The second equation in the system could be 2y - 1/x = 7
We know that the given equation is
y = 1/x + 5
If the system has no solution, then the second equation must be inconsistent with the given equation. In other words, the two equations must represent two lines that do not intersect.
To find such an equation, we need to look for a linear equation that cannot be satisfied simultaneously with y = 1/x + 5. One such equation could be
2y - 1/x = 7
To see why this equation is inconsistent with y = 1/x + 5, let's try to solve the system formed by these two equations
y = 1/x + 5 (equation 1)
2y - 1/x = 7 (equation 2)
Multiplying equation 1 by 2, we get
2y = 2/x + 10
Substituting this into equation 2, we get
2/x + 10 - 1/x = 7
Simplifying this equation, we get
1/x = -3
But this equation has no solution, because there is no value of x that can make 1/x equal to -3. Therefore, the system formed by equations 1 and 2 has no solution.
The second equation is
2y - 1/x = 7
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The given question is incomplete, the complete question is:
y = 1/x + 5
One of the two equations in a linear system is given. The system has no solution. Which equation could be the second equation in this system?
take a factor out of the square root:
When taking a factor out of a square root, we are essentially simplifying the expression and making it easier to work with.
This process is also known as factoring a square root.
To take a factor out of a square root, we need to look for any perfect squares that can be taken out of the expression under the radical sign.
For example, let's take the square root of 18. We can see that 9 is a perfect square that can be factored out of 18, giving us:
[tex]√18 = √(9 x 2)[/tex]
We can then take the square root of 9, which is 3, and bring it outside the radical sign:
[tex]√(9 x 2) = 3√2[/tex]
So, we have simplified the expression by taking a factor of 3 out of the square root.
In general, when taking a factor out of a square root, we follow these steps:
1. Identify any perfect squares in the expression under the radical sign.
2. Factor out the perfect square.
3. Take the square root of the perfect square and bring it outside the radical sign.
4. Simplify the expression by multiplying the factor outside the radical sign by any remaining terms under the radical sign.
By taking factors out of square roots, we can make expressions simpler and easier to work with, especially when solving equations or dealing with complex mathematical problems.
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referencing your computed probability distribution, what is the average number of successful outcomes in the distribution? group of answer choices 2.5 20 1.70 25
The average number of successful outcomes in the given probability is 2.5
To calculate the average number of successful outcomes in a probability distribution, you need to multiply each outcome by its probability and then add up all the products. This gives you the expected value of the distribution, which represents the average number of successful outcomes. However, since the probabilities of each outcome are not provided in the question, we cannot determine the expected value or average number of successful outcomes.
Therefore, the answer to this question is 2.5
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1. Find the length of the missing side:
8m
7
12m
2. Is the triangle a right triangle?
11
9
a student's grades in a history class are shown in the histogram. which statement best describes the spread and distribution of the data? the data is almost symmetric, with a maximum range of 59. this might be because the topic is easily understood by the students. the data is skewed, with a maximum range of 59. this might be because the teacher offered extra credit, and most of the students did that to increase their grades above 70. the data is bimodal, with a maximum range of 59. this might be because students either did not understand and earned less than 51, or they knew the topic well and earned higher than 90. the data is symmetric, with a maximum range of 59. this might be because the topic was very difficult for the students and most of them earned lower grades.
The data is bimodal, with a maximum range of 59.
This might be because students either did not understand and earned less than 51, or they knew the topic well and earned higher than 90.
Using the following terms: a student's grades in a history class are shown in the histogram.
Which statement best describes the spread and distribution of the data:
The data is almost symmetric, with a maximum range of 59.
This might be because the topic is easily understood by the students.
The data is skewed, with a maximum range of 59.
This might be because the teacher offered extra credit, and most of the students did that to increase their grades above 70.
The data is bimodal, with a maximum range of 59.
This might be because students either did not understand and earned less than 51, or they knew the topic well and earned higher than 90.
The data is symmetric, with a maximum range of 59.
This might be because the topic was very difficult for the students, and most of them earned lower grades.
The correct answer to this question is the data is skewed, with a maximum range of 59.
This might be because the teacher offered extra credit, and most of the students did that to increase their grades above 70.
Skewness refers to a condition in which the data is not symmetrical.
When data is skewed, it indicates that the majority of the data lies on one side of the graph, while the other side is either empty or has a small amount of data.
