how to find area of a triangle

In a hypothesis test of a regression coefficient, if the null hypothesis is rejected at the 5% level, it means that the evidence in the data provides strong evidence against the null hypothesis.

The 5% level refers to the level of significance, which is a threshold used to determine whether the results of the hypothesis test are statistically significant or not. If the null hypothesis is rejected at the 5% level, it means that the p-value, which is a measure of the strength of the evidence against the null hypothesis, is less than 0.05. In other words, the likelihood of obtaining the observed results if the null hypothesis were true is less than 5%. This is considered to be strong evidence against the null hypothesis, and we reject the null hypothesis in favor of the alternative hypothesis.

In conclusion, if a hypothesis test of a regression coefficient finds that the null hypothesis is rejected at the 5% level, it means that the evidence in the data provides strong evidence against the null hypothesis, and the results are considered to be statistically significant.

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Answer:86 yards

Step-by-step explanation:

We have the diameter, so the solution simply is:

D= 2 r= 2 x 43= 86 yards

P.S. I'm sorry if this isn't clear enough, but that's how i could explain.

The required volume of the solid obtained by rotating the region is  56π/15 cubic units.

To find the volume of the solid obtained by rotating the region enclosed by y = x² and y = 5x about the line x = 0 using the method of disks or washers, we need to first determine the bounds of the region.

The intersection of y = x² and y = 5x occurs when x = 1, so the region to be rotated is the portion of the graph of y = x² that lies above y = 5x and to the left of x = 1.

Next, we use the method of disks (or washers) to find the volume of the solid generated by rotating the region about the x-axis. The method of disks involves dividing the region into thin vertical slices, approximating each slice as a disk, and finding the volume of the sum of these disks.

The volume of each disk is given by the formula V = πr²h, where r is the radius (distance from the center of the disk to the circumference) and h is the height (distance from the center of the disk to the x-axis). In this case, the radius is equal to the height of the slice and the height is equal to the difference between the maximum and minimum values of y in that slice.

The bounds of integration for the radius are x = 0 to x = 1. We integrate from x = 0 to x = 1, finding the volume of the sum of the disks:

V = π [tex]\int_0^1[/tex] (x² - 5x)² dx =  π [tex]\int_0^1[/tex](x^4 - 10x³ + 25x²) dx

This definite integral can be solved to yield:

V = π × (x⁵/5 - 5x⁴/4 + 25x³/3) evaluated from x=0 to x=1

V = π × (1/5 - 5/4 + 25/3) = 56π/15 cubic units

So the volume of the solid generated by rotating the region enclosed by y = x² and y = 5x about the x-axis is 56π/15 cubic units.

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a) The like terms are B, D, F

b) The equivalent expression is option A

c) The little 5 outside would multiply all the exponents. Option D

We know that the like terms are the terms that have the same kind of algebraic exponents and can easily be added or subtracted as the case may be. Hence we have to look out for the factors that do have the same exponents.

We would have in the second question;

3x^2 + 2x - 4 + 5x^2 - 4x + 5

Collecting the like terms;

3x^2  + 5x^2 +  2x -  4x - 4 + 5

8x^2 - 2x + 1

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Amount of loaves of bread to be placed on each platter= 12 /7

The Total loaves of bread equal to 12

The Total number of platters to 7

find the amount of loaves of bread to be placed on each platter ?

In order to find the amount of loaves of bread to be placed on each platter, we will divide total loaves of bread by total number of platters.

Thus, amount of bread in each platter can be given by:

amount of loaves of bread to be placed on each platter= Total loaves of bread  / Total number of platters

Amount of loaves of bread to be placed on each platter= 12 /7

Therefore option D is correct.

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Velocity is the measure of the rate of change of position, or the speed of an object in a specific direction.

Since you drove from home to school and then back home, the velocity on the return home would be different than the velocity on the way to school, since the direction of travel is different.

The average speed for the trip can be calculated by dividing the total distance (25 miles) by the total time (1 hour). Therefore, the average speed of the trip is 25 miles per hour.

