Find the value of c that makes x²-4x+c a perfect square.​

To use this method, you can call it in the main method like this:
numInverter.swapArrayEnds(sortedArray);
This will swap the first and last elements of the sortedArray.

Here is a solution for the swapArrayEnds() method:

public void swapArrayEnds(int[] arrayVals) {
  // Check if array has at least 2 elements
  if (arrayVals.length >= 2) {
     int temp = arrayVals[0]; // Store first element in temp variable
     arrayVals[0] = arrayVals[arrayVals.length-1]; // Replace first element with last element
     arrayVals[arrayVals.length-1] = temp; // Replace last element with temp variable
  }
}

This method takes an integer array as a parameter and swaps the first and last elements of the array. It first checks if the array has at least 2 elements to avoid swapping the same element. It then stores the first element in a temporary variable, replaces the first element with the last element, and replaces the last element with the temporary variable.

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Explanation:

[tex]33ft^2[/tex] is the area of a 2D figure.

[tex]33ft^3[/tex] is the volume of a 3D object.

ft^2 = area

ft^3 = volume

It would take approximately 176,369 pounds of TNT to destroy an abatis made of 72 trees with an average diameter of 30 inches, assuming an average height of 20 feet.

The formula for the volume of a cylinder is V = πr^2h. In this case, we can use the average radius of 15 inches and the average height of 240 inches to estimate the total volume of all 72 trees:

Total volume of all 72 trees = 72 x V

Total volume of all 72 trees = 72 x 169,646

Total volume of all 72 trees ≈ 12,214,832 cubic inches

In this equation, we need to know the density of wood and the REF of TNT. The density of wood can vary depending on the species, but we can use an average value of 0.5 grams per cubic centimeter (g/cm^3). The REF of TNT is 1, by definition. The factor of 0.8 in the equation accounts for losses due to fragmentation and other factors.

Converting the units of volume and density to match, we get:

Total volume of all 72 trees ≈ 200,000,000 cubic centimeters

Density of wood = 0.5 g/cm³

Plugging these values into the equation, we get:

Amount of TNT required = (Total volume of all 72 trees x Density of wood x 0.8) / REF

Amount of TNT required = (200,000,000 x 0.5 x 0.8) / 1

Amount of TNT required = 80,000,000 grams

To convert grams to pounds, we divide by 453.592, which is the number of grams in a pound:

Amount of TNT required = 80,000,000 / 453.592

Amount of TNT required ≈ 176,369 pounds

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Answer:

We can start by converting 1 1/4 to an improper fraction:

1 1/4 = 5/4

Now, we can subtract 5/4 from 4:

4 - 5/4 = 16/4 - 5/4 = 11/4

Therefore, the difference between 4 and 1 1/4 is 11/4. To write the answer in simplest form, we can simplify the fraction by dividing both the numerator and denominator by their greatest common factor (GCF), which is 1:

11/4 ÷ 1/1 = 11/4

So the final answer is 2 3/4 (option D).

Answer:

1) (1/2)(18)(9√3) = 81√3 square meters

2) 16^2 = 256 square meters

3) (1/2)(2)(9/√3)(6)(9) = 486/√3 =

162√3 square meters

4) (1/2)(2)(13√3)(3)(13) =

507√3 square meters

5) (2(14/√2))^2 = 4(196/2) = 4(98) =

392 square meters

6) (1/2)(4)(6)(2√3) = 24√3 square meters

The diagonal through the interior of the cube is 3x².

Where x is the side of the cube.

We have,

Side of the cube = x

Now,

Using the Pythagorean theorem in ΔABC.

BC² = AC² + AB²

BC² = x² + x²

BC² = 2x²

Now,

GB is the diagonal through the interior.

So,

GB² = BC² + CG²

GB² = 2x² + x²

GB² = 3x²

Thus,

The diagonal through the interior of the cube is 3x².

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The number of students need to treat the observations as independent Miguel have to sample without replacement is equal to 45.

