A 32m tall building cast a shadow. The distance from the top of the building to the top of the shadow is 33m. Find the length of the shadow

Answer:

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The standard form of linear equation is:

Convert the given equation in below steps:

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 .

A function is defined as a relation between a set of inputs having one output each.

Say, there is an element x in the sets of input, now it can be paired with no more than one y in the sets of output. We should note that the same y can be paired with different x's, but not the reverse. All linear equations, with the exception of vertical and horizontal lines, are functions.

The function is generally written as "f(x)" where x is the input value.

let us take an example-

f(x) = x/2

here, f(x) is a function because each input "x" has a single output "x/2":

• f(2) = 1

• f(5) = 2.5

• f(−12) = −6

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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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Answer:

The point in which the three medians of the triangle intersec

Step-by-step explanation:

The minimum possible volume of this rectangular prism is 176.78 ft³.

The maximum possible volume of this rectangular prism is 131.11 ft³.

Mathematically, the volume of a rectangular prism can be calculated by using this formula:

Volume = L × W × H

Where:

In order to determine the minimum possible volume of this rectangular prism, we would add the greatest possible error to each measurement and then multiply as follows:

Vmin = (3.5 + 0.25) × (8.4 + 0.25) × (5.2 + 0.25)

Vmin = 3.75 × 8.65 × 5.45

Minimum possible volume, Vmin = 176.78 ft³.

In order to determine the maximum possible volume of this rectangular prism, we would subtract the greatest possible error from each measurement and then multiply as follows:

Vmax = (3.5 - 0.25) × (8.4 - 0.25) × (5.2 - 0.25)

Vmax = 3.25 × 8.15 × 4.95

Maximum possible volume, Vmax = 131.11 ft³.

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Answer:

m<8=1024

Step-by-step explanation:

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

Inequalities to support the questions

Mathematical expressions with inequalities are those in which the two sides are not equal. Contrary to equations, we compare two values in inequality. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.

Given:

Each factory operates for at most 12 hours each day.

let maximum profit by factory A be x and Factory B be y.

Then, Inequalities to support the questions

2x + y ≤ 12

and, 2x+ 3y ≤ 12

and, x ≥ 0, y ≥ 0

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The rule for translating △ABC to △A''B''C''  is (x, y) ⇒ (1, 3)

The translation of the triangles are given as

△ABC to △A'B'C' to △A''B''C'' .

Also, we have the vector transformation to be:

When these vectors are combined, we have

(x, y) ⇒ (-3, 5) + (4, -2)

Combine the vectors

(x, y) ⇒ (-3 + 4, 5 - 2)

Evaluate the like terms

(x, y) ⇒ (1, 3)

Hence, the translation rule is (x, y) ⇒ (1, 3)

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Complete question

A translation maps △ABC to △A'B'C' using the vector (-3, 5). A second translation maps △A'B'C' to △A'B'C' using the vector (4, -2). Write a rule for translating △ABC to △A''B''C'' .

Using the given information, the original fraction is 3/5

From the question, we are to determine the original fraction.

Let the numerator of the fraction be x and the denominator be y.

From the given information,

"The numerator of a fraction is 2 less than its denominator"

That is,

x = y - 2                 ----------- (1)

and

"When both the numerator and denominator are increased by 3, the fraction is increased by 3/20"

That is,

(x + 3)/(y + 3) = x/y + 3/20

Then,

(x + 3)/(y + 3) = (20x + 3y)/20y

(x +3)(20y) = (y + 3)(20x + 3y)           ---------- (2)

Substitute the value of x into equation (2)

((y - 2) +3)(20y) = (y + 3)(20(y - 2) + 3y)

(y - 2 +3)(20y) = (y + 3)(20y - 40 + 3y)

(y +1)(20y) = (y + 3)(23y - 40)

20y² + 20y = 23y² - 40y + 69y - 120

23y² - 20y² - 40y + 69y - 20y - 120 = 0

3y² + 9y -120 = 0

Divide through by 3

y² + 3y - 40 = 0

y² + 8y - 5y - 40 = 0

y(y + 8) -5(y + 8) = 0

(y - 5)(y + 8) = 0

y - 5 = 0 OR y + 8 = 0

y = 5 OR y = -8

Substitute the values of into equation (1)

x = y - 2

When y = 5

x = 5 - 2

x = 3

When y = -8

x = -8 - 2

x = -10

Ignoring the negative values, the fraction is 3/5

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Answer:

makes over a 90 digre angle

Step-by-step explanation:

The expression that shows the number of boxes ordered is 8p.

Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations.

Since the school custodian ordered p rolls of paper towels and the paper towels are sold in boxes of eight.

The expression will be:

= Number of rolls × 8

= p × 8

= 8p

The expression is 8p.

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The function pairs that are inverse functions are (c) f(x) = 5x - 3 and g(x) = (x + 3)/5

Function (a)

This function is given as

f(x) = 4x²

The function needs to be represented as an equation

So, we have

y = 4x²

Swap the positions of x and y

x = 4y²

So, we have

y² = x/4

Take the square root of both sides

y = 1/2√x

So, the inverse function is

g(x) = 1/2√x (not the same as the option)

Function (b)

This function is given as

f(x) = x² - 16

The function needs to be represented as an equation

So, we have

y = x² - 16

Swap the positions of x and y

x = y² - 16

So, we have

y² = x + 16

Take the square root of both sides

y = √x + 16

So, the inverse function is

g(x) = √ x+ 16 (not the same as the option)

Function (c)

This function is given as

f(x) = 5x - 3

The function needs to be represented as an equation

So, we have

y = 5x - 3

Swap the positions of r and y

x = 5y - 3

So, we have

5y = x + 3

This gives

y = (x + 3)/5

So, the inverse function is

g(x) = (x + 3)/5

Hence, the function pairs are (d) f(x) = 5x - 3 and g(x) = (x + 3)/5

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Answer:2 minus the square root of 3 divided by 2

Step-by-step explanation:

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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As per the multiplication operation, the value of 519 x 2 is 1038

Multiplication:

In math, multiplication means  the repeated addition of groups of equal sizes.

Given,

Here we need to find the value of 519 x 2.

AS per the multiplication table, the value of 519 x 2 is calculated by using the following steps:

=> 2 × 9 = 18.

∴ put down 8 and carry 1

=> 2 × 1 + 1 = 2 + 1 = 3.

∴ put down 3

=> 2 × 5 = 10.

∴ put down 0 and carry 1

Finally, combine all these values, the we get 519 x 2 = 1038.

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For 1, the number of positive divisors or factors is only one i.e. 1 itself. So, number one is not a prime number.

What are prime numbers ?

Prime numbers are numbers greater than 1. They only have two factors, 1 and the number itself. This means these numbers cannot be divided by any number other than 1 and the number itself without leaving a remainder.

Numbers that have more than 2 factors are known as composite numbers.

For a number to be called as a prime number, it must have only two positive factors. Now, for 1, the number of positive divisors or factors is only one i.e. 1 itself. So, number one is not a prime number.

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As described in the algebra the balancing amount is - 1.8375

what is algebra?

Mathematics has several different subfields, including algebra. Algebra, broadly stated, is the study of mathematical symbols and the guidelines for using these symbols in formulas.

Solution;

Balance of account = account amount - account used

                                = 1.10 - 0.25 * ( 47/2)

                                = 1.10 - 0.25* 11.75

                                = 1.10 - 2.9375

Balance of account = - 1.8375

Hence, by algebra the balancing amount of account is - 1.8375

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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 triangle center that is equidistant to the sides of a triangle is Incenter .

In the question ,

we have asked about the what is the name of the center that is equidistant from the sides of the triangle .

Incenter is defined as the meeting point of all the interior angle bisectors of the triangle .

We know that the inscribed circle is the circle that is inside triangle and touches all its sides.

and  we know that the center of the circle is equidistant from all points that lie on circle.

So, center of inscribed circle (incentre will be equidistant from all sides of the triangle.) .

Therefore , the incenter is equidistant to the sides of the triangle .

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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: 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:

8 + [8 + (-1*(-3)-4)]÷(-7) = 7/1 = 7

                    Hope this helped answer your question!

Answer:

7

Step by Step Explanation:

Answer: 2.6

Step-by-step explanation:

Use long division:

16.64 over 6.4

First multiply the numerator by 10 to get 166.4 over 64

Then divide 166.4 by 64 (using long division)

At the end you'll get 2.6

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:

8%

Step-by-step explanation:

1. Subtract:

  55000 - 50600 = 4400

2. Divide:

   4400/55000 = 0.08

The area of the paperboard remaining after a semicircle is cut out of it is 235.52 in².

The area is the amount of space within the perimeter of a 2D shape.

To calculate the area of the rectangular board that remain, we use the formula below.

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1

Hence, the area of the paperbaord left is 235.52 in².

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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 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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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