Acceleration is the rate of change of velocity, or the rate at which an object speeds up or slows down. In this case, you would have to accelerate when you reach the school in order to pick up your child and then accelerate again when you leave the school in order to return home.

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The equation of line is given by y = 3x - 1 and the slope is m = 3

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

Substituting the values in the equation , we get

y = 3x - 1   be equation (1)

And , equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

So , the slope of the line is m = 3

The y intercept of the line b = -1

Hence , the equation of line is y = 3x - 1 and the graph is plotted

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The mean is a statistics tool used to find the approximate "middle" in a set of data.

Statistic is a branch of mathematics that deal with the collection analyzes interpretation and presentation of data it is used to summarize analyze and compare data in order to draw conclusion and make decisions statistical method are used in a wide variety of field including economics finance business engineering medicine psychology social science and many others.

It is calculated by adding the values of the data set and dividing the sum by the number of items in the data set. The mean is also known as the average, and it can be used to compare sets of data and to measure the central tendency of a data set.

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If the account earns 6.5% simple interest per year , Diego will give his granddaughter a sum of $1130

To calculate the simple interest earned on an initial amount of $500 at 6.5% for 18 years, you can use the formula:

$I = Prt$, where

$I$ = interest earned

$P$ = initial amount ($500)

$r$ = interest rate (6.5%)

$t$ = time in years (18)

So, $I = 500 * 6.5 * 18 / 100 = 630$.

Thus, on the granddaughter's 18th birthday, Diego will give her $500 + 630 = $1130.

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The required value of integration of given function is 82.

To evaluate the integral  we need to find the anti-derivative of F(x) and then evaluate it at the limits of integration.

Since F(x) = 8 for x < 8 and F(x) = x for x ≥ 8, we can split the integral into two parts, one from 0 to 8 and another from 8 to 10

According to question:

[tex]$$\begin{aligned}& \int_0^{ 10} \mathrm{~F}(\mathrm{x}) \mathrm{dx} \\& =\int_0^8 F(x) d x+\int_8^{10} F(x) d x\end{aligned}\\$$[/tex]

The anti-derivative of

[tex]F(x)=8$ is $F(x)=8 x$, so:$$[/tex]

[tex]$$\begin{aligned}& \int_8^{10} F(x) d x \\& =\left.\left(x^2 / 2\right)\right|_8 ^{10} \\& =\left(10^ 2 / 2\right)-\left(8^2 / 2\right) \\& =50-32 \\& =18\end{aligned}$$[/tex]

Putting it all together

[tex]$\int_0^10 \mathrm{~F}(\mathrm{x}) \mathrm{dx}=64+18=82$[/tex]

So, the value of the integral [tex]$\int_0^{10} F(x) d x$[/tex] is 82.

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Complete question:

The number of shirts at which the cost would be same is 12. As, $352 < $380.75, First Company offers a better deal for an order of 35 shirts.

Charge of first company is $9.65 per shirt plus setup fee of $43 &

Charge of another company is $8.40 per shirt plus setup fee of $58

The number of shirts such that the cost of both the companies are same.

Let the required number of shirts be n which can be evaluated as following:

Cost of first company = Cost of another company

⇒ 9.65n + 43 = 8.40n + 58

⇒ 9.65n−8.40n = 58−43

⇒ 1.25n = 15

⇒ n = 151.25

⇒ n = 12

Thus, the number of shirts at which the cost would be same is 12.

First company charges $9.65 per shirt + setup fee of $43

35 shirts = 35 × 9.65 + 43

              = $380.75

Second company charges $8.40 per shirt + setup fee of $58

35 shirts = 35 × 8.40 + 58

              = $352

As, $352 < $380.75, First Company offers a better deal for an order of 35 shirts.

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The ratio of the orbital radii of the planets is  4:1.

The ratio of their periods is 8:1.

What is orbital radius and periods in circular motion?