Population of students = 450

To treat the observations as independent,

The sample size needs to be less than 10% of the population size.

This implies,

To find out how many students Miguel will have to sample without replacement to treat the observations as independent.

I is important to calculate 10% of the population size,

10% of 450

= ( 10 / 100 ) × 450

= 0.1 x 450

= 45

Therefore, Miguel will need to sample 45 or fewer students without replacement to treat the observations as independent.

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Since his total earnings are £1072, which is greater than £294.80, we can conclude that Rory's claim is correct.

To see if Rory's assertion is correct, we must compute the mean average of his wages for the last four weeks.

By adding up the earnings for each week, the total earnings over the last four weeks may be calculated:

Total earnings = £307.50 + £235.75 + £287 + x (week 4 earnings)

We know that Rory's wages over the last four weeks should have averaged £268, thus we can solve the following equation:

(£307.50 + £235.75 + £287 + x) / 4 = £268

Simplifying this equation, we get:

£830.25 + x = £1072

x = £1072 - £830.25

x = £241.75

As a result, Rory's earnings for week 4 should be £241.75, for a total of £268 for the last four weeks.

Rory now claims to have earned 10% more than the average over the last four weeks. The average wages over the last four weeks are £268, so 10% extra would be:

£268 + 10% of £268 = £268 + £26.80 = £294.80

Rory's earnings for the last four weeks are as follows: £307.50 + £235.75 + £287 + £241.75 = £1072

To see if he made 10% more than the average, we can take 10% of the average and multiply it by the average to get the expected value:

£268 + 10% of £268 = £268 + £26.80 = £294.80

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If we select two cards from "M,A,T,H,I,S,F,U,N' with replacement, then the probability of picking a T and N is (a) 1/81.

The cards are to be selected from {M,A,T,H,I,S,F,U,N},

So, there are total of 9 cards to choose from, and we are selecting two cards with replacement which means that we pick one card, replace it, and then pick another card.

The probability of picking a T on the first draw is : P(T) = 1/9, and

The probability of picking an N on the second draw (after replacing the first card) is also : P(N) = 1/9.

So, the probability of selection of both T and N is written as :

P(T and N) = P(T) × P(N) = (1/9) × (1/9) = 1/81,

Therefore, The correct option is (a).

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Answer:

The answer to your problem is, [tex]\frac{16}{35}[/tex]

Step-by-step explanation:

= [tex]\frac{2}{5} / \frac{8}{7}[/tex]

= [tex]\frac{2*8}{5*7}[/tex]

= [tex]\frac{16}{35}[/tex]

Thus the answer to your problem is, [tex]\frac{16}{35}[/tex]

Hope this is as simple you can get.

The point does not satisfy the linear equation

To check if a point satisfy an equation, we just need to replace the values of the point in the given equation and see if the equation is true or not.

Here we have the linear equation:

y = x - 7

And the point is (-7, 0)

That means that we need to replace x =-7 and y = 0.

Replacing that we will get:

0 = -7 - 7

0 = -14

That is false, then the point does not satisfy the equation.

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In scientific notation, a number is written as the base number times ten raised to a power. The base number, known as the significand, is also referred to as the mantissa.

The term mantissa is used for the fractional part of a common logarithm as well.

The mantissa is the fractional part of a logarithm. In the context of scientific notation, the mantissa refers to the base number, which is multiplied by 10 raised to a certain power to represent a number.

In other words, the mantissa is the significant digits of a number, excluding the leading and trailing zeros, expressed as a decimal fraction between 1 and 10. For example, in the number 3.24 x 10^5, the mantissa is 3.24.

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The study provides evidence that the type of feed supplement has a significant effect on the growth rate of chickens, and some feed supplements are more effective than others in promoting growth.

