PLEASE HELP!!
x y
0.8 2.7
1.3 6.1
2.2 9.4
2.9 9.4
3.7 33
5.1 49.9
9) The EXPONENTIAL curve-of-best-fit for the data in the table is given by the equation y = a·b^x, where
A) a = 2.04 and b = 0.75.
B) a = 2.17 and b = 1.95.
C) a = 3.64 and b = 1.57.
D) a = 4.34 and b = 0.15.

Answer:

(a) Maximax criterion: Order 200 books.

(b) Maximin criterion: Order 200 books.

(c) Equally likely criterion: Order 200 books.

(d) Criterion of realism with a = 0.7: Calculate the expected payoff based on the chosen value of a and select the corresponding option.

(e) Minimax regret criterion: Order 200 books.

Step-by-step explanation:

The maximax criterion involves selecting the option with the highest possible payoff. We will calculate the maximum payoff for each option and choose the one with the highest value.Payoff for ordering 50 books:

Revenue = 30 * 50 = $1500

Maximum payoff = $1500Payoff for ordering 100 books:

Revenue = 30 * 100 = $3000

Maximum payoff = $3000Payoff for ordering 150 books:

Revenue = 30 * 150 = $4500

Maximum payoff = $4500Payoff for ordering 200 books:

Revenue = 30 * 200 = $6000

Maximum payoff = $6000Based on the maximax criterion, Waldo should choose the option of ordering 200 books since it has the highest maximum payoff.(b) Maximin Criterion:

The maximin criterion involves selecting the option with the highest minimum payoff. We will calculate the minimum payoff for each option and choose the one with the highest value.Payoff for ordering 50 books:

Revenue = 30 * 50 - (20 * 50 - 4 * 50) = $900

Minimum payoff = $900Payoff for ordering 100 books:

Revenue = 30 * 100 - (20 * 100 - 4 * 100) = $1800

Minimum payoff = $1800Payoff for ordering 150 books:

Revenue = 30 * 150 - (20 * 150 - 4 * 150) = $2700

Minimum payoff = $2700Payoff for ordering 200 books:

Revenue = 30 * 200 - (20 * 200 - 4 * 200) = $3600

Minimum payoff = $3600Based on the maximin criterion, Waldo should choose the option of ordering 200 books since it has the highest minimum payoff.(c) Equally Likely Criterion:

The equally likely criterion assumes that each demand level is equally likely to occur. We will calculate the expected payoff for each option and choose the one with the highest value.Expected payoff for ordering 50 books:

Expected revenue = (30 * 50 + 4 * (50 - 50)) / 4 = $375

Expected payoff = $375Expected payoff for ordering 100 books:

Expected revenue = (30 * 100 + 4 * (50 - 100)) / 4 = $750

Expected payoff = $750Expected payoff for ordering 150 books:

Expected revenue = (30 * 150 + 4 * (50 - 150)) / 4 = $1125

Expected payoff = $1125Expected payoff for ordering 200 books:

Expected revenue = (30 * 200 + 4 * (50 - 200)) / 4 = $1500

Expected payoff = $1500Based on the equally likely criterion, Waldo should choose the option of ordering 200 books since it has the highest expected payoff.(d) Criterion of Realism with a = 0.7:

The criterion of realism involves assigning a weight (0 ≤ a ≤ 1) to the optimistic payoff and the remaining weight (1 - a) to the pessimistic payoff. We will calculate the expected payoff for each option using the given value of a and choose the one with the highest value.Expected payoff for ordering 50 books:

Expected revenue = a * (30 * 50) + (1 - a) * (30 * 50 - 20 * 50 + 4 * 50) = $450a

Expected payoff = $450aExpected payoff for ordering 100 books:

Expected revenue = a * (30 * 100) + (1 - a) * (30 * 100 - 20 * 100 + 4 * 100) = $900a

Expected payoff = $900aExpected payoff for ordering 150 books:

Expected revenue = a * (30 * 150) + (1 - a) * (30 * 150 - 20 * 150 + 4 * 150) = $1350a

Expected payoff = $1350aExpected payoff for ordering 200 books:

Expected revenue = a * (30 * 200) + (1 - a) * (30 * 200 - 20 * 200 + 4 * 200) = $1800a

Expected payoff = $1800aTo find the maximum expected payoff, we can compare the values of a * 450, a * 900, a * 1350, and a * 1800 for different values of a. The optimal value of a will determine the corresponding option.(e) Minimax Regret Criterion:

