metre is an area and can be any shape.The basic unit of length is the meter and is denoted as. In geometry, can be used as a variable to denote a line and can be used to name a point. In algebra, denotes the slope of a line in the equation y = m x + c .

The equation that could represent the relationship between [d] and [t] is d = 60t.

The general equation of a straight line is -

[y] = [m]x + [c]

where -

[m] → is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] → is the y - intercept i.e. the point where the graph cuts the [y] axis.

We have a person drives 120 kilometers in 2 hours. The distance traveled is proportional to the time taken.

We can write the equation that could represent the relationship between [d] and [t] with the help of the equation of a straight line.

y = mx + c

for c = 0

y = mx

m = 120/2

m = 60

So -

y = 60t

or

d = 60t

Therefore, the equation that could represent the relationship between [d] and [t] is d = 60t.

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The difference in pressure between the main line and the second floor is 91,100 Pa.

Bernoulli's theorem states that a drop in fluid pressure is connected with an increase in fluid velocity if the fluid flows horizontally so that there is no change in gravitational potential energy.

On the basis of the idea of energy conservation, Bernoulli's principle is explained. According to this law, the total amount of mechanical energy in a fluid travelling along a streamline will be the same at every point along that streamline in a steady flow.

Given ,

The settings provided;

The main line's water speed is 2.0 m/s,

The second floor's water speed is 7.0 m/s,

The water's density is 1.0 x 103 kg/m3.

The following formula can be used to compute the pressure difference between the main line and the second level using Bernoulli's equation:

[tex]p_1+1/2pv2/1+pgh1+ = p2+1/2pv2/2+pgh_2[/tex]

[tex]p1- p2 = 1/2pv2/2 - 1/2pv2/1 + pgh2 - pgh1[/tex]

[tex]p1 - p2 = 1/2p(v2/2 - v 2/1) + pg (h2- h1)[/tex]

p1 - p2 = 1/2(1000)(7² - 2²) + (1000 ×9.8)(5 - (-2))

p1 -  p2  = 91100 pa

Thus, the difference in pressure between the main line and the second floor is 91,100 Pa.

The complete question is : A water line enters a house 2.0 m below ground. A smaller diameter pipe carries water to a faucet 5.0 m above ground, on the second floor. Water flows at 2.0 m/s in the main line and at 7.0 m/s on the second floor. Take the density of water to be 1.0 × 103 kg/m 3 . The difference in pressure between the main line and the second floor is _______.

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Answer:

Step-by-step explanation:

its a

Answer:

m<8=1024

Step-by-step explanation:

Since they are asking for m<8, we do 128*8=1024.

The points of a triangle are known as vertices, and various triangle points are centroid, circumcenter, incenter and orthocenter.

A triangle is a three-sided polygon.

The triangle's three points are known as vertices.

Several triangle-related points:

Thus, the points of a triangle are known as vertices, and various triangle points are centroid, circumcenter, incenter and orthocenter.

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The property that defines the number sentence 6 + 0 = 6 is Additive Identity Property.

Given,

6 + 0 = 6

We have to find the property that defines the number sentence;

Additive Identity Property;

Additive identity property says that if zero is added to any real number, the resultant would be the same real number.

Here,

6 + 0 = 6

In this instance, we have added 0 to a real number (6) and have received back the same real number (6).

That is,

Additive Identity Property is the property that defines the number sentence 6 + 0 = 6

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1.4t - 0.4(t-3.1)=5.8

Combine terms in paratheses

1.4t - 0.4t + 1.24 = 5.8

Combine t's

(1)t + 1.24 = 5.8

Subtract 1.24 over

Answer:

8%

Step-by-step explanation:

1. Subtract:

  55000 - 50600 = 4400

2. Divide:

   4400/55000 = 0.08

The equidistant point of  the triangle is point O , which is shown below.

In the question ,

we have to find the equidistant point in the triangle ,

We know that the equidistant point from the vertices of the triangle is the circumcenter ,

let the circumcenter be point O .

The perpendicular bisectors of the given triangle ABC are AC and BC that intersect at point O .

We have to prove that point O lies on the perpendicular bisector of AB and it is equidistant from A , B and C .

So ,we draw OA ,OB and OC .

we know that any point on perpendicular bisector of a segment is equidistant from endpoints of the segment.

that means , OA = OC and OC = OB .

which means OA = OB .

we also know that any point that is equidistant from end points of a segment lies on its perpendicular bisector.

So, we can say that point O is on the perpendicular bisector of AB .

and

Since OA = OB = OC , the point O is equidistant from A , B and C .

Therefore , the equidistant point of the triangle is the circumcenter (point O) .

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The system of linear equations have variable unique solutions, infinitely many solutions and no solutions.

In algebra, a system of equations comprises two or more equations and seeks common solutions to the equations. "A system of linear equations is a set of equations which are satisfied by the same set of variables."

A system of equations as discussed above is a set of equations that seek a common solution for the variables included.

