Carly is in an air balloon. When Carly is at a height of 21.6 meters (m)
she looks down to notice that the top of a tree is in the center of a large reflection pond in a garden. Upon returning to the ground Carly made a sketch, as shown.




Carly determined that horizontal distance, BD, the air balloon was from the base of the tree
was 30.24m and that the base of the tree was 12.96m from the center of the reflection pond.
What is the height, in meters, of the tree, KD? If necessary, round to the nearest hundredth.

N! also called N factorial is the product of all positive non-integers equal to or less than N or simply is the product of the Nth integer and all integers below it.

N! is represented as 1x2x3x4.......x n which is also equivalent to n x (n-1_x(n-2w)x(n-3)......x1.  Therefore the formula for N factorial is N! = n × (n - 1)!. For whole numbers, the factorial is a product of natural numbers till 1 of the values is equal to or less than whole numbers.

N is also used to represent the set of natural numbers up to infinity. Natural numbers include the values from till infinity, they can be represented like N=[1,2,3,4,5,6........].

Examples of N! are:-

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Answer:

-4 x^3 y^2 thus: # 4

Step-by-step explanation:

Simplify the following:

(24 x^6 y^3)/(-6 x^3 y)

The gcd of 24 and -6 is 6, so (24 x^6 y^3)/(-6 x^3 y) = ((6×4) x^6 y^3)/((6 (-1)) x^3 y) = 6/6×(4 x^6 y^3)/(-x^3 y) = (4 x^6 y^3)/(-x^3 y):

(4 x^6 y^3)/(-1 x^3 y)

Combine powers. (4 x^6 y^3)/(-x^3 y) = (4 x^(6 - 3) y^(3 - 1))/(1 (-1)):

(4 x^(6 - 3) y^(3 - 1))/(-1)

6 - 3 = 3:

(4 x^3 y^(3 - 1))/(-1)

3 - 1 = 2:

(4 x^3 y^2)/(-1)

Multiply numerator and denominator of (4 x^3 y^2)/(-1) by -1:

Answer: -4 x^3 y^2

Answer: #4

Step-by-step explanation:

You would divide 24 by -6, leaving u with -4 then u would subtract the powers x to the power of 6 from x to the power of 3 leaving you with x to the power of 3 and then you would subtract y to the power of 3 by y leaving you with y squared.

-4x to the power of 3 y to the power of 2.

Therefore , the solution of the given problem of equation comes out to be 3.69x = y.

Equ is the translation of the Latin word for equivalent. Latin roots can be found in the base words of many English language words that are subject to modification, such as adequate, moderate, and equality. As both sides of either an equation are, in essence, "same" to one another, the Latin root term equ enters our variable quite easily.

Here,

Given :  Jimmy spends $3.69 per gallon of fuel he puts in his vehicle.

Thus,

To find the equation for the amount of money:

Let x be the number of times he refuel his gallon of fuel:

So,

Here y represents the total amount of  money.

3.69x = y

Therefore , the solution of the given problem of equation comes out to be 3.69x = y.

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Step-by-step explanation:

3×4(5)-10

12(5)-10

60-10

50

A map uses scaled drawings. The distance between the two considered cities on that specified map is 6.25 inches

How are scale drawings formed?

For a particular scale drawing, it is already specified that all the measurements' some constant scaled version will be taken. For example, let the scale be K feet to s inches.

Then it means

1ft : s/k in.

All feet measurements will then we multiplied by s/k to get the drawing's corresponding lengths.

For this case, it is specified that the map uses scaling such that:

3/4 of an inch on map = 3 miles in reality.

Dividing both the quantities by 3, we get:

1 mile in reality = 3/4  / 3  inches on map = 1/4 inches on map

Multiplying both the quantities by 25, we get:

25 miles in reality = 25/4 = 6.25  in map

Since 25 miles is the distance between those two considered cities.

Therefore, the distance between those two cities on map would be of 6.25 inches.