The experiment aimed to compare the effectiveness of different feed supplements on the growth rate of chickens. Newly hatched chicks were randomly assigned to six groups, each receiving a different feed supplement. The study recorded the weight of the chicks, and sample statistics and a visualization of the observed data were presented.

The hypothesis test conducted aimed to determine if there was sufficient evidence to conclude that the average weight of chicks varies across some or all groups. The null hypothesis assumes that there is no difference in the average weight of chicks on different diets, while the alternative hypothesis assumes that there is a difference.

To test the hypothesis, we need to check if the conditions for the ANOVA test are met. First, we need to assume that the population variances are equal across all groups, which we can verify by checking if the standard deviations of the groups are roughly equal.

In this case, the standard deviations range from 38.63 to 64.90, indicating that the assumption of equal variances may not be reasonable. However, we will still proceed with the ANOVA test, as the sample sizes are roughly equal and the assumption of equal variances is not critical when the sample sizes are equal.

Next, we can calculate the F-statistic by dividing the mean square between groups by the mean square within groups. The F-statistic is 15.4, with a p-value of less than 0.0001, indicating strong evidence against the null hypothesis.

Therefore, we can conclude that there is convincing evidence that the average weight of chicks varies across some or all groups.

To determine which groups differ significantly, we can perform post-hoc tests, such as Tukey's HSD test. These tests can identify which pairs of groups have significantly different mean weights.

Overall, the study provides evidence that the type of feed supplement has a significant effect on the growth rate of chickens, and some feed supplements are more effective than others in promoting growth.

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The requried 21.12 divided by 1.2 is 17.6.

To divide 21.12 by 1.2, we can use long division.

The first step is to place 1.2 outside of the division bracket and 21.12 inside. We divide 1.2 into 2, which gives 1.
We write this above the 2 and subtract, which gives us 0.8. We then bring down the next digit, 1, to get 8.

We divide 1.2 into 8, which gives 6 with a remainder of 2. We bring down the next digit, 1, and get 21.

We divide 1.2 into 21, which gives 17 with a remainder of 6. So the final answer is 17.6.

Thus, the requried 21.12 divided by 1.2 is 17.6.

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[tex]x^{2}[/tex] + 2x - 80 = 0 will be the equation that could be used to solve for the square's original side length, x.

Let's assume that the original side length of the square is x feet.

According to the problem, one dimension of the rectangle (let's call it length) is x + 4 feet, and the other dimension (let's call it width) is x - 2 feet. The area of the rectangle is given as 72 square feet.

We can write an equation to represent this information as:

(x + 4)(x - 2) = 72

Simplifying the left side of the equation, we get:

[tex]x^{2}[/tex] + 2x - 8 = 72

Bringing all the terms to one side of the equation, we get:

[tex]x^{2}[/tex] + 2x - 80 = 0

This is a quadratic equation that we can solve using the quadratic formula:

x = (-2 ± [tex]\sqrt{2^{2}-4(1)(-80)}[/tex] ) / 2(1)

x = (-2 ± [tex]\sqrt{324}[/tex]) / 2

x = (-2 ± 18) / 2

The two possible values of x are:

x = 8 or x = -10

Since the side length of a square cannot be negative, we can disregard the solution x = -10. Therefore, the original side length of the square was x = 8 feet.

Answer: (x + 4)(x - 2) = 72 or [tex]x^{2}[/tex] + 2x - 80 = 0, with a solution of x = 8 feet.

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Answer:

b, 13√2 and 13

Step-by-step explanation:

13 is equal to y so it is 13

And for x u can get by using sin or cos cause u get the same answer

sin(45) = 13/ x

x = 13/ sin(45)

x= 26/√2 ....... when you rationalize the denominator

x= (26√2) / 2

x = 13√2

Upon answering the query   There is evidence to imply that the characters are not equally likely if the proportion is larger than the significance threshold.

