The equation has two distinct real roots if 64 - 4c > 0, one real root if 64 - 4c = 0, and no real roots if 64 - 4c < 0.
The discriminant of a quadratic equation of the form [tex]ax^2 + bx + c = 0[/tex] is given by [tex]b^2 - 4ac[/tex]. In the given quadratic equation, a = 1, b = 8, and c = c. Therefore, the discriminant is:
[tex]b^2 - 4ac[/tex]
[tex]= 8^2 - 4(1)(c)[/tex]
[tex]= 64 - 4c[/tex]
Now, we can use the discriminant to determine the nature of the solutions of the quadratic equation. If the discriminant is positive, the equation has two distinct real roots. If the discriminant is zero, the equation has one real root (a double root). If the discriminant is negative, the equation has no real roots (two complex conjugate roots).
In this case, we do not have enough information about the value of c to determine the nature of the roots of the equation. All we know is that the discriminant is 64 - 4c.
Hence, if 64 - 4c > 0, we can state that the equation has two separate real roots, one real root if 64 - 4c = 0, and no real roots if 64 - 4c < 0.
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A company has hired 12 new employees and must assign eight to the dayshift and four to the night shift and how many ways can the assignment be made ?
There are 495 ways to assign 8 employees to the day shift and 4 employees to the night shift from a group of 12 employees.
How many ways can the company assign eight employees to the dayshift and four employees to the night shift?Given that, we need to find the number of ways to assign 8 employees to the day shift and 4 employees to the night shift from a group of 12 employees.
We can use combinations to solve this problem.
The number of ways to choose 8 employees from 12 for the day shift is:
C(12,8)
= 12! / ( 12 - 8 )! × 8!
= 495
Similarly, the number of ways to choose 4 employees from the remaining 4 for the night shift is:
C(4,4) = 1
= 4! / ( 4 - 4 )! × 4!
= 4!/4!
= 1
Therefore, the total number of ways to make the assignment is:
495 × 1 = 495
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Given A = (-3,2) and B = (7,-10), find the point that partitions segment AB in a 1:4 ratio
The point that partitions segment AB in a 1:4 ratio would be (-3/5, -1/5).
How to find the ratio?To find the point that partitions segment AB in a 1:4 ratio, we can use the section formula.
We can use the formula for finding the coordinates of a point that partitions a line segment in a given ratio. The formula is:
C = ((1 - r) * A + r * B) / 4
where, r is the ratio (in this case, 1:4, so r = 1/5).
Substituting the values for A, B, and r, we get,
C = ((1 - 1/5) * (-3, 2) + (1/5) * (7, -10)) / 4
Simplifying,
C = (4/5 * (-3, 2) + 1/5 * (7, -10)) / 4
C = (-12/5, 8/5 - 2) / 4
C = (-12/20, 8/20 - 10/20)
C = (-3/5, -1/5)
Therefore, the point that partitions segment AB in a 1:4 ratio is (-3/5, -1/5).
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pls answert this within 1 hour or else i will be DOOMED
In the fractions prompts given, the correct output are:
(1 ÷2) ÷ 4 = 1/8(1 ÷5) ÷ 2 = 1/10(1 ÷3) ÷ 5 = 1/15(1 ÷4) ÷ 4 = 1/16The solution to the problem for (1/2) ÷ 3 is given below.What is a fraction?A fraction represents a part of a whole. It consists of a numerator and a denominator, with the numerator indicating the number of parts and the denominator indicating the total number of parts.
The calculations are given as follows;
1 )
= (1/2) x (1/4) [dividing by a number is the same as multiplying by its reciprocal]
= 1/8
2) (1/5) ÷ 2
= (1/5) x (1/2)
= 1/10
3)
(1/3) ÷ 5
= (1/3) x (1/5)
= 1/15
4) (1/4) ÷ 4
= (1/4) x (1/4)
= 1/16
5) One day, Amy baked a cake and wanted to divide it equally among 3 of her friends. She realized she only had half a cake left, so she decided to divide it into equal parts. Each friend received 1/6 of a cake. To check her calculation, she multiplied 1/6 by 3 and got 1/2. Thus, (1/2) ÷ 3 = 1/6, since dividing by 3 is the same as multiplying by 1/3.