The minimax regret criterion involves calculating the regret for each option and selecting the one with the minimum regret. Regret represents the difference between the maximum possible payoff and the actual payoff.Regret for ordering 50 books:

Regret = 6000 - (30 * 50 - (20 * 50 - 4 * 50)) = $5250

Minimum regret = $5250Regret for ordering 100 books:

Regret = 6000 - (30 * 100 - (20 * 100 - 4 * 100)) = $4200

Minimum regret = $4200Regret for ordering 150 books:

Regret = 6000 - (30 * 150 - (20 * 150 - 4 * 150)) = $3150

Minimum regret = $3150Regret for ordering 200 books:

Regret = 6000 - (30 * 200 - (20 * 200 - 4 * 200)) = $2100

Minimum regret = $2100Based on the minimax regret criterion, Waldo should choose the option of ordering 200 books since it has the minimum regret.

Waldo Books is facing a decision theory problem. By different criteria, the decision to order books can change. By maximax, Waldo should order 200 books, by maximin, 50 books. By equally likely, realism, and minimax regret criteria, computations considering payoffs, optimism levels, and potential regrets are needed.

This is a "decision theory problem" in the field of business and economics. Let's calculate the profit from each option. Profit will be $10 for each book sold (revenue of $30 minus cost of $20) and a loss of $16 for each book not sold (cost of $20 minus resell value of $4).

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The derivative function for equations 1 and 2 will be

y' = -1/ [2√(1-x²)] and y' = 3/[2(1 + x²)] respectively

Here we need to find the derivative of

\(y = tan^{-1}\sqrt{\frac{1-x}{1+x} }\)

Let x = cos2z

Hence we get

\(y = tan^{-1}\sqrt{\frac{1-cos2z}{1+cos2z} }\)

\(or, y = tan^{-1}\sqrt{\frac{2sin^{2}z}{2cos^{2}z} }\)

\(or, y = tan^{-1}(tanz)\)

or, y = z

Hence dy/dx = dz/dx

We know that

x = cos2z

or, 2z = cos⁻¹x

or, 2 dz/dx = -1/√(1-x²)

Hence dy/dx = -1/ [2√(1-x²)]

The second equation is

\(y = 3tan^{-1}[x-\sqrt{1+x^{2}} ]\)

Let x = cotz

Hence we get

\(y = 3tan^{-1}[cotz-\sqrt{1+cot^{2}z} ]\)

\(y = 3tan^{-1}[cotz-\sqrt{cosec^{2}z} ]\)

or, y = 3tan⁻¹ [cotz - cosecz]

or, y = 3tan⁻¹ [cosz/sinx - 1/sinz]

or, y = 3tan⁻¹ [(cosz - 1)/sinz]

or, y = 3tan⁻¹ [-2sin²(z/2)/{2sin(z/2) cos(z/2)}]

or, y = 3tan⁻¹ [-sin(z/2)/cos(z/2)]

or, y = 3tan⁻¹ [-tan{z/2)]

or, y = 3tan⁻¹ [tan{-z/2)]

or, y = -3z/2

or, dy/dz = -3/2 dz/dx

We have

x = cotz

or, z = cot⁻¹z

or, dz/dx = -1/(1 + x²)

Hence we get

dy/dx = 3/[2(1 + x²)]

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Answer:

4x+24

Step-by-step explanation:

4*x+4*6

Answer:

y=1/4x-7

Step-by-step explanation:

y-y1=m(x-x1)

y-(-8)=1/4(x-(-4))

y+8=1/4(x+4)

y=1/4x+4/4-8

y=1/4x+1-8

y=1/4x-7

Answer:

every year the branches increase 75%

Step-by-step explanation:

Answer:

I think it is 0.257 kg

Step-by-step explanation:

To change units from the gram to kilogram, you need to divide by 1000, because 1kg=1000g:

257÷1000= 0.257 Kg

The mass of the fruits in kilogram (kg) is 3.556 kg

Given:

Mass of the bag containing fruits = 3.813 kg

Mass of the empty bag = 257 g

convert

257 g to kg

257 g = 0.257 kg

Mass of the bc fruits = Mass of the bag containing fruits - Mass of the empty bag

= 3.813 kg - 0.257 kg

= 3.556 kg

Therefore, the mass of the fruits in kilogram is 3.556 kg

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The only Inequality in which 4 is the lowest integer value that x could take is:x ≥ 4

To determine the inequalities in which 4 is the lowest integer value that x could take, we need to consider the conditions where x is greater than or equal to 4.