Planetary bodies circle the Sun according to Kepler's three laws. They explain how planets orbit the Sun in elliptical fashion, how they traverse the same amount of space in a given length of time regardless of where they are in their orbit, and how their orbital periods are related to the size of their orbits (its semi-major axis).

An object's orbital radius is the typical distance it travels around a bigger object. An illustration would be that the Sun and Earth are typically 150 million kilometres apart. The orbital radius is also this.

Let the mass of the planet be m and the mass of the star be M.

r = radius of ordit

v = speed

We know that

gravitational attraction = centripital force

GMm/[tex]r^{2}[/tex] = m[tex]v^{2}[/tex]/r

Hence

v  ∝ 1/

a) Here v₁/v₂ = v/2v =  

squaring both sides

1/4 = r2/r1

Thus r1/r2 = 4/1

Hence ratio of orbital radii is 4:1.

b) As per keplers law of planetary motion,

T^2 ∝ [tex]r^{3}[/tex]

Thus ratio of time periods is 8:1.

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Suri is right. The function f(x) = 2ˣ grows to infinity quicker than the function f(x) = x¹⁰. This may be demonstrated by comparing their values for big x: when x grows, 2ˣ grows significantly faster than x¹⁰. This suggests that 2ˣ approaches infinity more quickly than x¹⁰.

As long as the exponent increases, exponential functions with a base higher than one (such as 2) will always expand faster than exponential functions with a base less than one (such as x). Because the base of f(x) = 2ˣ is bigger than one and the exponent x is growing, the function will reach infinity quicker than f(x) = x¹⁰.

Here,

Suri is correct. The function f(x) = 2ˣ increases to infinity faster than f(x) = x¹⁰. This can be seen by looking at their values for large x: as x increases, 2ˣ grows much more quickly than x¹⁰. This means that 2ˣ approaches infinity faster than x¹⁰.

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Answer:

Adriana recorded a temperature of 38°C.

Step-by-step explanation:

It is because negative temperatures in Celsius is cold.

#LearnYourBasics!

The warmest temperature was recorded by Adriana. Because it's the highest temperature shown.

The concept of temperature is used to quantify how hot and cold an object is. You can use a thermometer to measure the temperature. The most common scales are the Celsius scale with the unit symbol °C, the Fahrenheit scale (°F) and the Kelvin scale (K).

Fahrenheit is primarily used in the United States. According to this ice-enclosed thermometer, the temperature is around 0 degrees Celsius, or 32 degrees Fahrenheit. The temperature would be about 274 if this thermometer read the Kelvin scale used by scientists.

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Lucy divides 1.8 into 6 groups of 0.3.

It is important to note that an expression is simply used to show the relationship between the variables that are provided or the data given regarding an information. In this case, it is vital to note that they have at least two terms which have to be related by through an operator.

Based on the information, Lucy solves 1.8 ÷ 0.3. This will be:

= 1.8 / 0.3

= 6

In conclusion, Lucy divides 1.8 into 6 groups of 0.3.

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Lucy solves 1.8 ÷ 0.3 using the diagram shown.

Use the drop-down menus to explain her reasoning.

Lucy divides ______

into _______

groups ______

of

To determine whether the sequence converges or diverges, we can use the Squeeze Theorem.

We can see that

4/ n+5n^2 < = An <= 4+3n^2/ n+5n^2

As n tends to infinity,  4/ n+5n^2  tends to 0 and 4+3n^2/ n+5n^2 tends to  4/5n^2 which also tends to 0.

So by the Squeeze Theorem, we can say that An tends to 0 as n tends to infinity. Hence the limit of the sequence is Lim n-> An = 0

We can also see that the numerator of An is a constant and the denominator is a polynomial with degree 2. Since the denominator's degree is greater than the numerator, the limit will be zero as n -> infinity.

Therefore, the sequence converges to 0.

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a) There are 10 different combinations of pairs of coins.

b) List of the combinations:

(10p, 1p), (10p, 50p), (10p, 2p), (10p, 20p), (1p, 50p), (1p, 2p), (1p, 20p), (50p, 2p), (50p, 20p), (2p, 20p)

A combination is a selection of items from a set that has distinct members, such that the order of selection does not matter.