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there are black, blue, and white marbles in a bag. the probability of choosing a black marble is 0.36 . the probability of choosing a black and then a white marble is 0.27 . to the nearest hundredth, what is the probability of the second marble being white if the first marble chosen is black?
There are black, blue, and white marbles in a bag. The probability of choosing a black marble is 0.75.
Let's assume that there are 100 marbles in the bag. If the probability of choosing a black marble is 0.36, there are 36 black marbles in the bag. Therefore, there are 64 marbles of other colors (white and blue) in the bag.
Using the same method, we can say that the probability of choosing a white marble after drawing a black one is [tex]\frac{0.27}{0.36}= 0.75[/tex] (rounded to the nearest hundredth). It means that there are 75 white marbles for every 100 black marbles in the bag.
Therefore, the probability of the second marble being white if the first marble chosen is black is
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on her way to visit her parents, jennifer drives 265 miles in 5 hours what is her average rate of speed in miles per hour?
Answer:
53 miles per hour
Step-by-step explanation:
To calculate Jennifer's average rate of speed in miles per hour, we can use the formula:
average speed = total distance / total time
In this case, Jennifer drove a total distance of 265 miles and it took her a total time of 5 hours, so:
average speed = 265 miles / 5 hours
Simplifying the expression, we get:
average speed = 53 miles per hour
Therefore, Jennifer's average rate of speed in miles per hour is 53 miles per hour.
Answer: 53 miles per hour
Step-by-step explanation:
To find Jennifer's average rate of speed in miles per hour, we divide the distance she traveled by the time it took her:
Average speed = distance ÷ time
Average speed = 265 miles ÷ 5 hours
Average speed = 53 miles per hour
Therefore, Jennifer's average rate of speed was 53 miles per hour.
4) A bus company charges $2 per ticket but wants to raise the price. The daily revenue is modeled by R(x)=-30(x-6)² + 320, where x is the number of $0.15 price increases and R(x) is the revenue in dollars. What should the price of the tickets be for a maximum profit? Hint: don't forget what price where you started.
Answer:
$2.90
Step-by-step explanation:
6 × 0.15 = 0.9
2 + 0.9 = 2.9
R(x) = -30(x - 6)² + 320
This equation for the revenue is a quadratic equation model written in the form of completing the square;
This form appears like so:
f(x) = a(x + b)² + c
It is quite useful, especially for this type of question;
Firstly, if a is positive, the quadratic equation will be a u shaped graph when illustrated, if negative, it will be an n shaped graph;
What this means is if a is positive, the vertex of the graph is the lowest point, i.e. the minimum value of f(x), and if a is negative, the vertex will be the highest point, i.e. the maximum value of f(x);
Secondly, the coordinates of the vertex will be:
(-b, c)
So, with regards to the question:
We have -30 in the position of a, the curve is therefore n shaped and the vertex is the highest point (known as the local maximum);
And in place of b and c, we have -6 and 320, so the coordinates of this local maximum are:
(6, 320)
We interpret this like so:
320 is the highest possible value of R(x), which represents revenue, so $320 is the maximum revenue according to this model, and it is achieved when x = 6, i.e. when the price is increased by $0.90 (= 6 × $0.15);
Finally, to get the new ticket price, we add this to the original price to get $2.90.
Looking for an answer to this: Every non zero number can be used twice, between two same non zero numbers is as many zeros as how large is the non zero number example is 40001041 and 300103100. How many 7 digit numbers are there that have two 1s and two 2s and not defined number 0s?
Thank you for any responses.
Answer:
50000
Step-by-step explanation:78473294724829384739284732984739824
find the area of a quadrilateral ABCD in each case.
The area of the quadrilateral ABCD for this case is of 4 square units.
How to obtain the area of the quadrilateral ABCD?The quadrilateral ABCD in the context of this problem represents a diamond, hence it's area is given by half the product of the diagonal lengths of the diamond.