1) x ≥ 4: This inequality includes all values of x that are greater than or equal to 4, so 4 is indeed the lowest integer value that x could take.

2) x > 4: This inequality includes all values of x that are strictly greater than 4, excluding the value 4 itself. Therefore, it does not satisfy the condition that 4 is the lowest integer value that x could take.

3) x ≥ 4.5: This inequality includes all values of x that are greater than or equal to 4.5, which is not an integer value. Therefore, it does not satisfy the condition that 4 is the lowest integer value that x could take.

4) x > 3: This inequality includes all values of x that are strictly greater than 3, which does not guarantee that 4 is the lowest integer value that x could take.

Therefore, the only inequality in which 4 is the lowest integer value that x could take is:

x ≥ 4

This inequality ensures that x is greater than or equal to 4, making 4 the lowest possible integer value for x.

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since we cannot have a fraction of a serving, we can only make 9 servings of soup with 2 quarts (or 8 cups) of chicken broth.  Therefore, the proportion we should use is 5 cups of chicken broth to 6 servings of soup.

To answer this question, we need to convert 2 quarts to cups. Since there are 4 cups in a quart, 2 quarts would be 8 cups.

Now that we know we have 8 cups of chicken broth, we can set up a proportion to determine how many servings of soup we can make.

5 cups of chicken broth = 6 servings of soup

x cups of chicken broth = y servings of soup

To solve for x and y, we can cross-multiply:

5y = 6x

x = 8 cups of chicken broth

y = (6/5) * 8 = 9.6 servings of soup

However, since we cannot have a fraction of a serving, we can only make 9 servings of soup with 2 quarts (or 8 cups) of chicken broth.

Therefore, the proportion we should use is 5 cups of chicken broth to 6 servings of soup.

 To determine how many servings you can make with 2 quarts of chicken broth, you should set up a proportion using the given information: 6 servings require 5 cups of broth. First, convert 2 quarts to cups (1 quart = 4 cups, so 2 quarts = 8 cups). Now, set up the proportion:

6 servings / 5 cups = x servings / 8 cups

Here, x represents the number of servings you can make with 8 cups (2 quarts) of chicken broth. By cross-multiplying and solving for x, you will find the number of servings possible with the available broth.

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The confidence interval (149.2, 206.4) can be written as ¯x ± me, where ¯x = 177.8 and me = 28.6. The sample mean (¯x) is the midpoint of the confidence interval

To express the confidence interval (149.2, 206.4) in the form of ¯x ± me, we need to calculate the sample mean (¯x) and the margin of error (me).

The sample mean (¯x) is the midpoint of the confidence interval and can be calculated by taking the average of the upper and lower bounds of the interval:

¯x = (149.2 + 206.4) / 2 = 177.8

Next, we calculate the margin of error (me) by finding the half-width of the confidence interval:

me = (206.4 - 149.2) / 2 = 28.6

Therefore, the confidence interval (149.2, 206.4) can be expressed in the form of ¯x ± me as:

¯x ± me = 177.8 ± 28.6

Hence, the confidence interval (149.2, 206.4) can be written as ¯x ± me, where ¯x = 177.8 and me = 28.6.

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The probability that a randomly chosen toaster will have a total resistance of 345-355 ohms is approximately 0.7996, or 79.96%.

To find the probability that a randomly selected toaster will have a total resistance of 345 to 355 ohms, we need to know the distribution of total resistance and parameters such as mean and standard deviation.

Expecting that the dispersion of add up to resistance takes after a typical conveyance with cruel μ and standard deviation σ, ready to utilize the standard ordinary dispersion to calculate the likelihood that the entire resistance will be between 345 and 355 ohms.

 First, we need to normalize the 345 and 355 values ​​with the following formula:

z = (x - μ) / σ

where x=desired value, μ = mean, σ = standard deviation, and z =corresponding z-score.

For x = 345 ohms:

z1 = (345 - μ) / σ

For x = 355 ohms:

z2 = (355 - μ) / σ

Next, we need to find the area under the standard normal distribution curve between z-scores z1 and z2. This represents the probability that the total resistance will be between 345 and 355 ohms.

