A City Park is in the Shape of a triangle where the sides have Lengths 163m, 145m, and 145m.if a fence was built around the perimeter the park, how long would the fence need to be?​

The area of the triangular side of the pyramid is given as follows:

21,852 m².

We consider that the side of the pyramid is triangular, hence we must consider that the area of a triangle is obtained as half the multiplication of the base by the height, that is:

Area = base x height / 2.

Considering b = 233, and dividing by the square root of 2, the coordinates of the endpoints of the base are given as follows:

(164.76, 0, 0) and (0, 164.76, 0).

Hence the length of the base is obtained using the distance between two points as follows:

Base = [tex]\sqrt{164.76^2 + 164.76^2}[/tex]

Base = 233.

The midpoint of the base has the coordinates given as follows:

(82.38, 82.38, 0).

The height is the distance between (0,0,147) and (82.38, 82.38, 0), hence it is given as follows:

Height = [tex]\sqrt{82.38^2 + 82.38^2 + 147^2}[/tex]

Height = 187.57.

Hence the area is of:

Area = 0.5 x 233 x 187.57

Area = 21,852 m².

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Answer:

El banco recibió 128 rollos de monedas de 10 centavos.

Step-by-step explanation:

Para saber cuantos rollos de monedas de 10 centavos recibió el banco, podemos dividir el total de monedas recibido entre el número de monedas por rollo.

(1 024 monedas) / (8 monedas/rollo) = (x rollos)

Donde x es el número de rollos recibido. Para calcular x se divide 1 024 entre 8

x = 1 024 / 8

x = 128

The volume of the rectangular prism is  10a⁵ - 30a⁴ + 10a³. Option A

The formula for determining the volume of a rectangular prism is expressed as;

Volume = l × w × h

Given that the parameters are;

We also have their values as;

Length, l = 5a

Width = 2a

h = (a³- 3a² + a)

Substitute the values, we get;

Volume = (5a . 2a. a³- 3a² + a)

Volume = 10a⁵ - 30a⁴ + 10a³)

Since they have different powers, it is impossible to add the like terms

Hence, the expression is  10a⁵ - 30a⁴ + 10a³

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The value of the expression is (x∧2m-15)Yy∧5n +1). Option B

You should understand that simplification involves making an expression more simpler to understand. Also, the expression is in index form that involves the division law of indices.

the given expression to be simplified is

(x∧3m-8)/x∧m-7) (y∧7n +1)/(y∧2n)

This can be simplifies as follows

(x∧3m-8-(m-7)(y∧7n+1(2n)

Simplify further to have the value

(x∧3n-8-m-7)(y∧7m-2n+1)

This implies that the value is

(∧2m-15)(y2n+1)

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So, on solving the provided question we can say that [tex]24\sqrt{ 75/7}[/tex] and [tex]\sqrt{67/2 }[/tex] these both are are radials from the given expressions

A radical is a symbol for the square root or nth root. Root expressions are those that contain square roots. A number or word that appears there is a radical's radicand. Examples are the radicals 7 and 2y+1. Radicals can also be characterized by the following terms: Equations containing radicals are referred to as radical equations. The expression found inside the square root is known as a "root expression." The digits 2, 372, 2x+7, and 41p serve as illustrations of radical representations.The term "root expression" refers to the expression found inside the square root. Examples of radical representations are the numbers 2, 372, 2x+7, and 41p.

[tex]24\sqrt{ 75/7}[/tex] and [tex]\sqrt{67/2 }[/tex] here,

these both are are radials from the given expressions

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The domain of the area of the given rectangle is; 0 < A < 1

The subject of a formula is defined as the variable that is being worked out. This subject of formula can be easily recognized as the letter that is on its own on one side of the equals sign. For example, in the formula for the area of a rectangle A = bh, the subject of the formula is A.

Now, we are told that the rectangle has perimeter of 8 m.

The formula for the perimeter of a rectangle is;

P = 2(L + W)

We are told that the perimeter is 8 m. Thus;

2(L + W) = 8

L + W = 4

W = 4 - L

Formula for area of a rectangle is;

A = LW

Thus;

A = L(4 - L)

A = 4L - 4L²

At A = 0, we have L = 0 OR 1

The value of A cannot be zero or 1 and as such the domain of A is the;

0 < A < 1

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Answer:

There is no mode for this set of numbers.

Step-by-step explanation:

The mode is the value that appears most frequently in a data set.

54,56,60,62,64,67,76,78

In this set of numbers no value appears more than once.

This means there is no mode for this set of data.

Answer:

The building is 36.62 m long.

Step-by-step explanation:

Answer:

Step-by-step explanation:

This is a quadratic function, which is a function of the form f(x) = ax^2 + bx + c, where a, b and c are constants. The function can be written in general form as f(x) = (x-4) / (x^2 +13x + 36).

