From the given information provided, In a series RCL circuit the frequency of the generator is approximately 283.7 Hz.
In a series RCL circuit, the resonant frequency is given by:
f = 1/(2π√(LC))
where L is the inductance in henries, C is the capacitance in farads, and π is a mathematical constant approximately equal to 3.14159.
We are given that the resonant frequency is 270 Hz. Let's assume that the capacitance C is known and try to solve for the inductance L:
270 = 1/(2π√(LC))
Simplifying:
2π√(LC) = 1/270
Squaring both sides:
4π²LC = 1/(270²)
Simplifying:
LC = 1/(4π²×270²)
LC = 6.272 x 10⁻⁹
We are also given that at the non-resonant frequency, the ratio of the inductive reactance to the capacitive reactance of the circuit is observed to be 4.93. This means that:
XL / XC = 4.93
where XL is the inductive reactance and XC is the capacitive reactance.
The inductive and capacitive reactances are given by:
XL = 2πfL and XC = 1/(2πfC)
where f is the frequency in Hz.
Substituting XC = 1/(2πfC) and simplifying the ratio:
2πfL / (1/(2πfC)) = 4.93
Multiplying both sides by (2πfC)²:
(2πf)²L = 4.93C
Substituting the value of C we found earlier:
(2πf)²L = 3.94 x 10⁻⁸
Substituting the value of L = 1/(4π²f²C) we found earlier:
(2πf)²/(4π²f²C) = 3.94 x 10⁻⁸
Simplifying:
f = 283.7 Hz
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1) Tom and Tim shared 72 sweets in the ratio 4:5
How many sweets did they each get?
Tom gets 32 sweets, and Tim gets 40 sweets
4:5
4+5 = 9
4/9 of 72 = 32
4:5
4+5 = 9
5/9 of 72 = 40
I'm not that sure cuz I took this a long time ago
but I think 1 of them took 4 and the other 1 took 5
You are offered a job that pays $46,000 during the first year, with an annual increase of 6% per year beginning in the second year. That is, beginning in year 2, your salary will be 1.06 times what it was in the previous year. What can you expect to earn in your fourth year on the job? Round your answer to the nearest dollar.
In your fourth year on the job, you can expect to earn $__
(Round to the nearest dollar.)
You can expect to earn $55,157.98 in your fourth year on the job.
What is variable salary?Often, it comes in the form of commission, bonus, or incentive compensation. It is based on the performance of the individual and the overall performance of the business. The majority of businesses incorporate the goal-setting procedure, which forms the basis of the variable payouts.
Given that, annual increase of 6% per year.
The expected salary can be calculated using the formula:
salary = initial salary x (1 + growth rate) raised to number of years.
Substituting the values we have:
salary in year 2 = $46,000 x (1 + 0.06)¹ = $48,760
salary in year 3 = $48,760 x (1 + 0.06)¹ = $51,822.40
salary in year 4 = $51,822.40 x (1 + 0.06)¹ = $55,157.98
Therefore, you can expect to earn $55,157.98 in your fourth year on the job.
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Tony and Yolani are measuring the volume of a supply box at school. Tony uses a ruler to measure the box's length, width, and height in centimeters; then he multiplies these measurements. Yolani fills the box with centimeter cubes, then counts the number of cubes. How will their answers compare?
Tony and Yolani's answers should be the same if they have measured the volume of the box accurately.
Tony's method of measuring the volume of the box is by multiplying the measurements of the length, width, and height. This gives him the total number of cubic centimeters that fit in the box.
On the other hand, Yolani's method of measuring the volume of the box is by filling it with centimeter cubes and counting the number of cubes. Since each cube has a volume of 1 cubic centimeter, the total number of cubes is equal to the volume of the box in cubic centimeters.
Both methods of measuring the volume of the box are valid and will give the same answer. This is because the volume of an object is a measure of how much space it occupies and is independent of the method used to measure it.