You can find this range using a standard regular table or calculator. For example, using the standard normal table, we can find the region between z1 and z2 like this:

P(345 ≤ x ≤ 355) = P(z1 ≤ z ≤ z2) = Φ(z2) - Φ(z1)

where Φ(z) is the standard cumulative normal distribution function (CDF), the probability that a standard normal random variable is less than or equal to z.

For example, if z1 = -1.5 and z2 = 1.5, then

P(345 ≤ x ≤ 355) = P(z1 ≤ z ≤ z2) = Φ(1.5) - Φ(-1.5) = 0.8664 - 0.0668 ≈ 0.7996

Therefore, the probability that a randomly chosen toaster will have a total resistance of 345-355 ohms is approximately 0.7996, or 79.96% (assuming the distribution of total resistance follows a normal distribution with a known mean and standard deviation).

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There are nC2 different votes possible, where n is the number of bands on the list and nC2 represents the number of ways to choose 2 bands out of n.

To calculate nC2, we can use the formula for combinations, which is given by n! / (2! * (n-2)!), where ! represents factorial.

Let's say there are m bands on the list. The number of ways to choose 2 bands out of m can be calculated as m! / (2! * (m-2)!). Simplifying this expression further, we get m * (m-1) / 2.

Therefore, the number of different votes possible is m * (m-1) / 2.

In the given scenario, we don't have the specific number of bands on the list, so we cannot provide an exact number of different votes. However, you can calculate it by substituting the appropriate value of m into the formula m * (m-1) / 2.

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The solution is, B) yes; -2/3, i.e. a proportional relationship exists & -2/3  is the constant ratio of y/x .

The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.

here, we have,

if it is proportional

then.,

y = kx

so, we get,

-2 = 3 k ⇒ k= (-2/3)

-4 = 6 k ⇒ k= (-2/3)

-8 = 12k ⇒ k= (-2/3)

Hence, The solution is, B) yes; -2/3, i.e. a proportional relationship exists & -2/3  is the constant ratio of y/x .

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Answer:

AC = 10

Step-by-step explanation:

We can use proportions to solve

AB         AC

------ = -----------

DE        DF

5        AC

---- = -------

3        6

Using cross products

5*6 = 3 AC

30 = 3AC

Divide by 3

30/3 = AC

10 = AC

Answer:

Step-by-step explanation:

❁ Hello! ❁

AB/DE = AC/DF => 5/3 = AC/6

5/3 = AC/6

5 × 6 = 3 × AC

30 = 3 × AC

30 ÷ 3 = AC

10 = AC

Success! ☺️

Answer:

x=12

Step-by-step explanation:

Since b would equal E

We can make an equation.

x^2 -5x = 84

So that can be solved down to

x^2 -5x -84= 0

(x-12)(x+7)=0

x=12

x=-7

Now we see which one equals 84.

(12)^2 -5(12)=84

-7^2-5(-7)=14

therefore 12 is the correct answer and -7 does not work.

Question :

justinapace7446

Yesterday

Mathematics

High School

+5 pts

Choco pies are cookies made from chocolate (c), sugar (s), and flour (. Chocolate costs $5 per pound, sugar costs

$3 per pound, and flour costs $2 per pound. You spend $50 on 18 pounds of food and buy twice as much flour as

sugar

Calvin wants to invest $12,000 in deposits. For tax purposes, he wants his total interest to be $600. He wants to put

$1000 more in a 2-year deposit than in a l-year deposit and invest the rest in a 3-year deposit. How much money

should he invest in each deposit?

Number of Years

Rate

2.0%

5.0%

6.0%

Answer:

1-year: $2200, 2-year: $3200, 3-year: $6600

Step-by-step explanation:

Assume y = Amount invested for 1 year.

y + 1000 = investment amount for 2 years

12000 - (y + y + 1000 ) = amount invested for 3 years

11000 - 2y = amount invested for 3 years

Total interest

Multiplying each by its corresponding rate

(0.02 × y) + (0.05 × (y+1000)) + (0.06 × (11000-2y)) = 600

0.02y + 0.05y + 50 + 660 - 0.12y = 600

-0.05y + 710 = 600

-0.05y = 600 - 710

-0.05y = - 110

y = 2200

Therefore first year = y = $2200

Investment for 2 years =y + 1000 = 2200 + 1000 = $3200

Investment for 3 years = 11000 - 2y = (11000 - (2*2200)) = (11000 - 4400) = $6600

Step 1: V(X+Y) = V(X) + V(Y)

Step 2: To show that V(X+Y) = V(X) + V(Y) when the correlation coefficient between X and Y is 1, we can start by using the definition of variance. The variance of a random variable X is defined as V(X) = E[(X - E(X))^2], where E(X) is the expected value of X.