The lengths for each diagonal of the diamond are given as follows:
Diagonal AC = 2 - 0 = 2.Diagonal BD = 4 - 0 = 4.The product of the diagonal lengths is given as follows:
AC x BD = 2 x 4 = 8 square units.
Hence half the product of these diagonal lengths, representing the area of the quadrilateral, is given as follows:
0.5 x 8 square units = 4 square units.
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give a binary representation for each number given below in hex. drop the leading zeroes in your binary representation. (a) a3 (b) 1fc (c) 2a0b
The binary representation is (a) a3 in binary is 10100011(b) 1fc in binary is 11111100(c) 2a0b in binary is 1010100000001011
In hexadecimal, each digit represents four bits, which means that two hexadecimal digits can represent eight bits. As a result, converting from hexadecimal to binary is straightforward. The four bits corresponding to each hexadecimal digit can be written down, resulting in an 8-bit binary value.
To convert hexadecimal to binary, simply convert each hexadecimal digit to binary, then combine them to get the final binary representation. For instance, in a, the hexadecimal digit a has a binary representation of 1010, while the digit 3 has a binary representation of 0011.
Combining these results in a binary representation of 10100011. Similarly, the binary representations of 1f and c are 00011111 and 00001100, respectively.
Combining them results in 11111100. Finally, the binary representation of 2a0b is obtained by converting 2, a, 0, and b to binary, resulting in 0010, 1010, 0000, and 1011, respectively. Combining them results in 1010100000001011.
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A number exceeds 20% of itself by 40. find the number.
WITH STEPS
Answer:
50
Step-by-step explanation:
Let the number = x.
20% of the number is 20% of x = 0.2x.
Since the number exceeds 20% of itself by 40, then teh number minus 20% of itself is 40.
x - 0.2x = 40
0.8x = 40
x = 40/0.8
x = 50
Terri pays a monthly cell phone fee of $10. She pays 5 cents for each minute that she talks. If Terri does not make any calls, what would her bill be?
Answer:
$10
Step-by-step explanation:
We Know
Terri pays a monthly cell phone fee of $10. She pays 5 cents for each minute that she talks.
Let C be the total cost, and x be the number of minutes she talks; we have the equation.
C = 0.05x + 10
If Terri does not make any calls, what would her bill be?
C = 0.05(0) + 10
C = $10
So, her bill will be $10
Assume that "a" is the average of p, 2q, and 4; "b" is the average of 2p, 4q, and 8; and "c" and the average of 6p, 3q, and 6. What is the average of "a, b, c" in terms of p and q?
a) p + q + 2
b) p + q + 4
c) 3p + 6q + 6
d) 9p + 6q + 2
The average of "a, b, c" in terms of p and q is a) p + q + 2
How to determine the averageThe question asks us to find out the average of a, b, and c in terms of p and q.
The given data in the question are -a, b, and c are the averages of p, 2q, and 4; 2p, 4q, and 8; and 6p, 3q, and 6, respectively.
We need to find the average of these averages.
Let's solve for a first:a = (p + 2q + 4) / 3
We can solve for b as:
b = (2p + 4q + 8) / 3
And, solving for c,c = (6p + 3q + 6) / 3
Now, let's sum a, b, and c:
a + b + c = [(p + 2q + 4) / 3] + [(2p + 4q + 8) / 3] + [(6p + 3q + 6) / 3]= [p + 2q + 4 + 2p + 4q + 8 + 6p + 3q + 6] / 3= (9p + 9q + 18) / 3= 3(p + q + 2)
Therefore, the answer is option A, p + q + 2.
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Frankie's dad made scrambled eggs for the family's breakfast. He started with a full carton of 12 eggs he used 8 of the eggs. What fraction of the carton of eggs did he use write at least two equivalent fractions
Frankie's dad used 2/3 of the carton of eggs for their breakfast. Two equivalent fractions are 16/24 and 24/36.
