Austin had to make a scale drawing of the school cafeteria for his architecture class. He used a scale that equaled 4 feet for every 1 inch depicted. If the scale drawing he made identified the cafeteria as being 16 inches in length, how long was the actual cafeteria?

A.
64 ft

B.
12 ft

C.
4 ft

D.
256 ft

In geometry, an angle is often measured in units of radians, which is a way to express the size of an angle in terms of the length of the arc it cuts off on the circumference of a circle.

This relationship between an angle and an arc length is given by the formula:

Arc Length = Radius * Angle (in radians)

Rearranging this formula to solve for the angle, we have:

Angle (in radians) = Arc Length / Radius

Plugging in the values for the radius (2.2) and the arc length (12.2), we get:

Angle (in radians) = 12.2 / 2.2 = 5.54

Rounding to the nearest 10th, the angle in radians is approximately 5.5.

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Answer:

Sunrise; $35

Step-by-step explanation:

Hope it helps! =D

∠1 and ∠5 = Corresponding angles.

∠2 and ∠8 = Same-side exterior angles.

∠4 and ∠5 = Alternate interior angles.

Lines in a plane that are consistently spaced apart are known as parallel lines. Parallel lines don't cross each other.

Given:

Two parallel lines cut by a traversal line.

Then,

∠1 and ∠5 = Corresponding angles.

∠2 and ∠8 = Same-side exterior angles.

∠4 and ∠5 = Alternate interior angles.

Therefore, all the required values are given above.

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Check the picture below.

so to get the EQUATion of each lines, we'll use those points you see in the picture for each, now we're only getting their "equation" only just yet, then we'll do the inequality part.

for the blue line

[tex](\stackrel{x_1}{0}~,~\stackrel{y_1}{-5})\qquad (\stackrel{x_2}{5}~,~\stackrel{y_2}{0}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{0}-\stackrel{y1}{(-5)}}}{\underset{\textit{\large run}} {\underset{x_2}{5}-\underset{x_1}{0}}} \implies \cfrac{0 +5}{5} \implies \cfrac{ 5 }{ 5 } \implies 1[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-5)}=\stackrel{m}{ 1}(x-\stackrel{x_1}{0}) \implies y +5 = 1 ( x -0) \\\\\\ y+5=x\implies \boxed{y=x-5}[/tex]

for the red line

[tex](\stackrel{x_1}{-4}~,~\stackrel{y_1}{3})\qquad (\stackrel{x_2}{6}~,~\stackrel{y_2}{-2}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-2}-\stackrel{y1}{3}}}{\underset{\textit{\large run}} {\underset{x_2}{6}-\underset{x_1}{(-4)}}} \implies \cfrac{-5}{6 +4} \implies \cfrac{ -5 }{ 10 } \implies - \cfrac{ 1 }{ 2 }[/tex]

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{3}=\stackrel{m}{- \cfrac{ 1 }{ 2 }}(x-\stackrel{x_1}{(-4)}) \implies y -3 = - \cfrac{ 1 }{ 2 } ( x +4) \\\\\\ y-3=- \cfrac{ 1 }{ 2 }x-2\implies \boxed{y=- \cfrac{ 1 }{ 2 }x+1}[/tex]

now, the dashed line for the red one, means the borderline is not included so whatever "y" is, is either > or <.

the solid line for the blue line means, the borderline is included, so whatever "y" is, is ⩾ or ⩽.

now, what area do we shaded, let's deal with the red one first.

well, do usually a true/false region check, so we pick a point on either side of the line, hmmmm for simplicity let's pick the origin, (0,0), which is below the red line, that means x = 0 and y = 0

[tex]y ~~ \square- \cfrac{ 1 }{ 2 }x+1\implies 0~~ \square-\cfrac{1}{2}(0)+1\implies 0~~ \square ~~ 1\implies 0 < 1[/tex]

so the sign that will make that statement true can only possible by "<", meaning that "0 is less than 1", that means that equation is

[tex]{\Large \begin{array}{llll} y ~~ < - \cfrac{ 1 }{ 2 }x+1 \end{array}}[/tex]

now let's deal with the blue line.

same gig, we'll do a true/false region check, hmm let's pick for the sake of simplicity and slacking the same point, (0,0) which is above the blue line

[tex]y ~~ \square ~~ x-5\implies 0~~ \square ~~0-5\implies 0~~ \square ~~-5\implies 0\geqslant -5[/tex]

so only sign that makes that true is "⩾" for the blue line, because "0 is indeed greater or equal than -5", so we get

[tex]{\Large \begin{array}{llll} y \geqslant x-5 \end{array}}[/tex]

now, bear in mind that we could have pick some other point, on either side, and the issue is, to make it a true or false statement by using either inequality, for example if we end up with two values such as -9 [  ] -1, well, -9 is lesser than -1, so it can only be -9 < -1 or -9 ⩽ -1 to make it true, now if we want to make that statement false, we simply do -9 > -1 or such, and that part is "no shaded", because is false, -9 is not greater than -1.