Tony's method of measuring the volume is based on the dimensions of the box, while Yolani's method is based on the number of cubic centimeter cubes that can fit inside the box. However, both methods will give the same result, as they are measuring the same thing - the volume of the box.
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A jacket had an original price of $80 and is on sale for $64. What is the percent of change in price?
The difference between the purchase price of $64 and the sale price of $80 represents a 20% price shift.
To find the percent of change in price between the original price of $80 and the sale price of $64, we can use the formula for percent change:
Percent Change = (|New Value - Old Value| / Old Value) x 100%
where the vertical bars around the (New Value - Old Value) expression represent the absolute value of the difference.
In this case, the old value is $80 and the new value is $64. So, we can substitute these values into the formula:
Percent Change = (|64 - 80| / 80) x 100%
Percent Change = (|-16| / 80) x 100%
Percent Change = (16 / 80) x 100%
Percent Change = 0.2 x 100%
Percent Change = 20%
Therefore, the percent of change in price between the original price of $80 and the Sale price of $64 is 20%. This means that the price of the jacket decreased by 20% from its original price of $80.
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Please help explain
I am art plugs egg CBGB hbu CBN bhj baby Vida Vida vs back baby
A jacket is reduced from $20 to $14. By what percentage was the price of the jacket reduced?
Answer: 30%
Step-by-step explanation:
20-14=6
this is the amount reduced
6/20 multiply this by 100, which is 600/20, which equals 30%
Hope this helps!
At the community pool Allie there’s 30 minutes swimming laps for every 18 minutes spent running water wheel spins 20 minutes swimming laps for every 12 minutes training water and Benjamin spent 16 minutes swimming laps for every nine minutes trending water
After answering the given query, we can state that . Due to his unitary method rapid rate of water training, Benjamin uses the least time overall swimming and water training combined.
What is unitary method ?The unit strategy is a method of problem-solving where you first calculate the value of just one unit, then multiply that value to get the answer. Simply stated, one single value is extracted from a supplied numerous using the unit method
We can use the idea of rates, which is the amount of work done per unit of time, to compare the swimming and water training periods for Allie, Water Wheel, and Benjamin. The time in this instance is measured in minutes, and the labor is the time spent swimming laps or practicing in the water.
Find each person's prices for swimming and water training first:
Swimming at a rate of 30/18 = 5/3 laps per minute, and training in the pool at a rate of 1/18 per minute, according to Allie.
Swimming pace (20/12 = 5/3 laps per minute) and water training rate (1/12 training water per minute) on the water wheel
Swimming at a rate of 16/9 laps per minute and training in the pool at a rate of 1/9 per minute, according to Benjamin
As a result, various people spend more or less time swimming laps or training in the water based on the activity. Due to his rapid rate of water training, Benjamin uses the least time overall swimming and water training combined.
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How many solutions does the following system have 2x+3y=12 2x+3y=18
The system 2x+3y=12 and 2x+3y=18 does not have any solution
The given system of equations is:
2x + 3y = 12 ...(1)
2x + 3y = 18 ...(2)
We can rewrite the equations in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept, as follows:
Equation (1): 3y = -2x + 12 => y = (-2/3)x + 4
Equation (2): 3y = -2x + 18 => y = (-2/3)x + 6
From the equations in slope-intercept form, we can see that the two lines have the same slope of -2/3, which means they are parallel.
Parallel lines never intersect, which means there are no solutions to the given system of equations.
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4. The number of questions Tyler answers correctly is within 2 of the number of Benjamin's correct answers. Part A Write and solve an absolute value inequality to determine the number of questions Tyler answers correctly. T-B22 or B-T ≤2 Part B Based on your answer to Part A, what prizes will Tyler win? Explain.
Part A) Tyler answers within 2 questions of Benjamin if he answers B+2, B+1, B, B-1, or B-2 questions correctly.
Part B) Based on the solution from Part A, Tyler will win prizes for correctly answering the corresponding number of questions.