Frankie's dad used 8 out of 12 eggs from a full carton. To express this as a fraction, we can write it as 8/12. However, this fraction can be simplified by dividing both the numerator and denominator by their greatest common factor, which in this case is 4. Thus, we get:
8/12 = (8 ÷ 4)/(12 ÷ 4) = 2/3
Alternatively, we can also express this fraction in different forms. One way to do this is by multiplying both the numerator and denominator by the same number. For example, if we multiply both by 2, we get:
8/12 = (8 × 2)/(12 × 2) = 16/24
Similarly, we can multiply by 3 to get:
8/12 = (8 × 3)/(12 × 3) = 24/36
Both of these fractions are equivalent to 2/3, and we can find infinitely many other equivalent fractions by multiplying both numerator and denominator by different numbers.
In summary, when Frankie's dad made scrambled eggs using 8 eggs from a full carton of 12 eggs, he used 2/3 of the carton. This fraction can be expressed in different forms that are equivalent to 2/3 by dividing both numerator and denominator by their greatest common factor or by multiplying both numerator and denominator by the same number.
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A man saves Rs.7,500 in first year. In each year after the first, he saves Rs. 2,000 more than he does in the preceding year. When will he be saved the total amount Rs.1,65,000? Find it.
Answer:
aeqtq34t
Step-by-step explanation:
q34t35t134
The population of a city was 20000. The next year it increased by 2% find the new population
The city had 20,000 residents. The next year, it went up by 2%. The new population of the city after a 2% increase is 20400.
To find the new population of the city after a 2% increase from 20000, we need to use the following formula:
New population = Old population + (Percentage increase x Old population)
Substituting the given values into the formula, we get:
New population = 20000 + (2/100 x 20000)
New population = 20000 + 400
New population = 20400
It is important to note that this calculation assumes that the increase in population is the only factor affecting the total population. In reality, there may be other factors that affect the population, such as migration, birth rates, and mortality rates.
Additionally, this calculation only gives the estimated population based on the percentage increase, and the actual population may differ due to various factors.
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PLS ANWSER ASAP VERY HARD FOR ME
Answer:
x = 6
Step-by-step explanation:
Verticle angles are equal to each other...
m∠A = m∠B
Thus...
4x + 6 = 2x + 18
Now, we isolate x:
4x + 6 = 2x + 18
Subtract 6 from both sides
4x = 2x + 12
Subtract 2x from both sides
2x = 12
Divide both sides by 2
x = 6
Austin has a dimes and y nickels, having at most 28 coins worth a minimum of $2
combined. At least 18 of the coins are dimes and no more than 6 of the coins are
nickels. Solve this system of inequalities graphically and determine one possible
solution.
The solution of system of inequalities solved graphically is (18,6).
What is system of linear inequalities?A group of two or more linear inequalities are graphed together on a coordinate plane to discover the solution that concurrently satisfies all the inequalities. This is known as a system of linear inequalities. The location where all the half-planes overlap is where the system is solved. Each inequality defines a half-plane on the coordinate plane. Every point in this area, which is referred to as the feasible region, fulfils all of the system's inequalities. To identify the optimum solution for an optimization problem given a set of constraints, systems of linear inequalities are frequently utilised.
Let us suppose the number of dimes = a.
Let us suppose the number of nickels = y.
According to the problem we have the following conditions:
a + y ≤ 28 (at most 28 coins)
0.10a + 0.05y ≥ 2 (worth at least $2)
a ≥ 18 (at least 18 dimes)
y ≤ 6 (no more than 6 nickels)
Using different values of a and y plot the points.
The solution of this system of inequality is any point that lies in the feasible region.
One such point is (18, 6).
Hence, the solution of system of inequalities solved graphically is (18,6).
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4) Ella drives 60 miles per hour. How far will she drive in 2% hours?
Answer: 1.2 miles
Step-by-step explanation:
1 hour = 60 min
60 x 0.02 = 1.2 1 minute and 20 seconds has elapsed
60 miles/ every 60 minutes or 1 mile a minute
1 x 1.2 = 1.2
she has traveled 1.2 miles
Answer: The answer is 120 mph (miles per hour)
Step-by-step explanation:
The one thing you need to do is to figure out how many mph did Ella drive for 2 hours.