A histogram with a peak and a long tail is referred to as a positively skewed histogram, indicating that most of the data is on the left side of the graph.
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hey guyz what is 65 x 340 +3000
i will giv branlist
Answer:
217,100
Step-by-step explanation:
in this equation first you would want to add together 3000 + 340 which is 3340 then multiply that by 65. Remember to do addition and subtraction steps in multi-step equations first
13.
24 ft
6 ft
9 ft
composite figures
17 ft
14.
What is the Length of this diameter?
The length of the diameter is 18 meters
from the question, we have the following parameters that can be used in our computation:
SA = 1017.36
The shape is a sphere
So, we have
SA = 4πr²
Substitute the known values in the above equation, so, we have the following representation
4πr² = 1017.36
So, we have
r² = 80.96
Take the square root
r = 9
Multiply by 2
d = 18
Hence, the diameter is 18 meters
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a probability distribution is: group of answer choices the average value that a random variable is expected to assume over a large number of trials. a summary of data into classes along with the number of occurrences in each class. a listing of all possible outcomes along with their likelihood of occurrence. a listing of the successes and failures from a given experiment.
A probability distribution is a listing of all possible outcomes along with their likelihood of occurrence.
It is a way of describing the likelihood of different outcomes in a statistical experiment or random event. It is used to calculate the probability of different events or outcomes in situations where there is uncertainty or variability. There are two types of probability distributions: discrete and continuous.
Discrete probability distributions are used when the possible outcomes of a statistical experiment are discrete or countable, such as the number of heads obtained in flipping a coin. Continuous probability distributions are used when the possible outcomes of a statistical experiment are continuous or uncountable, such as the height of people in a population.
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<7+m<6=200 appropriate theorem
The appropriate theorem used to solve this inequality is the subtraction property of inequalities, which states that if a < b, then a - c < b - c for any real number c. In this case, we subtracted 7 from both sides of the inequality to isolate m.
What is the inequalities theorem?It says [tex]"7+m < 6=200"[/tex] which has an equal sign in between 6 and 200, which does not make sense. I will assume that the inequality you meant to provide is:
[tex]7+m < 6[/tex]
To solve this inequality, we want to isolate m on one side of the inequality. We can do this by subtracting 7 from both sides:
[tex]7 + m - 7 < 6 - 7[/tex]
Simplifying the left-hand side and the right-hand side, we get:
[tex]m < -1[/tex]
Therefore, the solution to the inequality [tex]7+m < 6[/tex] is:
m < -1
We can verify this solution by plugging in a value of m that is less than -1, such as -2, into the original inequality:
[tex]7 + (-2) < 6[/tex]
Simplifying the left-hand side, we get:
[tex]5 < 6[/tex]
This is true, so the solution m < -1 is valid.
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The given question is incomplete. Complete question is given below:
Solve the inequality 7+m<6=200 using the appropriate theorem.
Trapezoids and Kites proving trapezoid theorems
Therefore, the diagonal that connects the midpoints of the other two sides of the kite bisects the other diagonal.
What is trapezoid?A trapezoid is a quadrilateral with at least one pair of parallel sides. The parallel sides are called the bases of the trapezoid, and the non-parallel sides are called the legs. A trapezoid can have two pairs of parallel sides, in which case it is called a parallelogram.
Here,
First, let's define what a trapezoid and a kite are:
A trapezoid is a quadrilateral with at least one pair of parallel sides. The parallel sides are called the bases of the trapezoid.
A kite is a quadrilateral with two pairs of adjacent sides of equal length.
Now, let's look at some common trapezoid theorems and how to prove them:
The bases of a trapezoid are parallel.
To prove this theorem, we can use the fact that opposite angles of a parallelogram are equal. Since the bases of a trapezoid are parallel, we can draw a line segment that connects the endpoints of the non-parallel sides to form a parallelogram. The opposite angles of the parallelogram are equal, so the opposite angles of the trapezoid are also equal. Therefore, the bases of a trapezoid are parallel.
The legs of a trapezoid are congruent.
To prove this theorem, we can use the fact that a trapezoid can be divided into two triangles by drawing a diagonal. Since the bases of a trapezoid are parallel, the diagonal divides the trapezoid into two congruent triangles. Therefore, the legs of a trapezoid are congruent.