What is inequality?Inequality can be defined as the relation of the equation containing the symbol of ( ≤, ≥, <, >) instead of the equal sign in an equation.
Here,
Part A:
Since we want to find the possible values of T, we can isolate T on one side of the inequality:
T - B ≤ 2
T ≤ B + 2
or
T - B ≥ -2
T ≥ B - 2
Therefore, Tyler answers within 2 questions of Benjamin if he answers B+2, B+1, B, B-1, or B-2 questions correctly.
Part B:
Based on the solution from Part A, Tyler will win prizes for correctly answering the corresponding number of questions.
This is because Tyler's score is within 2 questions of Benjamin's score. Therefore, he will receive the same prizes as Benjamin for answering the same number of questions, as well as additional prizes for answering 1 or 2 fewer questions than Benjamin.
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You want to buy a house and are able to afford monthly payments of $1500. The bank is willing to give you a 30-year loan with 7.14% interest rate. Answer the following:
a) How much money total will the loan amount be?
b) How much will you pay by giving $1400 a month for 30 years?
c) How much interest will you pay over the life of the loan?
a) The total loan amount will be $244,171.43.
b) You will pay $228,633.34 by giving $1400 a month for 30 years.
c) The total interest paid over the life of the loan will be $295,828.57.
What is interest rate?An interest rate is the amount of interest due per period, as a proportion of the amount lent, deposited, or borrowed.
a) To calculate the total loan amount, we can use the formula for a fixed payment mortgage:
Loan Amount = Payment / ((1 - (1 + r/n)^(-nt)) / (r/n))
where:
Payment = $1500 (monthly payment)r = 7.14% (annual interest rate)n = 12 (number of payments per year)t = 30 (number of years)Plugging in the values, we get:
Loan Amount = $1500 / ((1 - (1 + 0.0714/12)^(-12*30)) / (0.0714/12))
Loan Amount = $244,171.43
Therefore, the total loan amount will be $244,171.43.
b) To calculate how much you will pay by giving $1400 a month for 30 years, we can use the same formula and replace the payment amount:
Loan Amount = Payment / ((1 - (1 + r/n)^(-nt)) / (r/n))$1400 = $1400 / ((1 - (1 + 0.0714/12)^(-12*30)) / (0.0714/12))Plugging in the values, we get:
Loan Amount = $228,633.34
Therefore, you will pay $228,633.34 by giving $1400 a month for 30 years.
c) The total interest paid over the life of the loan can be calculated by subtracting the loan amount from the total payments made over the 30 years:
Total Interest = Total Payments - Loan Amount
The total payments can be calculated by multiplying the monthly payment by the total number of payments:
Total Payments = Monthly Payment x Total Number of PaymentsTotal Payments = $1500 x 12 x 30Total Payments = $540,000Substituting the values, we get:
Total Interest = $540,000 - $244,171.43
Total Interest = $295,828.57
Therefore, the total interest paid over the life of the loan will be $295,828.57.
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What is the volume, in cubic inches, of one cube with an edge length of 1/6 in. Show or explain your thinking.
Answer:
Below
Step-by-step explanation:
All of the side lengths of a CUBE are the same
VOLUME = L x W x H = 1/6 * 1/6 * 1/6 = 1/ (6^3) = 1 / 216 in^3
Question 1(Multiple Choice Worth 2 points)
(Volume of Cylinders MC)
A soccer player has a large cylindrical water cooler that measures 3 feet in diameter and is 4 feet tall. If there are approximately 7.48 gallons of water in a cubic foot, how many gallons of water are in the water cooler when it is completely full? Use π = 3.14 and round to the nearest hundredth.
28.26 gallons
113.04 gallons
211.38 gallons
845.54 gallons
Question 2(Multiple Choice Worth 2 points)
(Volume of Cylinders MC)
A cylinder has a volume of 1 and one sixteenth in3 and a radius of one fourth in. What is the height of a cylinder? Approximate using pi equals 22 over 7.