The probability of selecting a $10 dollar bill or a $5 dollar bill would be = 13/23

Probability is defined as the expression that can be used to represent the possible outcome of an event which may likely occur or not.

The quantity of $1 bill = 10

The quantity of $5 bill = 10

The quantity of $10 bill = 3

The sum total of bills in the box = 23

The probability of choosing a 5 or 10 bills;

= 10+3/23

= 13/23

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With the identification of plans, angles, Rectangles, and segments, you can find the shoe box in the attachment.

Every point on a Plano has the same level because it is a space with only two dimensions.

The ángulos are a component of a plan that is created from two recitals with a common vertex. In the case of our shoe box, all angles are right-angled, despite the perspective appearing to be greater or smaller than 90 degrees.

Semirrectas are rectus with a known beginning but no known end. We can extend two segments in the shoe box so that they become semi-rectangles.

The segments are straight lines with clearly defined beginnings and end. All of the lines that form in the shoe box are segments.

The following is identified in the drawing.

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The Full question:

Consider a traditional and illustrated shoe box. This illustration indicates or names the following. ​

The function that best models the data table is; Option D: h(T) = -0.85t² + 1.63t + 1.51

A mathematical function model is defined as a mathematical description  by means of a function or an equation- of a real-world situation such as size of a population, demand for a product, speed of a falling object, life expectancy of a person at birth, or cost of emission reductions, etc.

From the table, we see that at time, t = 0 s, height(h) = 1.5 m.

Looking at the options, it means that options A and C cannot be correct.

Finally, at t = 1, h = 2.3. Plugging 1 for t in option D gives;

h(1) = -0.85(1²) + (1.63)1 + 1.51

= -0.85 + 3.12

= 2.27

This is approximately 2.3 and will be the correct option

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Answer:The rate of speed is the rate at which the total distance is traveled in the time taken.

The Space Explorer B travel 6.67 times faster than Space Explorer A.

What is rate of speed?

The rate of speed is the rate at which the total distance is traveled in the time taken. Rate of speed can be given as,

Here,  is the distance traveled by the object and  is time taken but the object to cover that distance.

Step-by-step explanation:The equation given in the problem is,

Here,  represented the number of miles that the satellite, Space Explorer B, flies in hours.

The satellite, Space Explorer A, flies 24000 miles in 20 hours.

The speed of the Space Explorer A, which flies 24000 miles in 20 hours is,

Thus the Space Explorer A, travels 1200 miles per hour.

As the Space Explorer B, travel is 8000 miles per hour and the Space Explorer A, travels 1200 miles per hour. Thus the ratio of the speed of both is,

Thus the Space Explorer B travel 6.67 times faster than Space Explorer A.

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The percentage score is 50%, for instance, if you get a test score of 50 out of 100. This can be calculated as follows: Percentage is (50/100) × 100, or 50. Proportion: A proportion is a statement indicating the equality of two ratios.

Two ratios are equal if they are equal by a certain proportion. Simply divide one part by the whole to get the proportion's ratio.

While percentage expresses a ratio or fraction with a constant denominator of 100, proportion expresses the equivalent of two ratios or fractions.

In order to express a component of a total as a fraction or a decimal, percentages and proportions are two related ideas. Here is how to determine each of them:

One technique to express a number as a fraction of 100 is to use a percentage. You multiply the part by 100 and divide by the whole to get a percentage. The formula to determine a percentage is as follows:

Percentage is equal to (Part/Whole) × 100.

To obtain the ratio and calculate a proportion, divide one part by the total. If you wish to know how many apples make up 25% of a collection of 20 apples, for instance, you can set up a proportion as follows:

Part / Whole = Percentage / 100

Part / 20 = 25 / 100

Part = (25 / 100) × 20 = 5

So, 25% of the collection is 5 apples.