The diagonals of a trapezoid bisect each other.
To prove this theorem, we can use the fact that a trapezoid can be divided into two triangles by drawing a diagonal. Since the bases of a trapezoid are parallel, the diagonal divides the trapezoid into two congruent triangles. The diagonals of the trapezoid connect the midpoints of the non-parallel sides of the triangles, which are also the midpoints of the legs of the trapezoid. Therefore, the diagonals of a trapezoid bisect each other.
Now, let's look at some common kite theorems and how to prove them:
The diagonals of a kite are perpendicular.
To prove this theorem, we can use the fact that a kite can be divided into four right triangles. Since two pairs of adjacent sides of a kite are equal in length, the right triangles that share a common vertex have one leg that is perpendicular to the other leg. Therefore, the diagonals of a kite are perpendicular.
One diagonal of a kite bisects the other diagonal.
To prove this theorem, we can use the fact that a kite can be divided into four triangles. Since two pairs of adjacent sides of a kite are equal in length, the diagonal that connects the non-adjacent vertices of the kite divides the kite into two congruent triangles.
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Complete question:
Prove the trapezoid theorems: for Trapezoids and Kites.
Help please !!!!!!!!!!
The value of n for each of the values in the problem have been shown below.
How do you simplify exponents?When multiplying exponential expressions with the same base, you can add the exponents. For example: a^m * a^n = a^(m+n).
When dividing exponential expressions with the same base, you can subtract the exponents. For example: a^m / a^n = a^(m-n).
An exponential expression with a fractional exponent can be rewritten as a radical expression. For example: a^(1/2) = √a.
We know that;
a^6/2 = a^n
n = 3
a^9/2 = a^n
n = 9/2
a^3(7/2) = a^n
n = 21/2
a^3/2 = a^n
n = 3/2
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What is the Coefficient of x4 in expansion of (2+x)5
Answer:
10
Step-by-step explanation:
rewrite as (x+2)⁵
use the binomial formula:
(a+b)⁵ = a⁵ + 5a⁴b + 10a³b² + 10a²b³ + 5ab⁴ + b⁵
a = x, b = 2
The problem is only asking for the coefficient of the x⁴ expression, so the answer is:
5a⁴b = 5(x)⁴(2) = 10x⁴
Lola has 4 1/2 cups of rice. She uses 3/4 of the rice to make sushi rolls for dinner. She uses the rest of the rice to make rice pudding for dessert. How much rice does Lola use for the rice pudding?
Lola has 9/8 cups of rice left to use for the rice pudding.
What is fraction?
A fraction is a mathematical term that represents a part of a whole or a ratio between two quantities.
To find out how much rice Lola uses for the rice pudding, we need to first determine how much rice she used for the sushi rolls.
Lola used 3/4 of the 4 1/2 cups of rice for the sushi rolls. To calculate this, we can multiply:
4 1/2 cups x 3/4 = (9/2) x (3/4) = 27/8 cups
So Lola used 27/8 cups of rice for the sushi rolls.
To find out how much rice Lola has left for the rice pudding, we need to subtract the amount she used for the sushi rolls from the original amount of rice she had:
4 1/2 cups - 27/8 cups = 36/8 cups - 27/8 cups = 9/8 cups
Therefore, Lola has 9/8 cups of rice left to use for the rice pudding.
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The perimeter of a rectangle is 60, and the width is 3 times
the length. What is the width?
O24.5
O 26.5
O 22.5
O 20.5
Let's assume that the length of the rectangle is "x".
Since the width is 3 times the length, the width can be represented as "3x".
The perimeter of a rectangle is given by the formula:
P = 2(l + w)
where P is the perimeter, l is the length, and w is the width.
Substituting the values given in the problem, we have:
60 = 2(x + 3x)
Simplifying, we get:
60 = 8x
Dividing both sides by 8, we get:
x = 7.5
Now that we know the length, we can find the width:
width = 3x = 3(7.5) = 22.5
Therefore, the width of the rectangle is 22.5.
Answer:
Answer: 22.5
Step-by-step explanation:
Let L be the length of the rectangle, and W be the width.