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No, they are not similar. There is no postulate or theorem that can prove these two triangles are similar since they are not similar.

Similar triangles are triangles that have the same angle measures and the same side lengths. In order to determine if two triangles are similar, it is necessary to compare the sides and angles of the triangles.

In this case, the sides and angles of △fhk and △ghj are not the same, so they are not similar. Therefore, there is no postulate or theorem that can prove these two triangles are similar. No, they are not similar. There is no postulate or theorem that can prove these two triangles are similar since they are not similar.

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The given expression is equivalent to 486√3

Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.

Given is an expression, √4 of 3√3 of 3⁵

√4 of 3√3 of 3⁵ = 2×3√3×243

= 486√3

Hence, the given expression is equivalent to 486√3

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Answer:

9)  17 miles/hr

10)  7.14 miles

Step-by-step explanation:

See the attached worksheet.  Note the use of conversion factors.  In question 9 we want to convert minutes to hours.  We know there are 60 minutes/hr.  So we can set up a conversion factor in one of 2 ways:  (60 minutes/1 hr) or (1 hr/60 minutes).  Both are valid, and both are = 1, since the numerator and denominator are both equivalent.  This means we can invert a conversion factor and it is still = 1.  Since conversion facots are equal to 1, we can multiply them times anything, and the result is numerically the same (anything times 1 = anything) and only the units have changed.  For question 9, we want to convert miles/min to miles/hr.  I'll choose the conversion factor (60 min/1 hr), mostly because I like multiplication over division.  Note how the units cancel in the attachment, resulting in 17 miles/hr.  One may also use the factor (1hr/60min), but then a division is required.  Perfectly fine, but not my preferred route.

The same approach is used to answer question 10.  Again, note how he units cancel, leaving a number wth just the units desired,

Therefore , the solution to the given problem of mean comes out to be  the sample size yields the equivalent number of households is 30.

Regardless of whether many elements are discrete or continuous, averages can only be calculated for numeric variables. You may find this by dividing the total number of values in the dataset by the total number of values in the dataset. It is possible to perform computations using either raw data or data that has been compiled into frequency tables. The average value in mathematics is obtained by adding up all the numbers in a set of data and dividing the total by the total number of numbers.

Mean = 2 Four pets are two standard deviations away from the mean, and one standard deviation equals one pet.

We can determine that at least

100 (1-1k2)% = 100 (1-1/4)% = 75%

is within 2 standard deviations of the mean using Chebyshev's Rule with

k = 2. The percentage times the sample size yields the equivalent number of households:

75% x 40 = 30 Therefore , the solution to the given problem of mean comes out to be  the sample size yields the equivalent number of households is 30.

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On solving the provided question, we can say that the expression, we have here is 4 7. |10|= 470 or -470

In mathematics, it is possible to multiply, divide, add, or remove. The construction of an expression is as follows: Expression, number, and mathematical operator Numbers, variables, and functions are the building blocks of a mathematical expression (such as addition, subtraction, multiplication or division etc.) Expressions and phrases can be contrasted. Any mathematical statement with variables, numbers, and an arithmetic operation between them is called an expression or an algebraic expression. For instance, the expression 4m + 5 has the terms 4m and 5 as well as the variable m of the supplied expression, all of which are separated by the arithmetic sign +.

the expression, we have here is

4 7. |10|= 470 or -470

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No, not all the multiples of 2 are not prime numbers  only 2 itself is prime number other multiples of 2 are composite numbers.

As given in the question,

Given number is equal to :

2

Prime numbers are defined as the number which represents only two factors one and the number itself.

Multiples are defined as the given number when multiply by any integer.

Multiples of 2 are as follow :

2 × 1 = 2

2 × 2 = 4

2 × 3 = 6

2 × 4 = 8

2 × 5 = 10 ................ so on.

2 × n = 2n where 'n' belongs to any integer.

Only 2 has two factors.

other multiples of two has more than two factors.

Minimum number of factors of other multiples are :

One, two , and the number itself.

Other multiples represents composite number.