Using this definition, we can expand V(X+Y) as follows:

V(X+Y) = E[((X+Y) - E(X+Y))²]

      = E[(X+Y - E(X) - E(Y))²]

      = E[(X - E(X))² + 2(X - E(X))(Y - E(Y)) + (Y - E(Y))²]

      = E[(X - E(X))²] + 2E[(X - E(X))(Y - E(Y))] + E[(Y - E(Y))²]

      = V(X) + 2Cov(X,Y) + V(Y)

Since the correlation coefficient between X and Y is 1, Cov(X,Y) = σ(X,Y) / (σ(X) * σ(Y)) = σ(X) / (σ(X) * σ(Y)) = 1 / σ(Y), where σ(X,Y) is the covariance between X and Y, σ(X) is the standard deviation of X, and σ(Y) is the standard deviation of Y.

Therefore, V(X+Y) = V(X) + 2(1/σ(Y)) + V(Y) = V(X) + V(Y).

Step 3: When the correlation coefficient between two random variables is 1, it means that the variables have a perfect positive linear relationship. In this case, the variance of their sum, V(X+Y), can be expressed as the sum of their individual variances, V(X) and V(Y). This result holds because when two variables are perfectly correlated, any change in one variable is accompanied by an equal change in the other, resulting in their variances adding up.

Regarding the game where you draw one card from a standard deck, the outcome and payouts depend on the probabilities associated with each event. If you calculate the probabilities of drawing a face card of hearts, a non-face heart card, or any other card, and multiply them by their respective payouts or losses, you can determine the expected value of the game. If the expected value is positive, it would be advantageous to play the game as, on average, you would gain money. If the expected value is negative, it would be disadvantageous to play as, on average, you would lose money. Therefore, a decision to play the game or not depends on the calculated expected value.

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There are 4 variable terms in the given expression 3x³y + 5x² - 4y + z + 9,

The expression which was given to us is 3x³y + 5x² - 4y + z + 9, we have to find the number of terms which are variables in this expression

A variable is something whose value is not fixed and can be changed anytime and generally, we assign letters like x, y, and z as variable names

In 3x³y, we can see that x³y is a variable term

In 5x², we can see that x² is a variable term

In 4y, we can see that y is a variable term

In the 4th term, we can see that z is a variable term

The variable terms are x³y,  x²,  y,  z

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Based on the data given by the table on the number of lines of codes written per people are working, the best model would be y = 27x - 4.

The best model would be the one that gives y values that are closest to the number of codes written hourly per number of people working.

That model would be y = 27x - 4 which gives the results:

x                    Predicted y

2                         50

4                        104

6                         158

8                         212

10                        266

12                        320

These predicted y values are the closest to the actual y values which makes this the best model.

Full question is:

The table shows the estimated number of lines of code written by computer programmers per hour when x people are working. A 2-column table with 6 rows. The first column is labeled people working with entries 2, 4, 6, 8, 10, 12. The second column is labeled lines of code written hourly with entries 50, 110, 160, 210, 270, 320.

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Answer:

D. y=27x-4

Step-by-step explanation:

I just took the test on Edge

Answer:

For a Cylinder It is a circle, For a  rectangular prism it is a square  rectangular pyramid  a cross section is a rectangle

Step-by-step explanation:

I basically told you the answer so

Hope this helps :)

The solution is, b. x² = 12(y + 3) equation represents a parabola that has a focus of (0, 0) and a directrix of y = −6

The parabola is a plane curve which is mirror symmetrical and is approximately U-shaped. It fits several superficial different mathematical descriptions.

here, we have,

If the focus is (0,0) and the  directrix  is y=-6, the equation will be found as follows:

Let (x,y) be any point on the parabola. Find the distance between (x,y) and the directrix, then find the distance between (x,y) and the focus. Equate these two distance equations and the simplified equation in x and y is equation of the parabola.