So, you need to do 60 x 2, and you will get the answer 120.
And there's your answer!
Here are two closed containers and four balls just fit in each container. Each ball has a diameter of 54 mm. Which container has the smaller surface are? You must show your working
both containers have the same surface area and neither has a smaller surface area than the other.
Container 1:
Surface area of a single ball = π x (54/2)^2 = 3,092.62 mm^2
Total surface area of 4 balls = 12,370.48 mm^2
Container 2:
Surface area of a single ball = π x (54/2)^2 = 3,092.62 mm^2
Total surface area of 4 balls = 12,370.48 mm^2
Both containers have the same surface area.
To calculate the surface area of the two containers, I first calculated the surface area of one ball by using the formula π x (diameter/2)^2. I then multiplied this by 4 to get the total surface area of 4 balls. I repeated this process for both containers and found that both containers had the same surface area of 12,370.48 mm^2. both containers have the same surface area and neither has a smaller surface area than the other.
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Factor completely.
A) p^2-x^2+6x-9
B)b^2-c^2-10(b-c)
Thank you :DD
An expression is a combination of numbers, variables, and operations that can be evaluated to produce a value. Expressions can be simple or complex and can involve arithmetic, logical, or comparison operations.
What is the expression?A) To factor [tex]p^2-x^2+6x-9[/tex] first notice that the expression inside the parentheses is the difference of two squares, so we can use the formula:
[tex]p^2 - x^2 = (p + x)(p - x)[/tex]
Therefore, we can write the expression as:
[tex](p + x + 3)(p - x + 3)[/tex]
To check this, you can use FOIL to expand the expression:
[tex](p + x + 3)(p - x + 3) = p^2 - px + 3p + px - x^2 + 3x + 3p - 3x + 9 = p^2 - x^2 + 6x + 9[/tex]
B) To factor b^2-c^2-10(b-c), notice that the first two terms form a difference of squares, so we can use the formula again:
[tex]b^2 - c^2 = (b + c)(b - c)[/tex]
The expression can then be written as:
[tex](b + c)(b - c) - 10(b - c) = (b - c)(b + c - 10)[/tex]
To check this, we can use FOIL again:
[tex](b - c)(b + c - 10) = b^2 - bc - 10b - cb + 10c = b^2 - c^2 - 10(b - c)[/tex]
Therefore, the factored form of the expression is [tex](b - c)(b + c - 10)[/tex].
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44 friends evenly divided up an nnn-slice pizza. One of the friends, Harris, ate 111 fewer slice than he received. How many slices of pizza did Harris eat?
Write your answer as an expression
Harris ate x - 111 slices of pizza, So the total number of slices in the pizza is n ,where x is the number of slices each of the 44 friends received, and n is the total number of slices in the pizza, which must be a multiple of 44.
Let x be the number of slices each of the 44 friends received, then the total number of slices in the pizza is 44x. Since the pizza is evenly divided, the number of slices must be a multiple of 44.
Let y be the number of slices Harris received. Then, according to the problem, Harris ate 111 fewer slices than he received, so the number of slices he ate is y - 111.
Since the total number of slices in the pizza is 44x, we have:
y + 43x = 44x
Simplifying this equation, we get:
y = x
Therefore, Harris received the same number of slices as each of the other friends. So the number of slices he ate is:
y - 111 = x - 111
Substituting y = x, we get:
x - 111
Therefore, Harris ate x - 111 slices of pizza.
To find the value of x, we need to know the total number of slices in the pizza, which must be a multiple of 44. We can express this as:
44n = 44x
Dividing both sides by 44, we get:
n = x
So the total number of slices in the pizza is n.
Putting everything together, we get: Harris ate x - 111 slices of pizza, where x is the number of slices each of the 44 friends received, and n is the total number of slices in the pizza, which must be a multiple of 44.
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suppose the average gmat score of one university is 600 and such scores has a standard deviation of 100. what percentage of students has gmat scores between 400 and 800?
In conclusion, 95.4% of students have GMAT scores between 400 and 800.