119 twelfths inches
119 over 22 inches
119 over 44 inches
119 over 56 inches
Question 3(Multiple Choice Worth 2 points)
(Volume of Cylinders MC)
What is the volume of a right circular cylinder with a diameter of 6 meters and a height of 14 meters. Leave the answer in terms of π.
504π m3
396π m3
126π m3
84π m3
Question 4(Multiple Choice Worth 2 points)
(Volume of Cylinders MC)
What is the volume of the cylinder? Round to the nearest hundredth and approximate using π = 3.14.
cylinder with a segment from one point on the circular base to another point on the base through the center labeled 2.6 feet and a height labeled 4.4 feet
23.35 cubic feet
35.92 cubic feet
71.84 cubic feet
93.4 cubic feet
Question 5(Multiple Choice Worth 2 points)
(Volume of Cylinders MC)
Coins are placed into a treasure chest, and each coin has a radius of 1.4 inches and a height of 0.0625 inches. If there are 230 coins inside the treasure chest, how many cubic inches of the treasure chest is taken up by the coins? Round to the nearest hundredth and approximate using π = 3.14.
0.38 in3
126.39 in3
353.88 in3
88.47 in3
Question 6(Multiple Choice Worth 2 points)
(Volume of Cylinders MC)
A helium tank shaped like a cylinder has 2,401π in3 of space inside the tank. If the diameter of the helium tank is 14 inches, what is its height?
49 inches
28 inches
12.25 inches
7 inches
Question 7(Multiple Choice Worth 2 points)
(Volume of Cylinders MC)
Bradenton Bakery is baking a cake for a customer's quinceañera. The cake mold is shaped like a cylinder with a diameter of 12 inches and height of 8 inches.
Which of the following shows a correct method to calculate the number of cubic units of cake batter needed to fill the mold? Approximate using pi equals 355 over 113.
V equals 355 over 113 times 12 squared times 8
V equals 355 over 113 times 6 squared times 8
V equals 355 over 113 times 8 squared times 6
V equals 355 over 113 times 8 squared times 12
After answering the given query, we can state that Thus, the correct equation response is (C) 211.38 liters.
What is equation?In a math equation, two assertions are connected by the equals sign (=), which denotes equivalence. Through a mathematical statement, algebraic equations show that two mathematical expressions are equal. For instance, the equal sign separates the numbers 3x plus 5 and 14 in the equation 3x + 5 = 14. To comprehend the relationship between the two lines written on the opposing edges of a letter, use a mathematical formula. The logo and the specific program tend to correspond most of the time. An illustration would be 2x - 4 = 2.
Using the equation V = r2h, where r is the radius and h is the height, one can calculate the capacity of the water cooler. The cylinder has a 3 foot circumference, making its radius 1.5 feet. The sphere stands 4 feet tall.
V is equal to (1.5)2(4) = 28.26 cubic feet.
The water refrigerator holds about 7.48 cubic feet of water, so when it is fully filled, it holds the following amount of water:
7.48 times 28.26 = 211.38 liters.
Thus, the correct response is (C) 211.38 liters.
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If 9* = 243, what is the value of x?
Answer: 27
Step-by-step explanation: Because, (I am pretty sure that the " * " symbol means multiply) 243 divided by 9 is 27.
I hope my answer helps!
Answer:
Step-by-step explanation:
Mr.Morrie shared $1050 among his three children Daniel, Eva and Francis.Eva received $185.00 more than Daniel who received $175.00 less than Francis.How much money did each child receive?
Step-by-step explanation:
Let x be the amount of money that Daniel received.
Let y be the amount of money that Eva received.