In general, you can use these formulas to calculate percentages and proportions based on the information you have. The key is to always make sure you have the correct units and understand what the whole and part represent.

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The zeros are x = -5 and x = 1, and the graph can be seen at the end.

Here we have the quadratic function:

f(x) = (x + 5)*(x - 1)

The function is equal to zero when:

(x + 5)*(x - 1) = 0

And that happens if one of the two factors is zero, so:

x + 5 = 0  ----> x = -5

x - 1 = 0 -----> x= 1

So the function is equal to zero for x = -5 and x = 1, to graph them just graph the points (-5, 0) and (1, 0) on the coordinate axis.

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The circumference of the circle is 18.84 cm. Therefore, option C is the correct answer.

The circumference is the length of any great circle, the intersection of the sphere with any plane passing through its centre. A meridian is any great circle passing through a point designated a pole.

Given that, a circle has a diameter of 6 cm.

We know that, the formula to find the circumference of the circle is 2πr.

Here, radius = 6/2 =3 cm

Now, circumference = 2×3.14×3

= 18.84 cm

Therefore, option C is the correct answer.

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The value of integral ∫(0,8)  [4f(x) + 6g(x)] dx on the interval of (0,8) is 264

when ∫(0,8) f(x) dx = 39 and  ∫(0,8)g(x) dx =18.

Integration is a method of adding or summing up the parts to find the whole. It is a reverse process of differentiation, where we reduce the functions into parts.

Given that,

∫(0,8) f(x) dx = 39 and  ∫(0,8)g(x) dx =18

∫(0,8)  [4f(x) + 6g(x)] dx

Apply linearity rule of integration,

= ∫(0,8) 4f(x) dx + ∫(0,8) 6g(x) dx

=4 ∫(0,8) f(x) dx + 6∫(0,8) g(x) dx

= 4(39) + 6(18)

= 156 + 108

= 264

therefore, the value of integral ∫(0,8)  [4f(x) + 6g(x)] dx on the interval of (0,8) is 264

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Based on the sample data, there is a 95% chance that the true proportion of all smartphone users who would admit to walking into something or someone while texting on their cell phone is between 0.199 and 0.271.

A 95% confidence interval for the proportion of all smartphone users who would admit to walking into something or someone while texting on their cell phone can be calculated as follows:

Let p be the true proportion of all smartphone users who would admit to walking into something or someone while texting on their cell phone. Based on the sample of 750 respondents, the point estimate of p is 176/750 = 0.235.

Using the normal approximation to the binomial distribution, the standard error of the point estimate is estimated as [tex]\sqrt{ (p(1-p)/n)}[/tex], where n = 750. This gives us a standard error of [tex]\sqrt{(0.235 * 0.765/750)}[/tex] = 0.018.

A 95% confidence interval for the true proportion p is then given by the point estimate plus or minus 1.96 times the standard error. This gives us the following interval:

0.235 - 1.96 * 0.018 <= p <= 0.235 + 1.96 * 0.018

0.199 <= p <= 0.271

So, we are 95% confident that the true proportion of all smartphone users who would admit to walking into something or someone while texting on their cell phone is between 0.199 and 0.271.

Interpretation: Based on the sample data, there is a 95% chance that the true proportion of all smartphone users who would admit to walking into something or someone while texting on their cell phone is between 0.199 and 0.271.

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The percent of 125 is 25 when it is 20% and 70 is 14 when it is 20%

To determine the percentage, we have to divide the value by the total value and then multiply the resultant by 100.

To calculate the percentage of a number, we need to use a different formula such as:

P% of Number = X, where X is the required percentage.

If we remove the % sign, then we need to express the above formula as;

P/100 * Number = X

What percent of 125 is 25 and percent of 70 is 14?

Given:

To solve this, we need to set up a proportion. We know 25 is a certain percent of 125, and we want to find what that percent is.

So, we set up the proportion 25/125 = x/100, where x is the percent, we are looking for.

Now we can cross-multiply to solve for x.

We get 25 x 100 = 125 x, so x = [tex]\frac{25 \times 100}{125}[/tex], x = 20

Therefore, 25 is 20% of 125.

To solve this, we need to set up a proportion.

We know 14 is a certain percent of 70, and we want to find what that percent is.

So, we set up the proportion 14/70 = x/100, where x is the percent, we are looking for.

Now we can cross-multiply to solve for x.