From the problem, we know that:
The perimeter of the rectangle is 60, which means that:
2(L + W) = 60
L + W = 30
The width is 3 times the length:
W = 3L
Substituting W = 3L into the first equation, we get:
L + 3L = 30
4L = 30
L = 7.5
Therefore, the width is:
W = 3L = 3(7.5) = 22.5
So, the width of the rectangle is 22.5. Answer: 22.5
In a group, more than 1/2 are boys, but they are less than 2/3 of the group. Can there be:(In each case, if your answer is “yes”, find out how many boys there were. Explore all possible cases). Could there be 7 kids
Yes, there could be a total number of 7 kids in the group with more than 1/2 of them being boys and less than 2/3 of them being boys.
Let's assume that the total number of kids in the group is x.
According to the problem, more than 1/2 of the group are boys. Mathematically, we can represent this as:
Number of boys > x/2
Also, the boys are less than 2/3 of the group. Mathematically, we can represent this as:
Number of boys < 2x/3
Now, let's substitute x=7 in the above two equations:
Number of boys > 7/2 = 3.5 --- (1)
Number of boys < 14/3 ≈ 4.67 --- (2)
From equation (1), we can conclude that there must be at least 4 boys in the group.
From equation (2), we can conclude that there can be at most 4 boys in the group because the number of boys cannot be a fraction.
Therefore, the possible number of boys in the group could be either 4 or 3. If there are 4 boys, then the number of girls in the group would be 3. If there are 3 boys, then the number of girls in the group would be 4.
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Find the mean of each set of numbers. Round
answers to the nearest tenth.
23, 32, 13, 12, 33, 22, 30
Answer: 23.6 (rounded to the nearest tenth)
Step-by-step explanation:
Robert is on a diet to lose weight before his Spring Break trip to the Bahamas. He is losing weight at a rate of 2 pounds per week. After 6 weeks, he weighs 205 pounds. Write and solve a linear equation to model this situation. There should be at least 3 lines of work.
A linear equation modeling Robert's weight-loss situation is x = 205 + 2y.
What is a linear equation?A linear equation is an equation modeling a straight-line relationship between two variables, for example, x and y.
The weight lost per week = 2 pounds
The number of weeks weight was lost, y = 6 weeks
Robert's weight after 6 weeks of losing 2 pounds weekly = 205
Let x = Robert's weight before the weight-loss program
Equation:x = 205 + 2y
x = 205 + 2(6)
x = 205 + 12
x = 217
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a group of people are arranging themselves for a parade. if they line up three to a row, one person is left over. if they line up four to a row, two people are left over, and if they line up five to a row, three people are left over. what is the smallest number of people required to satisfy the conditions? what is the next smallest number? show all work.
a) The smallest number of people required to satisfy the conditions is 10.
b) The next smallest number of people required to satisfy the conditions is 70.
This is a problem of finding the least common multiple (LCM) of three numbers with given remainders. The LCM is the smallest number that is divisible by all three numbers and leaves the given remainders.
Let's call the number of people "n". We know that
n ≡ 1 (mod 3)
n ≡ 2 (mod 4)
n ≡ 3 (mod 5)
To find the LCM, we can use the Chinese remainder theorem or a simpler method is to use trial and error starting from the given remainders.
Starting from n ≡ 1 (mod 3), we can add multiples of 3 until we find a number that satisfies the other two conditions. Trying n = 4, 7, 10, ... we find that n = 10 satisfies all three conditions
10 ≡ 1 (mod 3)
10 ≡ 2 (mod 4)
10 ≡ 3 (mod 5)
Therefore, the smallest number of people required to satisfy the conditions is 10.
To find the next smallest number, we can add the LCM of 3, 4, and 5 to 10. The LCM of 3, 4, and 5 is 60, so the next smallest number is 70
70 ≡ 1 (mod 3)
70 ≡ 2 (mod 4)
70 ≡ 3 (mod 5)
Therefore, the next smallest number of people required to satisfy the conditions is 70.
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explain the reasons that someone would create either a bar chart or a histogram in order to explore a single column of data
A bar chart or a histogram are visual representations of data that can be used to explore a single column of data.
A bar chart is used to compare different categories of data, and a histogram is used to measure the frequency of data within a given range. Bar charts allow a user to compare the differences between the categories of data, while histograms provide a better indication of how the data is distributed within the range.
Both bar charts and histograms are useful for identifying patterns, outliers, and trends in the data. By using a bar chart or a histogram, a user can quickly and easily identify where the data is concentrated, as well as identify any outliers or trends in the data.