Let z be the amount of money that Francis received.
y = x + 185 (Eva received $185.00 more than Daniel)
x = z - 175 (Daniel received $175.00 less than Francis)
x + y + z = 1050
We can substitute the first two equations into the third equation to get:
(z - 175) + (x + 185) + z = 1050
2z + x + y = 1040
2z + 2x + 185 = 1040
2z + 2x = 855
z + x = 427.5
z + z - 175 = 427.5
2z = 602.5
z = 301.25
Now we can use the equation x = z - 175 to find x:
x = 301.25 - 175
x = 126.25
Finally, we can use the equation y = x + 185 to find y:
y = 126.25 + 185
y = 311.25
Therefore, Daniel received $126.25, Eva received $311.25, and Francis received $301.25.
y=6x
2x-7y=40
solve by system of subtraction
Answer:
Step-by-step explanation:
vgfjbm
The population of Town A in 1980 was 3000.
The population of Town A increased by 20% every decade. Let x represent the number of decades since 1980. The graph shows the population of Town B.
Compare the populations of the towns by calculating and interpreting the average rates of change from 2000 to 2020.
Step-by-step explanation:
The population of Town A in 2000 was 3000(1.2)^2 = 5184. The population of Town A in 2020 was 3000(1.2)^4 = 8947.2. The average rate of change of Town A from 2000 to 2020 is (8947.2-5184)/(2020-2000) = 188.64 people per year.
From the graph, the population of Town B in 2000 was approximately 5500. The population of Town B in 2020 was approximately 7000. The average rate of change of Town B from 2000 to 2020 is (7000-5500)/(2020-2000) = 75 people per year.
Therefore, the average rate of change of Town A's population is greater than that of Town B's population from 2000 to 2020.
Drag and drop the correct value next to its equivalent expression. Numbers may be used once or not at all. 10 5 6 28 14 2 3 20 1 4 27 2 3 20 3 4 Expression Value 2 3 × 42 5 12 × 26 11 15 × 20 3 8 × 54
The expressions are equivalent to any of the given values:
Expression Value
2 × 42 84
3 × 20 60
4 4
8 × 54 432
What is the equivalent expression?
Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we plug in the same value for the variable.
Expression Value
2 × 42 84
3 × 20 60
4 4
8 × 54 432
2 × 42 = 84 (multiplying 2 by 42 gives us a product of 84)
3 × 20 = 60 (multiplying 3 by 20 gives us a product of 60)
4 = 4 (4 is already a value, so it is equivalent to itself)
8 × 54 = 432 (multiplying 8 by 54 gives us a product of 432)
The remaining expressions (5 × 12 × 26, 11 × 15 × 20, 3 × 4) are not equivalent to any of the given values.
Hence, the expressions are equivalent to any of the given values:
Expression Value
2 × 42 84
3 × 20 60
4 4
8 × 54 432
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Please answer quickly !!
Answer: B
Step-by-step explanation:
There is no perfect square root for 0.4, there is a perfect square root for all other numbers though.
Answer:
And:- B
it is the irrational number
The table of values represents a quadratic function f(x).
x f(x)
−8 7
−7 2
−6 −1
−5 −2
−4 −1
−3 2
−2 7
−1 14
0 23
What is the equation of f(x)?
The equation of f(x) is f(x) = -6x^2 - 3x + 23.To find the equation of the quadratic function f(x) using the given table of values, we need to determine the coefficients of the quadratic equation in the form of f(x) = ax^2 + bx + c.
We can start by analyzing the pattern of the y-values (f(x)) corresponding to the x-values. Looking at the table, we notice that the y-values increase and then decrease, indicating that the quadratic function has a concave-down shape.
Next, we observe that when x = 0, f(x) = 23. This gives us the value of c, which is the constant term in the quadratic equation. Therefore, c = 23.To find the other coefficients, we can choose any two points from the table and substitute them into the general quadratic equation. Let's choose (-3, 2) and (1, 14).Substituting (-3, 2):
2 = a(-3)^2 + b(-3) + 23
9a - 3b + 23 = 2Substituting (1, 14):
14 = a(1)^2 + b(1) + 23
a + b + 23 = 14Simplifying both equations, we have:
9a - 3b = -21 ---(1)
a + b = -9 ---(2)
Solving equations (1) and (2), we find a = -6 and b = -3.