Only 2 is representing the prime number.

Therefore, in the multiple of 2 only 2 is the prime number other are composite number.

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We multiply by -3/2 to get rid of y and figure out the system of equations.

A mathematical assertion that has an "equal to" symbol between two expressions with equivalent values is called an equation.

As in 3x + 5 Equals 15, for instance.

Equations come in a variety of forms, including straight, quadratic, cubic, and others.

So, we have:

9x+3/4y=6 and 2x+1/2y=9

By removing y, we must solve a system of equations.

Therefore, we will first make the y-coefficient equal but with the opposite sign.

In the first equation, the y-coefficient is 3/4

The coefficient of y in equation two is half.

LCM: 3/4 and 1/2 = 3/2
To maintain the same coefficient of y, multiply the second equation by -3/2.

-3/2*2x-3/2*1/2y = -3/2*9

-3x-3/4y = -27/2

9x+3/4y = 6

Combine the two equations and get rid of the y variable.

-3x+9x = -27/2+6

6x = -15/2

x = -5/4

Therefore, we multiply by -3/2 to get rid of y and figure out the system of equations.

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Complete question:

Given the equations 9x+3/4y=6 and 2x+1/2y=9, by what factor the equation to eliminate y and solve the system through linea would you multiply the second equation to eliminate y and solve the system through linear combinations?

Options;

A.) -4/3

B.) -3/4

C.) -3/2

D.) -7/2

Answer:

3

Step-by-step explanation:

trust lil bru

Answer: no

Step-by-step explanation:

35 -9 = 26

you add 1+1 =2

then you look at the equal and that is your answer

Answer: they each carried 5 water bottles.

Step-by-step explanation: 8x5 equals 40

Answer: 5

Step-by-step explanation:

40 divided by 8

It is not possible to construct a triangle whose sides are 10.2 cm 6.8 cm and 4.6 cm because the sum of two sides are greater than the third sides.

In the given question, we have to check that it is possible to construct a triangle whose sides are 10.2 cm 6.8 cm and 4.6 cm.

To check whether the given sides can make a triangle or not, we have to check that the sum of two sides always greater than the third side.

To check this we firstly add the 10.2 and 6.8

10.2 + 6.8 > 4.6

17 > 4.6

Now we add 10.2 and 4.6

10.2 + 4.6 > 6.8

14.8 > 6.8

Now we add 6.8 and 4.6

6.8 + 4.6 > 10.2

11.4 > 10.2

It is possible to construct a triangle whose sides are 10.2 cm 6.8 cm and 4.6 cm because the sum of two sides are greater than the third sides.

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Therefore ,consider that the divided congruent triangle corresponding bases are equivalent as proof.

Given that it contains three sides & three vertices, a triangle qualifies as a polygon. It is a fundamental characteristic in geometry. Triangle ABC is the name given to a triangle with vertices A, B, & C. When the three components are not collinear, Euclidean geometry reveals an unique plane and triangle. The polygonal shape of a triangle has 3 components and three corners. The points where three sides touch each other end to end are referred to as the triangle's corners. The sum of the three triangle angles is 180 degrees.

Here,

Given :

This RHS theorem can be employed to demonstrate the equality of the respective.

bases of all those split congruents as well as the congruency of two independents that are produced by the altitude of such an isosceles from every given vertex.

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This means that the solution to the triangle issue is ABC, which is equivalent to XYZ.

Any shape with 3 sides and three points is a polygon. The fundamental form of geometry is this. The corners of the triangular Triangle ABC are A, B, and C. When four parts are not collinear in a geometric shape, a single plane plus triangle are produced. As triangles have three sides as well as a top right corner, they are included in polygons.

Here.

Thus,

To prove : ABC and XYZ are similar

hence ∠A =  ∠X.

The definition of  ∠B and  ∠Y is the same.

Because  ∠Z =  ∠C,

Similar to xy, line ab shares the same value.

There is no difference between lines bc and yz.

XZ corresponds to line ac.