Calculate z score need to find the proportion of scores that fall within the range of 400 to 800.
[tex]z=\frac{x- mean}{standard deviation}[/tex]
This formula tells us how many standard deviations away from the mean a given score is.
Given:
Mean= 600
Standard deviation = 100.
For the 400 scores:-
[tex]z=\frac{400-600}{100} \\z= -2[/tex]
For the 800 scores:-
[tex]z=\frac{800-600}{100} \\z=2[/tex]
Now we will use the standard normal distribution table to find the percentage of values between -2 and 2.
According to the standard normal distribution table, the percentage of values between -2 and 2 is approximately 95.45%.
Therefore, approximately 95.45% of students have GMAT scores between 400 and 800.
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Please Help ASAP
Help would be greatly appreciated
Answer: A
Step-by-step explanation: i thing its wrigth
How do you find height when you are doing volume with cubic units?
Answer:calculate the cube root of a cube's volume.
Step-by-step explanation:
) What is the measure of ∠x in the diagram below?
Answer:
Step-by-step explanation:
X+125=180 (angles on a straight line add to 180 (supplementary) ).
so x=55°
Given the functions f(x) = 1/x-1 + 1 and g(x)=1/x+2 +4 describe the transformation of the graph of function f onto the graph of function g
Transformation of the graph from parent function f(x) to g(x) is:
there is shift of 3 units towards the right to reach from -1 to 2 along x axis.there is a shift of 3 units upward to reach from 1 to 4 on y axis.Explain about the transformation of coordinates?That whenever a figure is relocated from one place to another without affecting its dimension, shape, or orientation, a transition known as translation takes place. If we are aware of the direction and magnitude of the figure's movement, we may draw the translation in the coordinate plane.
The x - axis and y values are reversed. 180° rotation about the origin Every x and y value reverses from what it was. Each current value becomes the counterpart of what it was after a 270° rotation of the origin. The two x and y values are reversed.
The given function:
f(x) = 1/x-1 + 1 and g(x)=1/x+2 +4
g(x) is obtained function after transformation:
transformation:
there is shift of 3 units towards the right to reach from -1 to 2 along x axis.there is a shift of 3 units upward to reach from 1 to 4 on y axis.Know more about the transformation of coordinates
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Can someone help me with this please? Thank you!
Answer:
a. f(10)= 20*10+14
f(10)=200+14
f(10)= 214
214
Please help, as it is greatly appreciated
when performing a hypothesis test based on a 95% confidence level, what are the chances of making a type ii error?
When performing a hypothesis test based on a 95% confidence level, the chances of making a type II error are 5%.
The process of hypothesis testing is used to determine whether or not a given statistical hypothesis is valid. The objective of this method is to determine whether the null hypothesis can be accepted or rejected based on the sample data obtained.
Hypothesis testing can be used to evaluate two hypotheses. The null hypothesis is the one that must be accepted or rejected, while the alternative hypothesis is the one that must be supported. In other words, hypothesis testing is a way of determining whether the null hypothesis is reasonable or not.
The Type II error is defined as the error that occurs when the null hypothesis is not rejected even though it is incorrect. In hypothesis testing, this type of error is referred to as a beta error or a false-negative error. The chances of making a Type II error depend on several factors, including the sample size, the level of significance, and the power of the test. When the level of significance is lowered to 0.05, the chances of making a Type II error are 5%.
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The perimeter of a square is 8 root 2x units. The area of a square is 56 units square. Find the value of x
According to the perimeter, the value of x is 7/2.
The problem tells us that the perimeter of a square is 8√2x units. We can use this information to set up an equation. Since all four sides of a square are equal, we can let s represent the length of one side of the square. Then, we know that:
Perimeter of square = 4s = 8√2x
We can simplify this equation by dividing both sides by 4:
s = 2√2x
Now, we can use this expression for s to find the area of the square. The area of a square is simply the length of one side squared. So, we have:
Area of square = s² = (2√2x)² = 8x
The problem tells us that the area of the square is 56 units square, so we can set up another equation:
8x = 56
Solving for x, we get:
x = 7/2
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