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In Juneau, Alaska, the 30-year annual snowfall average is 86.7 inches with a standard deviation of 40.4 inches. The last four years saw an average annual snowfall of 115.7 inches, 62.9 inches, 168.5 inches, and 135.7 inches. Hia performs a hypothesis test on this data to determine if the next 30-year norm will have a different average if the trend from the last four years continues. She uses a significance level of 5%. Which of the following is a conclusion that she may make?
The z-statistic is 1.44, so the null hypothesis cannot be rejected.
The z-statistic is 1.68, so the null hypothesis cannot be rejected.
The z-statistic is 1.85, so the null hypothesis should be rejected.
The z-statistic is 4.6, so the null hypothesis should be rejected.
The expected value of the amount of average snowfall for over 30 years is 86.7 inches with a standard deviation of 40.4 inches. To verify if this particular trend continues, we must check the significance value of the amount snowfall for the past four years. Given that the snowfall for past years are as follows: 115.7 inches, 62.9 inches, 168.5 inches, and 135.7 inches. Thus the mean of the sample would be: (115.7 + 62.9 + 168.5 + 135.7)/4 = 120.7 inches. To compute for the z-score, we have z-score = (x – μ) / (σ / √n) where x is the computed/measured value, μ is the expected mean, σ is the standard deviation, and n is the number of samples. Using the information we have, z-score (z) = (120.7 - 86.7) / (40.4/ √4) = 1.68 In order to reject the null hypothesis our probability value must be less than the significance level of 5%. For our case, since z = 1.68, P-value = 0.093 > 0.05. Therefore, the answer is B.
Please answer this question on circles WITH an explanation of the work please! I need this today!
Answer:
C
Step-by-step explanation:
the figure shows a tangent and a secant, then
the square of the measure of the tangent is equal to the product of the secant's external part and the entire secant, that is
(- 5 + x)² = (x - 7)(x - 7 + 5) ← expand left side using FOIL
25 - 10x + x² = (x - 7)(x - 2) ← expand using FOIL
x² - 10x + 25 = x² - 9x + 14 ( subtract x² from both sides )
- 10x + 25 = - 9x + 14 ( add 9x to both sides )
- x + 25 = 14 ( subtract 25 from both sides )
- x = - 11 ( multiply both sides by - 1 )
x = 11
Help me pleaseeeeeee
Which of the following equations represents a linear function?
y equals one fourth times x squared
y equals two thirds times x minus 7
x = 4
3x − 5 = 18
If you don't know don't bother wasting my point please I need this nowwwwwwwwwwwww
The equations that represent a linear functions are:
y = 2/3x - 7x = 43x - 5 = 18How to determine the linear functionsFrom the question, we have the following parameters that can be used in our computation:
The list of options
As a general rule
Linear functions are functions with a degree of 1
Using the above as a guide, we have the following equations with a degree of 1:
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Answer: it s B s
Step-by-step explanation:
3-pound fish stretches a spring 2 inches. how much work is done stretching it 4 more inches?
To calculate the work done stretching the spring 4 more inches, we can use the formula W = (kx^2)/2, where W is the work done, k is the spring constant, and x is the distance the spring is stretched.
First, we need to find the spring constant k. We can do this by rearranging the formula and plugging in the given values:
k = (2W)/x^2
Since we know that a 3-pound fish stretches the spring 2 inches, we can plug in these values to find k:
k = (2(3))/(2^2)
k = 6/4
k = 1.5
Now that we know the spring constant, we can plug it back into the original formula along with the additional 4 inches of stretch to find the work done:
W = (1.5(4^2))/2
W = (1.5(16))/2
W = 24/2
W = 12
Therefore, the work done stretching the spring 4 more inches is 12 foot-pounds.