To find the roots of the function (i.e. the points at which the function intersects the x-axis), we can use the quadratic formula:

x = [-b +/- sqrt(b^2 - 4ac)] / 2a

In this case, a = 1, b = 13 and c = 36.

Substituting these values into the quadratic formula, we get:

x = [-13 +/- sqrt(169 - 4(1)(36))] / 2

x = [-13 +/- sqrt(97)] / 2

x = [-13 +/- 9.8488578] / 2

x1 = -1.1744289

x2 = 11.1744289

Therefore, the roots of the function are x1 = -1.1744289 and x2 = 11.1744289.

The required, 11 goes into 40 three times with a remainder of 7.

Simplification involves applying rules of arithmetic and algebra to extract undeserved terms, factors, or processes from an expression. The goal is to obtain an expression that is easier to work with, manipulate, or solve. For example, simplifying an algebraic expression might involve combining like terms, factoring, or using the distributive property

11 goes into 40 three times with a remainder of 7.

We can use long division to find the answer:

      3

11 | 40

    33

    ---

     7

Therefore, 11 goes into 40 three times with a remainder of 7.

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Vertex: (4,1/6) Focus: (4,7/12) Directrix: x=2

Step-by-step explanation:

a/b is invalid, when b = 0.

so, F(x) is invalid, if (1 + sin(2x)) = 0.

(1 + sin(2x)) can only be 0, if sin(2x) = -1

sin(angle) = -1

angle = 2x = 270° or 3pi/2

x = 135° or 3pi/4

so,

x <> 135° or 3pi/4

well, more often than not we arrange a polynomial in a descending order per degree of term, now, depends on the operation needed for it, we do or we don't, but more often we do.

the assumption in the material is that there are some missing terms in the desscending order.  Check the picture below.

The equation y = 0.60x. The 0.60 represents the 0.60 feet in each second rise. The table is completed below.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

Every 10 seconds in the escalator step rise is 6 feet.

Let 'y' be the number of feet and 'x' be the number of seconds. Then the equation is given as,

y = 0.60x

Then the table is given as,

Time (x)           Distance escalator rises (feet)

     10                                   6

    20                                  12

    30                                  18

    40                                  24

The 0.60 represents the 0.60 feet in each second rise.

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Answer:

Ryan

Step-by-step explanation:

Let's calculate the probabilities of John and Ryan hitting the target center

Let P(J) and P(R) be the respective probability representations

For John

John hits the center 1 time for every 3 tries(arrows)
Therefore

[tex]P(J) = \dfrac{1}{3}[/tex]

Out of 30 arrows (and therefore 30 attempts)  the expected number of times that John can hit the center is given by

[tex]30\cdot \dfrac{1}{3} = 10\\[/tex]

Since you need to hit the center more than 10 times, John is not expected to win the merit badge

For Ryan

Ryan Hits the center 2 times for every 5 arrows (attempts)

[tex]P(R) = \dfrac{2}{5}[/tex]

With 30 arrows the expected number of times that Ryan hits the target is:
[tex]30\cdot \dfrac{2}{5} = 18\\\\[/tex]

So Ryan is expected to win the Archery Merit Badge.

Important Note

Here you have to be careful of the words you use and interpret the results with some reality checks.

Probabilities after all are based on previous trials and represent only an estimate of guarantees of future events. That's why I have repeatedly used the word expected.

After all, John maybe able to hit the center a 11th time and thus he too will earn a merit badge.

In my opinion a poorly worded question

The correct answer is C. You've got that right.

The people whose scores on the bar chart do not match the data given in the table are Georgia and Eleanor.

In Mathematics, a bar chart (bar graph) simply refers to a type of chart that is used for the graphical representation of a population (data set), especially through the use of rectangular bars and vertical columns.

Based on the given bar chart which represents people's test scores in English and French, we can reasonably infer and logically deduce that table showed that Eleanor scored 12 in her English test while it was recorded as 14 on the bar chart.

Similarly, the table showed that Georgia scored 18 in her English test while it was recorded as 15 on the bar chart.

In conclusion, both Georgia and Eleanor were not correctly recorded on the bar chart.

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Answer:

Step-by-step explanation:

Thandi's statement that 20% of Alaskan totem poles featured in the book have eagles carved in them is not accurate.

A two-way table, also known as a contingency table, is used to organize and display the relationship between two categorical variables. The table shows the frequency or count of observations for each combination of the two variables. In this case, the two variables are the animals carved in the totem poles and the regions where the totem poles are located.

To find the percentage of Alaskan totem poles that have eagles carved in them, we need to divide the number of Alaskan totem poles with eagles by the total number of Alaskan totem poles and multiply by 100. This can be calculated as:

(Number of Alaskan totem poles with eagles / Total number of Alaskan totem poles) * 100

Without the data for the two-way table it's impossible to check if the statement is correct or not. It's important to note that without the data it is also impossible to know the context of the statement and the information provided in the book.