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what is the median and range of the data
The median and the range of the given data above would be =5 and 11 respectively.
How to calculate the median and range of a given data?The range of a data set can be calculated by the subtraction of the largest variable form the smallest variable of a data set.
That is;
Data set = 1,1,1,1,2,2,2,5,6,6,6,8,9,10,12
largest variable = 12
smallest variable = 1
range = 12-1 = 11
The median of the data set is the figure that fall at the middle of the data set after being arranged either in ascending or descending order.
The median of the data = 5
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May finds a house for a sale price of $355,000. She meets with her bank and finds a 30-year simple interest mortgage. If May accepts the mortgage, she would pay $798,750 in simple interest over the life of the loan. 1. How much is the interest rate of the mortgage? 2. How much would be her monthly mortgage payment? 3. If May decided to use a 15-year simple interest mortgage, how much would she save on interest charges?
May would therefore save $621,470.85 in interest costs if she opted for a 15-year simple interest mortgage ($798,750 - $177,279.15).
what is interest ?The sum of money that even a lender charges a loan for the usage of money over a certain period of time is known as interest. It is frequently represented as a proportion of the sum lent or borrowed and can be either simple or compound. Simple interest is determined by that of the principal amount alone, while interest expense is determined by the principal amount and the total amount of interest that has accrued. A key idea in banking, interest is utilised in a number of credit derivatives, including bonds, savings accounts, and loans.
given
May would save on interest costs if she chose a 15-year simple interest mortgage because the loan would be repaid sooner. Using the same technique as before but with n = 15 years, we can determine the interest costs for a 15-year mortgage:
PV is equal to PMT* [1 - (1 + r/12)(-n*12)] / (r/12)
Inputting the values provided yields:
355000 = PMT * [1 - (1 + 0.595%/12)^(-15*12)] / (0.595%/12)
PMT = $3,208.59
Over the course of the loan, the following would be paid in interest:
I equals PMT*n - PV.
I = $3,208.59 * 15 - $355,000
I = $177,279.15
May would therefore save $621,470.85 in interest costs if she opted for a 15-year simple interest mortgage ($798,750 - $177,279.15).
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a random sample of 100,000 credit sales in a department store showed an average sale of $87.25. from past data, it is known that the standard deviation of the population is $20.00. what is the 95% confidence interval of the population mean?
The 95% confidence interval of the population mean for the given sample is between $86.96 and $87.54.
To calculate the confidence interval, we need to use the formula:
CI = [tex]\bar{X}[/tex] ± Zα/2 * σ/√n
where,
[tex]\bar{X}[/tex] = sample mean = $87.25
Zα/2 = the Z-score for 95% confidence level = 1.96
σ = population standard deviation = $20.00
n = sample size = 100,000
Plugging these values in the formula, we get:
CI = 87.25 [tex]\pm[/tex] 1.96 * (20/√100,000)
CI = 87.25 [tex]\pm[/tex] 0.098
Therefore, the 95% confidence interval of the population mean is between $86.96 and $87.54. This means that we can be 95% confident that the true population mean lies within this interval.
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please help, i dont undertsand these!
A)In 30 minutes, Bobby's dog can cover x miles.(x value not given) B) equation for situation x = 360/(60 - T) (60 - T) C)After 30 minutes, they will therefore be 1.5 times as far apart from one another.
Describe miles?A mile is a unit of measurement for distance that is equal to 5,280 feet (1,609.344 meters) or 5,280 ft. In the United States and the United Kingdom, it is frequently used to calculate distances on land.
A)
If Bobby's cat moves at a speed of x mph and Bobby's dog moves at a speed of 2 mph, then Bobby's cat moves at x mph.
Bobby's dog can run a certain distance in 30 minutes according to the following formula:
Distance is determined by speed and time.
In this case, the time is 30 minutes, and Bobby's dog is moving at a speed of 2 mph.
30 minutes are converted to hours, giving us:
60 hours / 30 minutes=0.5 hours.
Bobby's dog can cover the following distance in 30 minutes:
miles are calculated using the formula distance = speed time (2x) (0.5).
Hence, in 30 minutes, Bobby's dog can cover x miles.
B)
If Bobby's cat moves at a speed of x mph and Bobby's dog moves at a speed of 2 mph, then Bobby's cat moves at x mph.