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What is the answer to this equation
2x+8y=6
5x+20y=15
What is the following sets has the larger standard deviation? A = {1,2,3,4,5} B = {1,4,15,21,27}
The set B has the larger standard deviation.
Standard deviation is a measure of the dispersion of a set of data from its mean. The more spread apart the data, the higher the deviation. In other words, the larger the standard deviation, the more the data deviates from the average.
To calculate the standard deviation of a set of data, you can follow these steps:
1. Calculate the mean of the data set.
2. Subtract the mean from each data point to get the deviations.
3. Square each deviation.
4. Find the mean of the squared deviations.
5. Take the square root of the mean of the squared deviations.
For set A:
1. Mean = (1+2+3+4+5)/5 = 3
2. Deviations = {-2, -1, 0, 1, 2}
3. Squared deviations = {4, 1, 0, 1, 4}
4. Mean of squared deviations = (4+1+0+1+4)/5 = 2
5. Standard deviation = √2 = 1.41
For set B:
1. Mean = (1+4+15+21+27)/5 = 13.6
2. Deviations = {-12.6, -9.6, 1.4, 7.4, 13.4}
3. Squared deviations = {158.76, 92.16, 1.96, 54.76, 179.56}
4. Mean of squared deviations = (158.76+92.16+1.96+54.76+179.56)/5 = 97.44
5. Standard deviation = √97.44 = 9.87
As you can see, the standard deviation of set B (9.87) is larger than the standard deviation of set A (1.41). Therefore, set B has the larger standard deviation.
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X+9 x+9
1
Pls help me
Answer:
Step-by-step explanation:
Assuming you meant to write (x + 9) * (x + 9), this is a multiplication of two binomials, which can be expanded using the FOIL method:
(x + 9) * (x + 9) = x^2 + 9x + 9x + 81
Simplifying further, we can combine like terms:
x^2 + 18x + 81
Therefore, (x + 9) * (x + 9) = x^2 + 18x + 81.
Look at the inequality 12 + 6x > 99
Drag and drop each statement into "True" or "False" depending on if the statement is true or false.
Hence, x > 14.5 is the answer to the contradiction 12 + 6x > 99. This suggests that the inequality will be satisfied by any x value that is bigger than 14.5
What does math inequality mean?"Inequality" in mathematics refers to the relationship between two reactions and quantities that is not the same as one another. As a result, inequality results from an imbalance.
You can use algebra to isolate one variable x solely on a single side of the inequality and utilize that information to solve the inequality 12 + 6x > 99.
The stages to resolving the inequality are as follows:
First, take 12 away both from sides of the inequality:
12 + 6x - 12 > 99 - 12
Simplify:
6x > 87
Then, to identify the variable x, split both side of the equality by 6:
6x/6 > 87/6
Simplify:
x > 14.5
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Find the area of the following circles= if radius=15mm
Answer:
225π mm²
Step-by-step explanation:
The formula for circle's area is πr². We are given with radius of 15 mm (milimeter/milimetre unit). Therefore, the area of circle with radius of 15 mm is:
π(15)² = π(225)
= 225π
Therefore, the area of circle is 225π mm².
Question 5 of 10
Circle H is shown where points D,T, S, and V lie on the circle and chords DS and TV intersect at point M. mVD= (132+4). mTS = (82), and m/VMD-(11z-2)
H.
What is the value of ?
D
M
S
T
The value of x in the circle is 8
How to find the value of x in the circle?The Angles of Intersecting Chords Theorem states that "If two chords intersect inside a circle, then the measure of the angle formed is one-half the sum of the measure of the arcs intercepted by the angle and its vertical angle".
Thus, we can write:
mVMD = 1/2(arc VD + arc TS)
(11x-2) = 1/2[(13x+4)+(8x)]
2(11x-2) = [(13x+4)+(8x)]
22x - 4 = 21x + 4
22x - 21x = 4 + 4
x = 8
Therefore, the value of x is 8
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