1.

y = -2x + 3 ...eq(i)

y = 1/2x - 7 ...eq(ii)

The solutions to the linear equations (x,y) are (4, -5)

2.

y = 2x - 7 ...eq(i)

y = 5x + 5 ...eq(ii)

The solutions to the linear equations (x,y) are (-4, -15)

3.

3y = -12x + 6 ...eq(i)

y = -4x + 2 ...eq(ii)

The linear equations (x, y) have infinitely many solutions

4.

y = -2x + 3 ...eq(i)

y = 2x - 1 ...eq(ii)

The linear equations (x,y) have solutions of (1, 1)

5.

y = 5x + 4 ...eq(i)

y = 5x - 2 ...eq(ii)

The linear equations have no solutions

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Answer:

Rate = 72 km per hour
Distance traveled in 2 hours = 144 km

Step-by-step explanation:

The car speed is given as 20 meters per second

There are 3600 seconds in an hour

So in 1 hour the car would travel 20 x 3600 = 72,000 meters. This is equivalent to 72,000 meters per hour

There are 1000 meters in a kilometer

So, in terms of kilometers, the car would travel 72,000/1000 = 72 km i one hour. This is equivalent to a speed of 72 km per hour

In 2 hours the car would travel 72 x 2 = 144 km

Comparing the box-and-whisker plots for both data of each city, we have:

a. City B had more noon temperatures above 76°F

b. Both had the same interquartile range.

c. City B had a larger median noon temperature

d. City A had the largest noon temperature.

The box-and-whisker plot has the following values it displays about a data distribution:

Interquartile range = Q3 - Q1

Analyzing the box-and-whisker plots given above, we have the following to conclude:

a. City B had more noon temperatures above 76°F because about more than 50% of the data are above 76°F.

b. Interquartile range for City A = Q3 - Q1 = 75 - 68 = 7

Interquartile range for City B = Q3 - Q1 = 80 - 73 = 7

Both had the same interquartile range.

c. Median for City A = 70

Median for City B = 78

City B had a larger median noon temperature

d. City A had the largest noon temperature of 85.

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The maximum value of the parabola is represented by y-vertex whose value is 9.

What is a Quadratic Function?

The quadratic function can represent a quadratic equation in the Standard form: ax²+bx+c=0 where: a, b and c are your respective coefficients. In the quadratic function, the coefficient "a" must be different than zero (a≠0) and the degree of the function must be equal to 2.

For solving a quadratic function you should find the discriminant: Δ=b²-4ac . And after that you should apply the discriminant in the formula:[tex]x=\frac{-b\pm\sqrt{\Delta} }{2a}[/tex] .

The question gives a quadratic equation and two points, but you do not know some coefficients. Then, you should find the unknown coefficients and after that, you should find the y-vertex of the parabola ([tex]y_v=\frac{-{\Delta} }{4a}[/tex]).

             y = a(x - 1)² + k  ->  points (2, 6.5) and (-1, -1), thus

            6.5=a(2-1)² + k (1)

            -1=a(-1-1)² + k   (2)

         Simplifying the equations

             6.5=a(1)² + k  ( 1 )

            -1=a(-2)² + k  (2)

            6.5=a+ k      ( 1 )

            -1=4a+ k      (2)

         Multiply equation 1 by -1

            -6.5=-a- k    ( 1 )

            -1=4a+ k      (2)

          Sum equations 1 and 2

           -7.5=3a

              a= -2.5

        If a= -2.5, from equation 1, you have

            -6.5=-a- k    

            -6.5=-(-2.5)- k  

            -6.5=2.5- k

            k=2.5+6.5

            k=9

Then , the parabola equation is y= -2.5 (x-1)² +9. You can rewrite it as:

y=-2.5(x²-2x+1)+9

y= -2.5x²+5x-2.5+9

y= -2.5x²+5x+6.5

[tex]y_v=\frac{-{\Delta} }{4a}=y_v=\frac{-{(b^2-4ac)} }{4a}=\frac{-{(5^2-4*(-2.5)*(6.5))} }{4*(-2.5)}=\frac{-90}{-10} =9[/tex]

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The number of points gained overall by Julia playing the game is 30 point

From the question, we have the following parameters that can be used in our computation:

Tax paid for a new quest = 2.5 points

Total points gained playing the game = 75 points

The above parameters can be represented as

The number of points gained overall = Total points gained playing the game/Tax paid for a new quest

Substitute the known values in the above equation, so, we have the following representation

The number of points gained overall = 75/2.5

Express as a correct fraction

So, we have the following representation

The number of points gained overall = 750/25

Evaluate the quotients

So, we have the following representation

The number of points gained overall = 30

Hence, the number of points gained overall =is30

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Answer: 11.99 + 0.45t ≤ 16 The most toppings you can have is 8

Step-by-step explanation:

11.99 + 0.45 is a basic cheese pizza plus one topping
11.99 + 0.45t represents a pizza plus an undefined amount of toppings
11.99 + 0.45t ≤ 16 The cost of the pizza has to be 16$ or less
Subtract 11.99 from each side
0.45t ≤ 4.01
Divide both sides by 0.45
t ≤ 8.9111
You can't have a partial number of toppings, and 9 is too much, so we round down to 8.