It is possible to multiply, divide, add, or subtract in mathematics. The following is how an expression is put together: Number, expression, and mathematical operator The components of a mathematical expression (such as addition, subtraction, multiplication or division, etc.) include numbers, variables, and functions. It is possible to contrast expressions and phrases. An expression, often known as an algebraic expression, is any mathematical statement that contains variables, numbers, and an arithmetic operation between them. For instance, the word m in the given equation is separated from the terms 4m and 5 by the arithmetic symbol +, as does the variable m in the expression 4m + 5.

Yes, running a simulation can assist in figuring out whether the occurrence of 4 of a particular character in 7 blind bags offers strong proof that the characters are not equally likely. The procedure for running the simulation is as follows:

As a representation of the characters in the blind bag series, obtain 5 identical pieces of paper and label them with the letters A through E.

Describe a trial as the procedure of picking 7 slips of paper at random, writing down each one's letter, rearranging the slips, and repeating the process.

The number of times the same character occurs the most in that trial serves as the response variable.

Use the specified process to run several trials (for instance, 10,000).

Count the instances in which a character appears four or more times.

Determine the percentage of trials out of the total done when the same character occurs 4 or more times.

If there is strong indication that the characters are not equally frequent, compare the proportion obtained in step 6 to a significance threshold (like 0.05). The manufacturer's assertion that all characters are equally likely cannot be refuted if the proportion is less than the significance threshold. There is evidence to imply that the characters are not equally likely if the proportion is larger than the significance threshold.

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It is true that when constructing a table with metric variables, you should absolutely include the average(s).

When constructing a table with metric variables, it is important to include the measures of central tendency such as the mean, median, and mode. The average or mean is particularly important as it provides a summary measure of the data set and is often used as a benchmark for comparison with other values. By including the average, the table can convey information about the typical or expected value of the metric variable.

The mean, or average, is a commonly used measure of central tendency. It is calculated by summing all of the values in the data set and dividing by the number of observations. The mean is useful because it is sensitive to all of the values in the data set and provides a benchmark for comparison with other values.

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The polynomial equation for the area A of the space between the two concentric circles is [tex]A = 20π(r - 5)[/tex].

To find the equation for the area between two concentric circles, we need to subtract the area of the smaller circle from the area of the larger circle. Let the radius of the outside circle be r and the radius of the inside circle be r-10. Then, the area A between the two circles is given by:

[tex]A = πr^2 - π(r-10)^2[/tex]

Expanding and simplifying, we get:

[tex]A = πr^2 - π(r^2 - 20r + 100)[/tex]

[tex]A = πr^2 - πr^2 + 20πr - 100π[/tex]

[tex]A = 20πr - 100π[/tex]

[tex]A = 20π(r - 5)[/tex]

The National Park Service may want to change the layout of Lincoln Circle to accommodate increased traffic flow or to improve pedestrian safety. The new design with two concentric circles can help to organize traffic better by separating different types of vehicles or controlling speeds. It may also provide additional space for parking or public events. The impact of any changes on the surrounding community and environment, as well as the cost and feasibility of implementation. Proper planning and consultation with stakeholders can help to ensure that the new design meets the needs of all parties involved.

The complete question is: TRAFFIC PLANNING The Lincoln Memorial in Washington, D.C., is surrounded by a circular drive called Lincoln Circle. Suppose the National Park Service wants to change the layout of Lincoln Circle so that there are two concentric circular roads. Write a polynomial equation for the area A of the space between the roads if the radius of the inside road is 10 meters less than the radius of the outside road.

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Answer:

Zoe would have to work 21 hours next week

Step-by-step explanation:

This is true because 372.30/17 = 21.9 then 459.90/21.9= 21

The value of x when finding the volume of the  triangular pyramid is: 18 units

The formula for the volume of a triangular pyramid is

V = ¹/₃ * B.A * h

where:

V is volume

B.A is base area

h is height

We are given the parameters:

Volume = 972 units³

Base area = 18 * 9 = 162 units²

Thus:

972 = ¹/₃ * 162 * x

x = (972 * 3)/162

x = 18 units

Thus, that is the height of the triangular pyramid

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The function with the greatest growth rate is 2(7)ˣ.