Given,

Angela has coins of

10p, 1p, 50p, 2p, 20p

a) Combination of pulling out two coins

= ⁵C₂

= (5!)/(5-2)!×(2!)

= 5 × 4 × 3 × 2 × 1/3 × 2 × 1 × 2 × 1

= 120/12

= 10

b) Taking 10p as one coin

(10p, 1p), (10p, 50p), (10p, 2p), (10p, 20p),

Taking 1p as one coin, as repetition is not allowed

(1p, 50p), (1p, 2p), (1p, 20p),

Taking 50p as one coin, as repetition is not allowed

(50p, 2p), (50p, 20p),

Taking 2p as one coin, as repetition is not allowed

(2p, 20p)

a) Hence, 10 is the total number of combinations of pairs of coins

b) All combinations are:

(10p, 1p), (10p, 50p), (10p, 2p), (10p, 20p), (1p, 50p), (1p, 2p), (1p, 20p), (50p, 2p), (50p, 20p), (2p, 20p)

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The complete question is as follows:

Angela has the following coins in her pocket:

10p 1p 50p 2p 20p

She pulls out two coins at random.

a) How many different combinations of pairs of coins are there

b) List all of the combinations,

write your answers like this: (10p, 1p)

You must write all of your answers on one line.

Answer:

Step-by-step explanation:

The slope of a line perpendicular to another line with slope m is the negative reciprocal of m. So if the slope of line G is 5/4, the slope of line H, which is perpendicular to line G, would be -4/5.

B) Yes: A WZX-A YZX because ZWZXZYZX and WZ YZ:1a

The statement is incorrect. It should be:- B) Yes: A WZX ~ A YZX because corresponding angles ZWZX and ZYZX are congruent and corresponding sides WZ and YZ are proportional, with a scale factor of 1.

A scale factor is a numerical representation of the size disparity between two comparable figures. When two figures have the same shape but different sizes, they are said to be comparable. To put it another way, one figure is an expansion or contraction of the other.

The ratio of the lengths of the corresponding sides in the two figures is the scale factor. For instance, if the scale factor is 2, one figure will be twice as large as the other, and if it is 1/2, one figure will be half as large as the other. The comparable sides in one figure are typically k times longer than the corresponding sides in another if the scale factor is k.

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The student can only work a whole number of hours, the student should work 8 hours at the doctor's office each week. The student should then tutor for 12 hours each week in order to earn at least $375.

Let x represent the number of hours the student works at the doctor's office each week, and let y represent the number of hours the student tutors each week. The system of inequalities that represents the given constraints can be written as:

x + y ≤ 20

15x + 25y ≥ 375

To maximize the number of hours the student works at the doctor's office while still earning at least $375, we must solve this system of inequalities. To do this, we can subtract 15x from both sides of the second inequality to isolate y:

25y ≥ 375 - 15x

We can then divide both sides of this equation by 25 to solve for y:

y ≥ (375 - 15x) / 25

We can then substitute this expression for y in the first inequality to solve for x:

x + (375 - 15x) / 25 ≤ 20

We can then rearrange and solve this equation for x:

15x + 375 ≤ 500

15x ≤ 125

x ≤ 8.33.

Since the student can only work a whole number of hours, the student should work 8 hours at the doctor's office each week. The student should then tutor for 12 hours each week in order to earn at least $375.

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For  y=sin [(x – 1)^2(x + 1)], the differentiation of y will be

y'=cos[(x-1)^2(x+1)]((x-1)^2+2(x^2-1)).

What is differentiation?

In calculus, differentiation is one of the two important concepts apart from integration. Differentiation is a method of finding the derivative of a function. Differentiation is a process, in Maths, where we find the instantaneous rate of change in function based on one of its variables. The most common example is the rate change of displacement with respect to time, called velocity. The opposite of finding a derivative is anti-differentiation.