To come up with a solution, Cpct was used.

Triangle segments that match each other are congruent.

The solution to the triangle problem is ABC is proportional with XYZ as a result.

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Answer: it's Y  because i took the test, also when doing this type of math  problem you wouldn't start from X or Z because they are starting points

Step-by-step explanation:   I TOOK the test

Answer:

I believe… ( it might be wrong… )

Reflect across the line y = x.

translate 1 unit right.

Step-by-step explanation:

i took the same test before but i believe i had a question just like this and got it right soooo….. ye

The value of the integration of the expression [tex]$$\int x^3+\frac{1}{x^{0.5}} d x$$[/tex] will be  [tex]\frac{1}{4} x^4+2 x^{0.5}+C[/tex]

[tex]$$\int x^3+\frac{1}{x^{0.5}} d x$$[/tex]

Split the single integral into multiple integrals.

We will get: [tex]$$\int x^3 d x+\int \frac{1}{x^{0.5}} d x$$[/tex]

By the Power Rule, the integral of x^3 with respect to x is (1/4)x^4.

[tex]\frac{1}{4} x^4+C+\int \frac{1}{x^{0.5}} d x[/tex]

Let u=x^{0.5}.

Then [tex]d u=\frac{0.5}{x^{0.5}} d x[/tex],

So [tex]$\frac{x^{0.5}}{0.5} d u=d x$[/tex].

Now, we will rewrite the above using u and du.

Let u=x^{0.5}.

Finding the value of (du/dx)

Differentiate x^{0.5}.

[tex]\frac{d}{d x}\left[x^{0.5}\right][/tex]

Differentiate using the Power Rule which states that [tex]$\frac{d}{d x}\left[x^n\right]$[/tex] is n x^{n-1} where n=0.5.

We will get: 0.5 x^{-0.5}

Simplify.

Rewrite the expression using the negative exponent rule

[tex]b^{-n}=\frac{1}{b^n}\\0.5 \frac{1}{x^{0.5}}[/tex]

Combine 0.5 and [tex]\frac{1}{x^{0.5}}[/tex] we will get [tex]\frac{0.5}{x^{0.5}}[/tex]

Rewrite the problem using u and du.

We will get it as:

[tex]\frac{1}{4} x^4+C+\int 2 d u[/tex]

Apply the constant rule, we will get: [tex]\frac{1}{4} x^4+C+2 u+C[/tex]

Simplifying we will get it as: [tex]\frac{1}{4} x^4+2 u+C[/tex]

Replace all occurrences of u with x^{0.5}.

We will get it as: [tex]\frac{1}{4} x^4+2 x^{0.5}+C[/tex]

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The equation can be used to find the number of pie he need to sell to break event.

c. 5x + 30 = 12x

Given :Mrs. Ramirez is making pies to sell at the local farmer’s market. It costs her $5 to make each pie, plus a one-time cost of $30 for baking supplies. She plans to sell the pies for $12 each.

To Find: Which equation can be used to find the number of pies she needs to sell to break even.

Solution:

Let no. of pies be x

It cost her $5 to make each pie

So, cost of making x pies = 5x

Since there is a one-time cost of $30 for baking supplies.

So, total cost for her is 5x+30

If she sells each pie for $12

Then cost of pies = 12x

Now,

The equation can be used to find the number of pies she needs to sell to break even:

c) 5x+30=12x

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Answer:

Below

Step-by-step explanation:

This IS basically an experiment with  15 hits out of 45 at-bats

   15/45 = .333    or  33.3 %  experimental probability

Answer:

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

Given:

Find the experimental probability.

Probability of getting a hit is:

(0,2) and (3,0) are the required  two solutions of the given equation in an ordered pairs .

The given equation is 2x+3y<=6.

When, x=0,y=2

When, y=0,x=3

Hence,

(0,2) and (3,0) are the two solutions of the given equation

in order to determine the x x and y y values to form the ordered pair.