Answer:

=Have Eagles

=50%

Step-by-step explanation:

11x = 99z

x = 9z

3y = 99z

y = 33z

1x + 1y + 1z = 9z + 33z + 1z = 43z

The integers that -3.425 lie between are -3 and -4.

The rational numbers  that -3.425 lie between to the nearest tenth are -3.4 and -3.5.

The rational numbers  that -3.425 lie between to the nearest hundredth are -3.42 and -3.43.

Integers are numbers without decimals and fractions. They are whole numbers. Integers can either be positive, negative or zero. Examples of integers are -5 and 10.

A rational number is a number that can be expressed as a fraction of two integers. Examples of rational numbers are 1/4, -2/3  

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The difference between the functions G(x) and h(x) is 4 units.

The function is defined as a mathematical expression that defines a relationship between one variable and another variable.

The functions are given in the question, as follows:

G(x)=-f(x)+10 and h(x)=-f(x-4)+10

Since the functions, g and h differ

This can be seen by subtracting G(x) from h(x):

h(x) - G(x) = (-f(x-4) + 10) - (-f(x) + 10)

h(x) - G(x) = 4.

This means that for any value of x, the output of h(x) will be 4 units greater than the output of G(x).

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Answer:

C, E and F

Step-by-step explanation:

Answer:

103

Step-by-step explanation:

because its the actual answer

Answer:

There should be 8 of them

- 2 - 3i

- 2 + 3i

2 - 3i

2 + 3i

- 3 - 2i

- 3 + 2i

3 - 2i

3 + 2i

Thanks

absolute value is the real part squared + the complex part squared and the root of the things you get.

|a + ib|

= √(a²+b²)

so the sign doesn't matter

In given fractions 8/9 is 1/36 large than 31/36

Finding the larger and smallest fraction in between two or more fractions is known as comparing fractions.

We need to change fractions with unlike denominators into fractions with similar denominators in order to compare them. For this, we will find the denominators' Least Common Multiple (LCM).    

If the denominators are the same then it is easy to compare the fractions.

Here we have

31/36 and 8/9

To find the largest fraction convert both denominators into the same  

Here LCM(36, 9) = 36  

Now multiply both numerator and denominators of fractions with a number to change the denominators  

=> [tex]\frac{31}{36} \times \frac{1}{1} = \frac{31}{36}[/tex]  

=> [tex]\frac{8}{9} \times \frac{4}{4} = \frac{32}{36}[/tex]  

From the above calculations given fractions are 31/36 and 32/36

Difference = [tex]\frac{32}{36} - \frac{31}{36} = \frac{1}{36}[/tex]  

Therefore,

In given fractions 8/9 is 1/36 large than 31/36

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The value of the expression - 9(18 - 9 + 12) + 12(- 9 + 18 + 18) is 135.

If a system of equations only contains two linear equations with two variables, the system's equation can be graphed, the graph will have two straight lines, and the intersection point(s) of those lines will be the system's solution.

There are only three matching forms of solution for a given system of equations because there are only three different ways that two straight lines in the plane can graph.

Let, The rectangle be x, the triangle by y, and the star be z.

Therefore,The three linear equations are,

x + 3y + z = 57...(i)

12x + 5y = 234...(ii)

8x - 6x + 3x = 60...(iii)

5x = 60.

x = 12.

Putting the value of x in eqn(ii) we have,

12(12) + 5y = 234.

144 + 5y = 234.

5y = 90.

y = 18.

Now, Putting the value of x and y in eqn(i) we have,

12 + 3(18) + z = 57.

12 + 54 + z = 57.

z = - 9.

So, The value of the expression z(y + z + x) + x(z + y + y) is,

= - 9(18 - 9 + 12) + 12(- 9 + 18 + 18).

= - 9(21) + 12(27).

= - 189 + 324.

= 135.

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Answer:

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

The speed limit is 65 mph, the speed of the car is at least 74 mph.

The difference m is the over the speed limit value.

Set an inequality:

Answer:

64 mph

Step-by-step explanation:

46 x 5 = 230

710 - 230 = 480 is the distance that he has left

distance = rate x times

480 = rate x 7.5       (12.5 -5 = 7.5)

480 = r(7.5)  Divide both sides b y 7.5 to find the rate

480/7.5 = [ r(7.5) ]/7.5

64 = r

Answer:

The principal of the bond can be calculated using the formula Principal = Interest / Rate x Time. In this case, the interest is $3,875, the rate is 7.75%, and the time is 25 years. Therefore, the principal of the bond is: Principal = $3,875 / 0.0775 x 25 = $20,000.

Step-by-step explanation:

The principal of the bond can be calculated using the formula Principal = Interest / (Rate x Time), where Interest, Rate and Time are given in the problem statement.

By using this formula, the principal of the bond is $20,000. This is the amount of money that was invested to earn the interest of $3,875 over 25 years with the interest rate of 7.75%.