If x is a variable and y is another variable, then the rate of change of x with respect to y is given by dy/dx. This is the general expression of derivative of a function and is represented as f'(x) = dy/dx, where y = f(x) is any function.

Let y = f(x) be a function of x. Then, the rate of change of “y” per unit change in “x” is given by:

dy/dx

Now,

Given function

Y=sin[(x-1)^2(x+1)]

therefore its differentiation is

y'=cos[(x-1)^2(x+1)]((x-1)^2*1+(x+1)*2*(x-1))

y'=cos[(x-1)^2(x+1)]((x-1)^2+2(x^2-1))

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Right Question:-

Which of the following expressions is y' given that y=sin [(x – 1)^2(x + 1)]

The correct answer is E: y' = (3x – 1) (2π – 1) cos [(x – 1)π (x + 1)].

The derivative of a function is a mathematical concept that describes the rate of change of the function at a particular point. It represents the slope of the function at that point and provides information about how the function is changing with respect to its input.

Formally, the derivative of a function f(x) at a point x is defined as the limit of the change in the function value as the change in the input approaches zero, i.e.:

f'(x) = lim h -> 0 (f(x + h) - f(x)) / h

The derivative can be calculated using various techniques, including differential calculus and numerical methods.

The derivative has many applications in physics, engineering, and economics, among other fields. For example, in physics, the derivative of the position function of an object gives its velocity, while the derivative of the velocity function gives its acceleration. In finance, the derivative of a stock price function gives the rate of change of the stock price, which is an important measure of risk.

The derivative of y = sin [(x – 1)π (x + 1)], using the chain rule, is:

y' = cos [(x – 1)π (x + 1)] * [(x + 1)π – (x – 1)π]

= cos [(x – 1)π (x + 1)] * 2π

= 2π cos [(x – 1)π (x + 1)]

So, the correct answer is E: y' = (3x – 1) (2π – 1) cos [(x – 1)π (x + 1)].

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Using row elimination method the solution of the system equation is [tex]x_1=12,x_2=-7[/tex].

What is equation?

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

Here the given system equation is

[tex]2x_1+4x_2=-4[/tex]

[tex]5x_1+7x_2=11[/tex]

The augmented matrix of the given equation is

=> B = [A ,b] = [tex]\left[\begin{array}{ccc}2&4&-4\\5&7&11\\\end{array}\right][/tex]

Multiply the 1st row by 1/2 then

=> [tex]\left[\begin{array}{ccc}1&2&-2\\5&7&11\\\end{array}\right][/tex]

Add -5times the first row to the second row then

=> [tex]\left[\begin{array}{ccc}1&2&-2\\0&-3&21\\\end{array}\right][/tex]

Multiply 2nd row by -1/3 then

=> [tex]\left[\begin{array}{ccc}1&2&-2\\0&1&-7\\\end{array}\right][/tex]

Add 2 times the second row to the first row then

=> [tex]\left[\begin{array}{ccc}1&0&12\\0&1&-7\\\end{array}\right][/tex]

Hence the given system equation reduce to [tex]x_1=12 , x_2=-7[/tex] which is required solution.

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The solution to this system of equations is x = -6, y = 9, and z = 5.

To solve this system of equations using row operations or elementary matrices, we can first start by subtracting 4x from both sides of the first equation. This leaves us with 3x - 3x = -6. Since the x terms cancel out, this equation is now true for any value of x. We can then use this equation to substitute -6 for the x terms in the other two equations. In the second equation, we have 5y - 2y - 6 = -16. We can then subtract 5y from both sides of the equation to get -2y - 6 = -16. Dividing both sides by -2 gives us y = 9. The third equation is now 3y - 3z - 4z - 4z = -6. We can then subtract 3y from both sides of the equation to get -3z - 4z = -15. We can then divide both sides of the equation by -3 to get z = 5. Therefore, the solution to this  system of equations  is x = -6, y = 9, and z = 5.

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Answer:

120

Step-by-step explanation: 125.4/104.5x100

By using Heron's formula, it can be calculated that the material used for the entire kite is 48 square inches.