An ordered pair,  is a pair of elements in which it have a specific importance for the order of their required placements. Ordered pairs are mainly used in coordinate geometry in order to represent a point on a coordinate plane and it is also  used to represent elements of a relation .

An ordered pair is defined as pair formed by two elements which  are separated by a comma and written inside the parentheses.  example, (x, y) represents an ordered pair, where 'x' is called the first element and 'y' is called the second element of the ordered pair. These elements which  have specific names according to that  context they are being used and that  can be either variables or constants. The order of the elements which  has a certain importance in an ordered pair. It means that  (x, y) may not be equal to (y, x)at  all the time.

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The domain of the function f/x = 4x is all real numbers.

The domain of a function is the  et of all values that can be plugged into the equation and produce a valid output. Since any real number, positive, negative, or zero, can be plugged into the equation and produce a valid output, the domain of the function f/x = 4x is all real numbers.

The domain of a function is the set of values that can be plugged into the equation and produce a valid output. In the case of the function f/x = 4x, the domain is all real numbers; that is, any value, positive or negative, can be plugged into the equation and produce a valid output. This means that the domain of the function f/x = 4x includes all real numbers, from the smallest negative number to the largest positive number, as well as zero.

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Brooklyn could calculate how many arithmetic problems she completed and how many pages she read using the equations x = 2y and 2x + 3y = 70.

let

number of math problems Brooklyn solved = x

number of pages she read = y

Time to solve each math = 2 minutes

Time to read each page = 3 minutes

Brooklyn read twice as many pages as there were arithmetic problems to be done.

x = 2y

2x + 3y = 70

Substitute x = 2y into

2x + 3y = 70

2(2y) + 3y = 70

4y + 3y = 70

7y = 70

divide both sides by 7

y = 70/7

y = 10

Recall,

x = 2y

x = 2(10)

x = 20

Therefore, Brooklyn completed 20 math problems and read 10 pages, which equals 20 math problems and 10 pages, respectively.

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When MN = 5x + 10, the lengths of MN, RS, and NP are 410, 400, and 320, respectively in this triangle .

A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric forms. The name given to a triangle with the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.

given

as AMNP-ARST

the x = 80

so MN = 5 * 80 + 10

= 410

RS = 6* 80 - 8

= 400

When MN = 5x + 10, the lengths of MN, RS, and NP are 410, 400, and 320, respectively in this triangle .

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a) The quadratic function g(x) = 2f(x-4) + 5 is defined as a transformed version of the original quadratic function f(x). The transformation applied to f(x) is a horizontal shift of 4 units to the left and a vertical shift of 5 units upward. This can be observed from the fact that x is replaced with (x-4) in the function g(x). The function is also scaled by a factor of 2.

How does a quadratic function work?

f(x) = ax2 + bx + c, where a, b, and c are numbers and an is not equal to zero, is a quadratic function. A parabola is the shape of a quadratic function's graph. Although the "width" or "steepness" of a parabola can vary as well as its direction of opening, they all share the same fundamental "U" form.

b) The turning point of the quadratic function f(x) is (-3, 2). To find the turning point of g(x), we must first apply the horizontal shift of 4 units to the left to the x-coordinate, and then apply the vertical shift of 5 units upward to the y-coordinate.

The turning point of g(x) is (-3+4, 2+5) = (1,7)

So, the turning point of the transformed function g(x) is (1,7)

We can see that the transformation of g(x) moves the turning point of f(x) to the right and up, as expected from the transformation.

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Third quadrant the complex plane is where the number -14 - 5i is situated.

Based on the common knowledge, the complex number's real and imaginary components are considered as the x- and y- coordinates of an ordered pair in a 2-D plane.

first quadrant a+bi =(a,b)

second quadrant -a+bi= (-a,b)

third quadrant -a-bi=(-a,-b)

fourth quadrant a,-b=(a,-b)

According to the question,-14-5i is located in third quadrant(-14,-5)

As a result, the complex plane's third quadrant is where the number -14 - 5i is situated.

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