We get 14 x 100 = 70 x

x = [tex]\frac{1400}{70}[/tex]

So, x = 20.

Therefore, 14 is 20% of 70.

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Answer: 19/20

Step-by-step explanation:

Probability of tomato spaghetti = tomato sauce and probability of spaghetti

Probability (tomato sauce) = 1/4
Probability (spaghetti) = 1/5
Probability (tomato spaghetti) = 1/4 x 1/5 = 1/20
Probability of not tomato spaghetti = 1- probability of tomato spaghetti
= 1 - 1/20  = 19/20

The nature and scope of the conclusion that a study can reach refers to the limitations and generalizability of the results obtained.

It depends on the research design, methodology, and sample size used. The conclusion can only be applied to the specific population and conditions studied.

The study may also have limitations due to biases or confounding variables that can affect the validity of the conclusion. To have a stronger conclusion, it is important to have a well-designed study with a large and representative sample, and to control for extraneous variables.

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Ken borrowed P8,077.84 from Haguel for a period of 2 years and a month.

To calculate the amount Ken borrowed,

We need to use the formula for compound interest:

A = P * (1 + r/n)^(nt)

Where:

A is the amount after t years

P is the principal amount (the amount borrowed)

r is the annual interest rate (8% in this case)

n is the number of times the interest is compounded in a year (4 times in this case, since the interest is compounded quarterly)

t is the number of years

We know the amount after 2 years and 1 month,

So we can use that information to solve for the principal amount P.

First, we need to convert the number of years and months into a single value in terms of years:

2 years and 1 month = 2 + 1/12 = 2.0833 years

Next, we can plug in the values into the formula:

A = P * (1 + r/n)^(nt)

A = P * (1 + 0.08/4)^(4 * 2.0833)

A = P * (1.02)^(8.3333)

A = P * 1.2288

We also know that Ken is paying P2,500 every 3 months,

So we can multiply that by 4 (since there are 4 quarters in a year) to find the annual payment:

P2,500 * 4 = P10,000

And we know that A = P * 1.2288,

So we can substitute in the values we have:

P10,000 = P * 1.2288

Now we can solve for P:

P = P10,000 / 1.2288

P = 8077.84

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The statistical test that Juan wants to use to test the hypothesis about the mean sales dollars among three shopping malls is an Analysis of Variance (ANOVA).

ANOVA is a hypothesis testing technique used to compare the means of multiple groups. In this case, the three shopping malls are the groups and the mean sales dollars are the variables. The purpose of ANOVA is to determine if there is a significant difference in the means of the groups.

ANOVA uses a null hypothesis that all the means are equal, and an alternative hypothesis that at least one mean is different. The test statistic calculated by ANOVA is the F-value, which is the ratio of the between-group variance to the within-group variance. If the F-value is large, it indicates that the differences between the means are significant, and therefore, the null hypothesis is rejected.

In conclusion, Juan can use ANOVA to test the hypothesis about the mean sales dollars among the three shopping malls. ANOVA provides a powerful tool to compare means across multiple groups and helps to determine if there are any significant differences between them.

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The vector parametric equations that describe the helical path you take from the point (28, 0, 0) to the point (28, 0, 40) as you make 4 revolutions during the time interval 0 ≤ t ≤ 1 are:

x(t) = 28 + 18 cos(πt / 15)

y(t) = 18 sin(πt / 15)

z(t) = 50t

To find a vector parametric equation for the helical path, we need to describe the position of a point on the spiral staircase as it moves from (28, 0, 0) to (28, 0, 40) while making 4 revolutions during the time interval 0 ≤ t ≤ 1.

Let's define the following parameters:

R: Radius of the spiral staircase = 18 feet

H: Height of the spiral staircase = 50 feet

N: Number of revolutions during the time interval = 4

T: Total time taken to complete N revolutions = 1 hour (or 60 minutes)

The parametric equations for the helical path can be given as follows:

x(t) = 28 + R × cos(2πNt/T)

y(t) = R × sin(2πNt/T)

z(t) = H × t

Where:

x(t), y(t), z(t) are the coordinates of the point on the helical path at time t.

R × cos(2πNt/T) and R × sin(2πNt/T) describe the circular motion of the point in the xy-plane as it makes N revolutions over the time interval.

H × t describes the linear motion of the point along the z-axis.