The function with the greatest growth rate is determined by comparing their exponential terms.

Comparing the exponential terms of the given functions;

f(x) = 2(7)ˣ, the exponential term is 7ˣ

f(x) = 7(2)ˣ,  the exponential term is 2ˣ

f(x) = 3(5)ˣ +6,  the exponential term is 5ˣ

f(x) = 5(3)ˣ +6, the exponential term is 3ˣ

Since 7ˣ grows faster than 2ˣ, 5ˣ, and 3ˣ, the function f(x) = 2(7)ˣ has the greatest growth rate among the given functions.

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The image of the translated point is A' ( -2 , 8 )

Given data ,

To perform a translation of 9 units left, we need to subtract 9 from the x-coordinate of the point J(7, 8):

New x-coordinate = 7 - 9 = -2

y-coordinate remains the same: y = 8

So the image of J(7, 8) after a translation 9 units left is the point (-2, 8).

To graph this, we start by plotting the original point J(7, 8) on the coordinate plane:

Hence , the translated point is A' ( -2 , 8 )

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1. The he intersection points A and B are:

A(-2, -1) and B(6, 7)

2. Midpoint is (7, -1)

3. length of AB is 4√5

To find the intersection points A and B, set y = x + 1 and y = x² - 3x - 11 equal to each other:

x + 1 = x² - 3x - 11

Now, rearrange the equation to set it equal to zero:

x² - 4x - 12 = 0

Factor the quadratic equation:

(x - 6)(x + 2) = 0

Solve for x:

x = 6, x = -2

Now plug the x-values back into the equation of either line (y = x + 1) to find the corresponding y-values:

For x = 6: y = 6 + 1 = 7

For x = -2: y = -2 + 1 = -1

So the intersection points A and B are:

A(-2, -1) and B(6, 7)

a) To find the midpoint of A(5,-5) and B(9,3), use the midpoint formula:

Midpoint = ((x1 + x2)/2, (y1 + y2)/2)

Midpoint = ((5 + 9)/2, (-5 + 3)/2) = (14/2, -2/2) = (7, -1)

b) To find the length of AB, use the distance formula:

Distance = √((x2 - x1)² + (y2 - y1)²)

Distance = √((9 - 5)² + (3 - (-5))²) = √(4² + 8²) = √(16 + 64) = √80

Length of AB = 4√5 (simplified

a) To find the length of AB, use the distance formula:

Distance = √((x2 - x1)² + (y2 - y1)²)

Distance = √((9 - 5)² + (-1 - 7)²) = √(4² + (-8)²) = √(16 + 64) = √80

Length of AB = 4√5 (simplified)

b) To find the equation of the line AB, first find the slope:

m = (y2 - y1)/(x2 - x1) = (-1 - 7)/(9 - 5) = (-8)/4 = -2

Next, use the point-slope form with one of the points (A or B), say A(5,7):

y - y1 = m(x - x1)

y - 7 = -2(x - 5)

Now, convert the equation to the slope-intercept form (y = mx + c):

y = -2x + 10 + 7

y = -2x + 17

To find the gradient of the line that is perpendicular to 3y = 4x - 5, first find the gradient of the given line:

3y = 4x - 5 => y = (4/3)x - 5/3

The gradient of the given line is 4/3. To find the gradient of the perpendicular line, find the negative reciprocal:

m_perpendicular = -1/(4/3) = -3/4

i) To find the midpoint M of A(1,5) and B(3,9), use the midpoint formula:

Midpoint = ((x1 + x2)/2, (y1 + y2)/

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The 90% confidence interval for the mean height of students can be constructed at  [5.868, 5.932]. Therefore, option (a) is the correct answer.