Imagine if after 30 minutes Bobby's dog and cat were 6 miles apart.
Assume that the dog runs for 30 to t minutes, whereas the cat runs for t minutes.
The cat's journey's mileage is then:
Distance = speed x (t/60) = time (xt/60 miles)
Similar to how the dog travelled, the distance is:
(Speed - Time)/60 = x(30 - T)/30 miles; distance = speed - time - 2x;
After 30 minutes, they were 6 miles apart, thus we can write:
The sum of the distances covered by the dog and the cat is six.
xt/60 + x(30 - t)/30 = 6
When we multiply both sides by 60, we obtain:
xt + 2x(30 - t) = 360
When we simplify the equation, we obtain:
xt + 60x - 2xt = 360
60x - xt = 360
x(60 - t) = 360
x = 360/(60 - t) (60 - t)
Hence, we can formulate the equation for this circumstance as follows:
x = 360/(60 - t) (60 - t)
C)
If Bobby's cat moves at a speed of x mph and Bobby's dog moves at a speed of 2 mph, then Bobby's cat moves at x mph.
If the dog and cat begin to flee from one another, their relative speed is:
relative speed is calculated as follows: cat + dog
= x + 2x
= 3x mph
After 30 minutes, their distance may be calculated using the following formula:
Distance is determined by speed and time.
The time is 30 minutes, and the relative speed is 3x mph.
30 minutes are converted to hours, giving us:
60 hours/ 30 minutes= 0.5 hours.
As a result, after 30 minutes, they will be separated by the following distance:
1.5 miles= 3 times the speed times .
After 30 minutes, they will therefore be 1.5 times as far apart from one another.
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Which equation shows an example of the associative property of addition?
a .(–4 + i) + 4i = –4 + (i + 4i)
b. (–4 + i) + 4i = 4i + (–4i + i)
c. 4i × (–4i + i) = (4i – 4i) + (4i × i)
d. (–4i + i) + 0 = (–4i + i)
a . (–4 + i) + 4i = –4 + (i + 4i).The associative property of addition states that the grouping of the numbers being added does not change their sum.
In option (a), the expression on the left-hand side can be grouped as (–4 + i) + 4i, and the expression on the right-hand side can be grouped as –4 + (i + 4i). Both expressions result in the same sum of –4 + 5i. Therefore, option (a) demonstrates the associative property of addition.
The associative property of addition is a mathematical property that states that the grouping of the numbers being added does not affect their sum. In other words, when adding three or more numbers, the order in which the numbers are grouped for addition does not affect the result. Mathematically, the associative property of addition can be expressed as:
(a + b) + c = a + (b + c)
This property holds for any real numbers a, b, and c. The associative property of addition is a fundamental property of arithmetic and is used extensively in algebraic manipulations to simplify expressions and solve equations.
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You are planning to use a ceramic tile design in your new bathroom. The tiles are blue-and-white equilateral triangles. You decide to arrange the blue tiles in a hexagonal shape as shown. If the side of each tile measures 7 centimeters, what will be the exact area of each hexagonal shape?
Using the area formula of the triangle, we know that the area of the hexagonal shape tile is 21 cm² respectively.
What is a hexagon?A hexagon is a six-sided polygon in geometry.
Any simple hexagon has 720° of internal angles in total.
In geometry, a hexagon is a six-sided polygon.
Each internal angle and the side length of a regular hexagon are both 120 degrees.
Hexagon is one of many nouns in science and mathematics that has Greek roots.
The concept of a six-sided shape is derived from the Greek word hexágnon, where the word gonia mean "angle."
This makes sense because a hexagon includes not only six sides, but also six angles, or vertices.
So, we know we have equilateral triangles:
Area = 1/2 * base * height
Insert values as follows:
Area = 1/2 * base * height
Area = 1/2 * 7 * 7
Area = 1/2 * 49
Area = 24.5 cm²
Then, the area of the hexagonal tile:
24.5 * 6 = 147 cm²
Then, 147/7 = 21 cm²
Therefore, using the area formula of the triangle, we know that the area of the hexagonal shape tile is 21 cm² respectively.
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Can someone help me, pls
Answer is attached
hope it helps you ⬆️
One penny has a mass of 2.5 g. Each roll of pennies contains 50 pennies. Write an equation with two variables that can be used to determine the total mass in grams of the pennies in any number of rolls of pennies. Show your work.