Heron's formula is used for finding the area of a triangle in terms of the lengths of its sides.

Area = √s(s - a)(s - b)(s - c) where:

s = half the perimeter = (a + b + c)/2

a,b,c = sides of the triangle

A kite is made up of two isosceles triangles, ΔKIT and ΔKET.

Area ΔKIT=  17 square inches

KI = 6 in

ET = 8 in

KT = 10 in

Start by calculating the perimeter of ΔKET:

perimeter = KE + ET + TK

                = 8 + 8 + 10

                = 26 in

The area of ΔKET can be obtained using Heron's formula:

Area = √s(s - a)(s - b)(s - c)

        = √ 13 (13 - KE) (13 - ET) (13 - TK)

        = √ 13 (13 - 8) (13 - 8) (13 - 10)

        = √ 13 · 5 · 5 · 3

        = √ 975

        = 31.22 square inches

Since the quadrilateral KITE is composed of ΔKIT and ΔKET, then its area is equal to the total area of the triangles:

Area KITE = Area ΔKIT + Area ΔKET

                 = 17 + 31.22

                 = 48.22

                 ≈ 48 square inches

Thus, the material used for the entire kite is 48 square inches.

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Bar notation is used to show the decimal is repeating.

So,

"We use bar notation to show that a decimal is terminating" is an incorrect statement.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Bar notation is used in decimal numbers to show that the number is repeating.

Example:

1/3 = 0.33333333

This can be written as,

1/3 = 0.[tex]\over3[/tex]

Thus,

Bar notation is used to show the decimal is repeating.

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The relation is not a function, enter NONE in the Domain is possible x values from the graph i.e (-infinity,-2) U [2,infinity)

Range is all possible functional values i.e (-infinity,4] U (7,infinity)

A) vertical line test :

the vertical line through the point x = -2 cuts the graph at two points

the points on the graph are (-2,-1) and (-2,5)

that is x=-2 assigned to two values -1,5.

recollect that a relation represents a function when each element of x-coordinate associated with unique element of y-coordinate

therefore, this relation is not a function.

Domain is none and codomain is also none.

B) any vertical line through graph cuts the line at only one point.

that is each element of x coordinate associated with the unique element of y-coordinate. so, it represents a function.

Domain is possible x values from the graph i.e (-infinity,-2) U [2,infinity)

Range is all possible functional values i.e (-infinity,4] U (7,infinity)

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The height of the building is 120 ft.

According to Pythagoras theorem, we can write the relation between hypotenuse, base and perpendicular as -

(hypotenuse)² = (base)² + (perpendicular)²

(h)² = (b)² + (p)²                                                        ... Eq { 1 }

Given is that Barrett is looking at a building on the school grounds which is shaped like a rectangle as shown. He knows the building has a height of {25x} feet and a width of {28x} feet with a diagonal of 180 feet.

We can apply the Pythagoras theorem to the building as -

(diagonal)² = (height)² + (width)²

180 x 180 = 625x² + 784x²

32400 = 1409x²

x² = 32400/1409

x² = 23

x = 4.8                                   ... Eq { 1 }

Height of the building would be -

{h} = 25x = 25 x 4.8

{h} = 120 ft

Therefore, the height of the building is 120 ft.

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The value of tan C is 5/12.

There are three commonly used trigonometric identities.

Sin x = 1/ cosec x

Cos x = 1/ sec x

Tan x = 1/ cot x or sin x / cos x

Cot x = cos x / sin x

We have,

From the figure,

BA = 15

BC = 36

AC = 39

So,

Tan C = BA / BC = 15/36 = 5/12

Thus,

Tan C is 5/12.

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The proportional relationship that models the situation is given as follows:

y = 2x/3.

A proportional relationship is defined as follows:

y = kx.

In which k is the constant of proportionality.

The variables for this problem are given as follows:

Hence the constant is given as follows:

k = 2/3.

Then the relationship is given as follows:

y = 2x/3.

The problem is incomplete, hence the proportional relationship is given so it can be used to obtain the desired amounts.

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