The distance between (x,y) and (0,0) is √(x²+y²)

The distance between (x,y) and the directrix, y=-6 is ly+6l

Equate the two distance expressions and square on both sides

√(x²+y²)=ly+6l

x²+y²=(y+6)²

simplifying and bringing terms together we get:

x²-12y-36=0

make x² the subject:

x²=12y+36

x²=12(y+3)

Hence, Answer :b. x² = 12(y + 3)

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complete question:

Which equation represents a parabola that has a focus of (0, 0) and a directrix of y = −6 ?

a. x² = 12y

b. x² = 12(y + 3)

c. x² = −3y

d. x² = −3(y + 3)

Answer:

C

Step-by-step explanation:

Answer:

283038 or 2.83038×10⁵

Step-by-step explanation:

In an arithmetic sequence, the difference between every pair of consecutive terms in the sequence is the same.

The general formula for the nth term of an arithmetic sequence is:

aₙ = a + (n - 1)d

where:

a is first term

n is position of term

d is common difference

Thus, we see that the difference between consecutive terms is always the same as common difference.

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Hay 1200 gomas de borrar en total en las 4 cajas.

Para saber la cantidad de gomas de borrar que hay en 4 cajas, Don Jacinto necesita multiplicar la cantidad de gomas de borrar en cada caja (300) por la cantidad de cajas (4).

La operación que debe hacer es:

300 * 4

El resultado de esta multiplicación es:

300 * 4 = 1200

Es importante notar que en el escenario dado, la información inicial acerca de que Don Jacinto tiene 230 cuadernos no es relevante para encontrar el número de borradores en las 4 cajas. Solo necesitamos considerar el número de gomas de borrar en cada cuadro (300) y el número de cajas (4) para realizar la multiplicación y calcular el número total de gomas.

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Answer:

a. 1/4

b. 13/51

c. 12/51

Step-by-step explanation:

Note:
The formula to find probability is:

P(A) = n(A) / n(S)

where:

For question:

a.

There are 13 hearts in a standard deck of 52 cards, so the probability of drawing a heart is 13/52.

The probability that the first card drawn is a heart is 13/52 = 1/4.

b.

Since the first card was not a heart, there are 13 hearts left in the deck. There are also 51 cards left in the deck overall, so the probability of drawing a heart is 13/51.

The probability that the second card drawn is a heart given that the first card drawn was not a heart is 13/51.

c.

Since the first card was a heart, there are 12 hearts left in the deck. There are also 51 cards left in the deck overall, so the probability of drawing a heart is 12/51.

The probability that the second card drawn is a heart given that the first card drawn was a heart is 12/51.

After evaluating the limit  lim x→0 \(x^2+5x-14/x-2\), we got limit of the expression x²+5x-14/x-2 as x approaches 0 is equal to 5.

To evaluate the limit lim x→0 x²+5x-14/x-2, one can use various methods such as direct substitution, factoring, or L'Hopital's rule.Direct substitution: When we substitute 0 for x in the expression x²+5x-14/x-2, we get an indeterminate form of 0/0. This indicates that direct substitution cannot be used to find the limit.Factoring: The expression can be factored as (x-2)(x+7)/(x-2).

Simplifying the expression, we get x+7 as the limit as x approaches 0. Hence, the limit is 7. L'Hopital's rule: This rule states that if the limit of a function f(x)/g(x) as x approaches a is of the form 0/0 or ∞/∞, then the limit can be evaluated by differentiating both f(x) and g(x) with respect to x, evaluating the limit of their ratio as x approaches a and taking the limit again.

Using L'Hopital's rule, we getlim x→0 x²+5x-14/x-2= lim x→0 (2x+5)/(1)=5/1=5Therefore, the limit of the expression x²+5x-14/x-2 as x approaches 0 is equal to 5.

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The base of the triangle is 15 meters.

Here, we are given that the height of a triangle is 5 m longer than the base.

Let the height of the triangle be h

Then, the base of the triangle will be = h - 5

Further, we are given that area of the triangle = 150 meter square

We know that area of a triangle = 1/2 × base × height

⇒ 150 = 1/2 × h × (h-5)

150 × 2 = h(h-5)

300 = \(h^{2}\) - 5h

\(h^{2}\) - 5h - 300 = 0

Now, we solve the above quadratic equation by splitting the middle term.

\(h^{2}\) + 15h - 20h - 300 = 0

h( h + 15) - 20( h + 15) = 0

(h - 20) (h + 15) = 0

Thus, h = 20 or -15

But since height cannot be negative, h = 20

⇒ base = h - 5

= 20 - 5

= 15 meters

Thus, the base of the triangle is 15 meters.

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