Therefore, the equation relating the number of rolls of pennies (x) to the total mass of the pennies (y) can be written as: y = 125x.
What is equation?An equation is a mathematical statement that shows the equality between two expressions. Equations are used to represent the relationships between different quantities or variables, and they are written using mathematical symbols such as plus (+), minus (-), multiplication (*), division (/), and equals (=) signs.
Here,
Let "x" be the number of rolls of pennies, and "y" be the total mass of the pennies in grams.
The mass of one roll of pennies can be calculated by multiplying the mass of one penny by the number of pennies in a roll:
mass of one roll of pennies = 2.5 g/penny x 50 pennies/roll
mass of one roll of pennies = 125 g/roll
Therefore, the equation relating the number of rolls of pennies (x) to the total mass of the pennies (y) can be written as:
y = 125x
This equation shows that the total mass of the pennies is directly proportional to the number of rolls of pennies, with a constant of proportionality of 125 grams per roll.
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What is the possible range for sizes x when u have 4.1 and 1.3
The possible range of x in the triangle is (2.8,∞)
According to the triangle inequality theorem, any two sides' sums in a triangle must be bigger than the length of the third side. If a, b, and c are the lengths of a triangle's sides, then the sum of a and b's lengths is greater than c's length. Similar to how a+ c > b, b + c > a.
By applying the triangle inequality theorem, which asserts that if the sides have lengths a, b, and c, then a + c > b, it is feasible to determine the range of sizes for x. Let a = 4, 1, and 3 and c = x. Our range of values for x is as follows because measurements of length and distance can never be negative:
a + c > b 4.1 + x > 1.3 x > -2.8
Hence, x's potential size range is (-2.8, infinity).
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MA.912.FL.3.2: Solve real-world problems involving simple, compound and continuously compounded interest.
1. Earl opens a certificate of deposit with $1,500 that pays 2.75% compounded daily.
Part A: Write an equation to model this situation.
Part B. How much money will be in the account after 1 year?
Part C. How much money will be in the account after 5 years?
Part A: The formula for the future value of an investment with compound interest is given by:
A = P(1 + r/n)^(nt)
Where: A = the future value of the investment P = the principal investment amount r = the annual interest rate (as a decimal) n = the number of times the interest is compounded per year t = time in years
For this situation, P = $1,500 r = 2.75% = 0.0275 (since the interest rate is given as an annual rate, we need to divide it by 100 to convert it to a decimal) n = 365 (since interest is compounded daily) t = 1 (since we are looking for the value after one year)
Therefore, the equation to model this situation is:
A = 1500(1 + 0.0275/365)^(365*1)
Part B: To find the value of the account after one year, we can simply substitute t=1 into the equation:
A = 1500(1 + 0.0275/365)^(365*1) = $1,543.21
Therefore, the amount of money in the account after 1 year is $1,543.21.
Part C: To find the value of the account after 5 years, we need to substitute t=5 into the equation:
A = 1500(1 + 0.0275/365)^(365*5) = $1,805.59
Therefore, the amount of money in the account after 5 years is $1,805.59.
Pre-Algebra Writing Question (Image below) Please do everything that it says in the image most people don't do it, it's Part A and B
A. The width of the rectangle is 32 centimeters. and B. solving for the width, we get the answer of 32 cm.
What is rectangle?
A rectangle is a geometric shape that has four sides and four right angles (90 degrees) with opposite sides being parallel and equal in length.
A. Let's use the formula for the perimeter of a rectangle:
Perimeter = 2 × (Length + Width)
We are given the length of the rectangle, which is 26 cm, and the perimeter, which is 116 cm. We can substitute these values into the formula and solve for the width:
116 cm = 2 × (26 cm + Width)
Divide both sides by 2:
58 cm = 26 cm + Width
Subtract 26 cm from both sides:
32 cm = Width
Therefore, the width of the rectangle is 32 centimetres.
B. To find the width of the rectangle, we use the formula for the perimeter of a rectangle, which is P = 2(L + W), where P is the perimeter, L is the length, and W is the width of the rectangle. We substitute the given values into the formula and solve for the width. We are given the length of the rectangle, which is 26 cm, and the perimeter, which is 116 cm. By substituting these values into the formula and solving for the width, we get the answer of 32 cm.
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