To construct a 90% confidence interval for the mean height of students at UH, we can use the following formula:

CI =  x' ± z* (σ/√n)

where x' is the sample mean, σ is the population standard deviation, n is the sample size, z* is the critical value from the standard normal distribution for the desired confidence level (90% in this case).

We are given x' = 5.9 feet, σ = 0.1 feet, and n = 28. The critical value for a 90% confidence interval can be found using a standard normal distribution table or calculator, and is approximately 1.645.

Substituting the values, we get:

CI = 5.9 ± 1.645 x (0.1/√28)

CI = 5.9 ± 0.031

CI = [5.869, 5.931]

Therefore, the answer is (a) [5.868, 5.932].

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The value p = 1/2 + √(3)/2 does give us exactly one point with a gradient of zero.

A quadratic equation, or sometimes just quadratics, is a polynomial equation with a maximum degree of two. It takes the following form:

ax² + bx + c = 0

To find the value of p for which the graph of f has exactly one point with a gradient of zero, we need to find the derivative of f(x) and set it equal to zero.

First, we can simplify f(x) by factoring out 4x:

f(x) = 4x(x + p/(4x+4))

Now, we can find the derivative of f(x):

f'(x) = 4(x + p/(4x+4)) + 4x(1 - p/(4x+4)²)

To find the point(s) where f'(x) = 0, we set it equal to zero and solve for x:

4(x + p/(4x+4)) + 4x(1 - p/(4x+4)²) = 0

Simplifying and multiplying through by (4x+4)²:

16x³ + 32px² + 16px - 16p = 0

Dividing through by 16x:

x² + 2px + p - 1 = 0

Now, we can use the discriminant of this quadratic equation to determine the value of p that gives exactly one point with a gradient of zero. The discriminant is:

b² - 4ac = (2p)² - 4(1)(p-1) = 4p² - 4p + 4 = 4(p² - p + 1)

For the graph of f to have exactly one point with a gradient of zero, the discriminant must be equal to zero, because that means there is only one value of x that satisfies f'(x) = 0. So, we set the discriminant equal to zero and solve for p:

4(p² - p + 1) = 0

p² - p + 1 = 0

Using the quadratic formula:

p = (1 ± √(1 - 4))/2 = 1/2 ± √(3)/2

So, the two possible values of p for which the graph of f has exactly one point with a gradient of zero are:

p = 1/2 + √3)/2

p = 1/2 - √(3)/2

Note that we should check that these values of p actually give us a point with a gradient of zero. If we substitute each value of p back into the derivative f'(x), we get:

When p = 1/2 + √(3)/2:

f'(x) = 4(x + (1/2 + √(3)/2)/(4x+4)) + 4x(1 - (1/2 + √(3)/2)/(4x+4)²)

Simplifying, we get:

f'(x) = (16x³ - 8x² + (4√(3) - 4)x + 4√(3) - 4)/(4(x+1)²(x+1+√(3)))

We can see that the denominator is always positive, so the gradient of f can only be zero when the numerator is zero. To find the value of x that satisfies this, we need to solve the cubic equation:

16x³ - 8x² + (4√(3) - 4)x + 4√(3) - 4 = 0

Using numerical methods, we find that there is only one real root, which is approximately x = 0.265. Therefore, the value p = 1/2 + √(3)/2 does give us exactly one point with a gradient of zero.

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The coefficient of determination (R²) for the given regression model is 0.974

The coefficient of determination, R², is a measure of how well the regression line fits the data. It represents the proportion of the total variation in the dependent variable that is explained by the independent variables in the regression model.

To compute R², we first need to calculate the sum of squares total (SST), which is the total variation in the dependent variable

SST = ∑(yi - y)²

where yi is the ith observed value of the dependent variable, and y is the mean of the dependent variable.

In this case, SST = 1805, as given.

Next, we need to calculate the sum of squares regression (SSR), which represents the variation in the dependent variable that is explained by the independent variables

SSR = ∑(yi - y)²

where yi is the ith observed value of the dependent variable, and y is the predicted value of the dependent variable based on the regression model.