Now, let's plug in the given values:

R = 18 feet

H = 50 feet

N = 4

T = 60 minutes

And simplify the equations:

x(t) = 28 + 18 × cos(2π × 4t / 60)

y(t) = 18 × sin(2π × 4t / 60)

z(t) = 50 × t

Simplifying further:

x(t) = 28 + 18 × cos(π × t / 15)

y(t) = 18 × sin(π × t / 15)

z(t) = 50 × t

These equations describe the helical path you take from the point (28, 0, 0) to the point (28, 0, 40) as you make 4 revolutions during the time interval 0 ≤ t ≤ 1.

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Answer:

They are exactly the same size and shape

Step-by-step explanation:

The congruence postulates covered in this lesson are

- Side-Side-Side (SSS)

- Side-Angle-Side (SAS)

- Angle-Side-Angle (ASA)

- Angle-Angle-Side (AAS)

The product of the expression (a + b) and (a - 2b) will be a² - ab - 2b².

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

The expressions are given below.

(a + b) and (a - 2b)

Then the product of the expression is given as,

⇒ (a + b)(a - 2b)

⇒ a² - 2ab + ab - 2b²

⇒ a² - ab - 2b²

The product of the expression (a + b) and (a - 2b) will be a² - ab - 2b².

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To choose the best option for the company, it is important to consider the total amount of interest that will be paid over the life of the loan.

With the 30-year loan, the total interest paid over the life of the loan will be higher than with the 15-year loan, because the interest rate is higher and the loan is paid over a longer period of time.

However, the shorter loan term means that the monthly payments are higher, which could be a financial burden for the company. Therefore, it is important to compare the total interest paid over the life of the loan for both options to determine which is the best option for the company.

Complete question:

A company i planning to purchae a plot of land for $200,000 to build a factory there are two option offered by a lending intitution. The first option is to make a down payment of $200,000 and take a $600,000 30-year mortgage loan with an interest rate of 3.5%. The second option is to make a $100,000 down payment and take a $700,000 15-year mortgage loan with an interest rate of 3.0%.

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Answer:

To calculate the monthly payment for a loan, you can use the following formula: P = L[c(1 + c)^n]/[(1 + c)^n – 1]

Step-by-step explanation:

See the attachment for detail

The first pair of numbers is a decimal number and a large whole number. The second pair is a large whole number and decimal number. The third pair is a smaller whole number and the same decimal as the second pair.

The first pair of numbers is 4.24 and 3150. This means that 4.24 is a decimal number and 3150 is a large whole number. In order to understand this pair of numbers, it is important to know how to read decimal numbers. A decimal number is written with a decimal point that separates the whole number part from the fractional part. The number 4.24 is read as "four and twenty-four hundredths", which means that 4.24 is 4 whole numbers and 24 hundredths. The second pair of numbers is 345 and 4.240. This is a large whole number and another decimal number. In this pair, 345 is the large whole number and 4.240 is the decimal number. To read 4.240, first read the whole number part (4) and then the fractional part (240). This means that 4.240 is read as "four and two hundred and forty thousandths". The third pair of numbers is 45 and 4.240. This is a smaller whole number and the same decimal as the second pair. To read 4.240 in this pair, it is the same as reading it in the second pair. This means that 4.240 is read as "four and two hundred and forty thousandths".

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For the velocity function v(t) = t³ - 3t² + 12t + 4, with interval 0 ≤ t ≤ 3, the maximum acceleration is option D: 21 m/s².

What is velocity?

The pace at which an object's position changes in relation to a frame of reference and time is what is meant by velocity. Although it may appear sophisticated, velocity is just the act of moving quickly in one direction. Since it is a vector quantity, the definition of velocity requires both magnitude (speed) and direction.

The velocity function is v(t) = t³ - 3t² + 12t + 4.

The interval is given as - [0,3]

Maximize the function to obtain the value of t.

v'(t) = a(t) = 3t² - 6t + 12

Maximize it again -

a'(t) = 6t - 6 = 0

6t = 0 + 6

t = 6/6

t = 1

Now there are three critical points for t = {0,1,3}

1 and 3 are endpoints of the interval [0,3].

To get the maximum acceleration, plug in the values of t in the equation .

First substitute the value t = 0 -

a(0) = 3t² - 6t + 12

a(0) = 3(0)² - 6(0) + 12

a(0) = 12

Now substitute the value t = 1 -

a(1) = 3t² - 6t + 12

a(1) = 3(1)² - 6(1) + 12

a(1) = 3 - 6 + 12

a(1) = 15 - 6

a(1) = 9

Now substitute the value t = 3 -

a(3) = 3t² - 6t + 12

a(3) = 3(3)² - 6(3) + 12

a(3) = 27 - 18 + 12

a(3) = 39 - 18

a(3) = 21

So, the maximum acceleration is 21 m/s² when t =3.

Therefore, the maximum acceleration is 21 m/s².

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Ji-Yoon's loading speed is 6 trucks per hour.

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

Ji-Yoon loaded 84 Trucks in 14 hours

Ji-Yoon's loading speed an be calculated by dividing the total number of trucks loaded (84) by the number of hours it took to load them (14):

This is repesented as

84/14 = 6

Hence, the speed is 6 trucks per hour

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Answer:

6

Step-by-step explanation:

If 5r+25=30, r=1. Therefore, r+5 would be 6.

Answer:

r has to be equal to 1, because 5 + 25 = 30, so r would be equal to 1 because 1 * 5 = 5 therefore the value will not change.

Now that we know that r = 1, the answer to r + 5 =

1 + 5 = 6

Step-by-step explanation:

Hope it helps! =D

Let P(t)=36(1−e^(−kt))+56 represent the expected core for a student who studied t hour for a test, suppose k=0. 24 so student scored 56% without studying.

If the student don't study then,

It corresponds to t= 0 .

We can evaluate the function with the t=0 so we can have

P(t) = 36(1−e^(−kt)) + 56

were k = 0.24

P(0) = 36 (1 - [tex]e^{0.24(t)}[/tex]) + 56

= 36 (1 - [tex]e^{0.24(0)}[/tex]) + 56

= 36 (1 - 1 ) + 56

=56%

Therefore, Let P(t)=36(1−e^(−kt))+56 represent the expected core for a student who studied t hour for a test is 56%.

The derivative of a function of a real variable in mathematics quantifies the sensitivity of the function's value (output value) to changes in its argument (input value). Calculus's core tool is the derivative. The velocity of an item, for instance, is the derivative of its position with respect to time; it quantifies how quickly the object's position varies as time passes.

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For the given triangles ΔABC ≈ ΔADE, the measurement  of angle ACB is, 87°

Triangles with the same shape but different sizes are said to be similar triangles. Squares with any side length and all equilateral triangles are examples of related objects. In other words, if two triangles are similar, their corresponding sides are proportionately equal and their corresponding angles are congruent. Triangle resemblance is shown here by the symbol "≈"

Given that,

One triangle, ΔABC

one segment DE which is intersecting sides AB & AC

ΔABC has one similar triangle inside, which is ΔADE

Triangle ΔABC and ΔADE similar,

So, we can say ΔABC ≈ ΔADE

And it is known that

for similar triangles, ratio of corresponding angles of both the triangles are equal for similar triangles

so, ∠DAE/∠AED  = ∠CAB/∠ABC

⇒  62°/(11x -2)°  =  62°/(6x + 13)°

⇒  (11x -2)°  = (6x + 13)°

⇒   11x - 6x = 13 + 2

⇒    5x  = 15

⇒      x = 3

So,

∠ADE = 11x - 2 = 11 x 3 - 2 = 31°   =  ∠ABC

It is known that,

Sum of all the interior angles of triangle is 180°

Now,

∠ACB + ∠CAB + ∠ABC = 180°

∠ACB + 62° + 31°  = 180°

∠ACB  = 180° - 93°

           =  87°

Hence, the angle ACB is 87°

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The equation would be written in exponential form as follows: [tex]$$\ln(m) = n \Rightarrow m = e^n$$[/tex]

The equation ln(m)=n can be rewritten in exponential form as m=e^n. This can be seen by taking the natural logarithm (ln) of both sides of the equation. The natural logarithm of m is equal to n, so we have ln(m)=n. Applying the exponential function, e^x, to both sides of the equation gives us m=e^n. This can be further understood by calculating the exponential of both sides.

For example, if n = 1, then ln(m)=1, so m=e^1. Applying the exponential function, e^x, to both sides of the equation, we have m=e^1. Calculating e^1 gives us m=e^1=2.718. Thus, ln(m)=1 can be rewritten in exponential form as m=2.718.

The equation in Latex would be written as follows: [tex]$$\ln(m) = n \Rightarrow m = e^n$$[/tex]

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