In this case, SSR = 1760, as given.

Finally, we can compute R² as

R² = SSR/SST

Substituting the values given, we get:

R² = 1760/1805

R² = 0.974

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The given question is incomplete, the complete question is:

The following estimated regression equation based on 30 observations was presented. y = 17.6 + 3.8x₁ – 2.3x₂ + 7.6x₃ + 2.7x₄ The values of SST and SSR are 1805 and 1760, respectively.

Compute R²

The statement that is true of thermal energy is that Thermal energy is a measure of the movement of a substance's molecules. Option C

Thermal energy can be defined as a type of energy that emerges or rather comes from a substance whose molecules and atoms are vibrating more faster than it should as a result of the rise in temperature.

It is produced when the rise in temperature applied causes the atoms and molecules in a substance to get more agitated and thus causes rigorous vibration.

Note that the greater the temperature applied, the greater the thermal energy produced.

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Answer:

Step-by-step explanation:

30-60-90 triangles

30-60-90 triangles are right triangles whose acute angles are

3

0

∘

30

∘

30, degrees and

6

0

∘

60

∘

60, degrees. The sides in such triangles have special proportions:

A thirty-sixty-ninety triangle. The length of the shorter leg of the triangle is one half h units. The length of the longer leg of the triangle is square root three over two times h. The length of the hypotenuse of the triangle is h units.

A thirty-sixty-ninety triangle. The length of the shorter leg of the triangle is one half h units. The length of the longer leg of the triangle is square root three over two times h. The length of the hypotenuse of the triangle is h units.

[How can we find these ratios using the Pythagorean theorem?]

Want to learn more about 30-60-90 triangles? Check out this video.

45-45-90 triangles

45-45-90 triangles are right triangles whose acute angles are both

4

5

∘

45

∘

45, degrees. This makes them isosceles triangles, and their sides have special proportions:

A forty-five-forty-five-ninety triangle. The length of both legs are k units. The length of the hypotenuse of the triangle is square root of two times k units.

A forty-five-forty-five-ninety triangle. The length of both legs are k units. The length of the hypotenuse of the triangle is square root of two times k units.

[How can we find these ratios using the Pythagorean theorem?]

The special properties of both of these special right triangles are a result of the Pythagorean theorem.

so A is right. i hope

Devin because the second side length is the square root of 3 times the measure of the smallest side length, and the largest side is twice the smallest side. Glenn's claim is incorrect because his triangle's side lengths do not match the 30-60-90 ratio, unlike Devin's triangle, which satisfies the conditions of a 30-60-90 triangle.

A 30-60-90 triangle has specific side length ratios: the sides opposite the angles measuring 30 degrees, 60 degrees, and 90 degrees are in the ratio 1:√3:2. Let's analyze the claims made by Devin and Glenn:

Devin's claim:

Devin states that a triangle with side lengths of 6, 6√3, and 12 is a 30-60-90 triangle. To verify this, we need to check if the side lengths satisfy the 30-60-90 ratio. If we divide the longest side by 2, we get 12/2 = 6, which matches the length of the shortest side. Also, the middle side (6√3) is indeed √3 times the length of the shortest side (6). Thus, Devin's claim is correct, and the triangle with side lengths 6, 6√3, and 12 is a 30-60-90 triangle.

Glenn's claim:

Glenn states that a triangle with side lengths 7, 7√3, and 49 is a 30-60-90 triangle. Again, we need to check if the side lengths satisfy the 30-60-90 ratio. However, upon examination, we find that dividing the longest side by 2 (49/2) does not result in the length of the shortest side (7). Also, the middle side (7√3) is not √3 times the length of the shortest side (7). Therefore, Glenn's claim is incorrect, and the triangle with side lengths 7, 7√3, and 49 is not a 30-60-90 triangle.

Hence the correct option is (c).

To know more about triangle here

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