Applying the triangle inequality theorem and the exterior angle theorem, we have:
1. m∠1 > m∠3
2. MI > IX
3. 3 < MX < 27
4. m∠4 = 115°
What is the Triangle Inequality Theorem?The triangle inequality theorem states that the sum of any two sides of a triangle must be greater than the third side of that triangle.
What is the Relationship of Sides to Interior Angles in a Triangle?The longest side is opposite to the largest interior angle while the shortest side of the triangle is always directly opposite the shortest interior angle in that triangle.
What is the Exterior Angle Theorem?The exterior angle theorem states that the sum of the opposite angles to an exterior angle in a triangle equals the measure of that exterior angle.
1. The angles of a triangle are relative to the length of their opposite sides. Therefore, if MI which is relative to ∠1 is 15 and IX which is relative to ∠3 is 12, it implies that m∠1 is greater than m∠3.
2. Given, m∠1 = 65° and is relative to side MI, and m∠3 = 50° and is relative to side IX, therefore, side MI is longer or greater than side IX.
3. Given, MI = 15; IX = 12, based on the triangle inequality theorem, the measure of MX would be determined as shown below:
15 - 12 < MX < 15 + 12
3 < MX < 27
4. Given, m∠2 = 65°; m∠3 = 50°. Based on the exterior angle theorem, we have:
m∠4 = m∠2 + m∠3
Substitute
m∠4 = 65 + 50
m∠4 = 115°
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what is 585.055 rouned to the tenths place
Answer:
585.1
Step-by-step explanation:
I hope that helps!!!
In HIJ, the measure of J=90°, HI = 65 feet, and IJ = 31 feet. Find the measure of
H to the nearest tenth of a degree.
Answer:
28.5
Step-by-step explanation:
28.5 delta said it was correct
Suppose a person travels at a rate of 5 ft/hr toward the foot of a street lamp pole 61 ft high. The height of the person is 5.5 ft. At what rate is the distance from the head of the person to the top of the street lamp changing when 85 ft from the bottom of the street lamp? Note: Round your answer to 4 decimal places. 0.2389 ft/hr 4.0622 ft/hr none of the other answers -4 ft/hr 4.1866 ft/hr 0 ft/hr -0.2389 ft/hr 3.9380 ft/hr
A person is moving towards a street lamp at a rate of 5 ft/hr. They are 85 ft away from the lamp. The problem requires determining the rate at which the distance from the person's head to the top of the lamp is changing.
Let's define the following variables:
x: distance from the foot of the lamp to the person
y: distance from the top of the lamp to the person's head
h: height of the lamp
Using similar triangles, we can establish the relationship: y / (h - x) = 5.5 / x.
Rearranging this equation, we get y = (5.5h - 5.5x) / (h - x).
To find the rate of change of y with respect to time, we differentiate both sides of the equation implicitly. This gives us dy/dt = (5.5(h - x) + 5.5x) / (h - x)^2 * dx/dt.
Substituting the given values: h = 61 ft, x = 85 ft, dx/dt = 5 ft/hr, we can calculate dy/dt. After the calculations, we find that dy/dt is approximately 3.9380 ft/hr.
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5x(x - 4) = 3x + 4 someone help me pls
Answer: x=23±√609/10
Step-by-step explanation:
f(4)=2x-5 what's the answer?
Answer:
f(4)=3
Step-by-step explanation:
f(4)=2(4)-5
f(4)=8-5
f(4)=3
Six times the sum of a number and negative one is the same as two more than eight times the number
Answer:-5/4
Step-by-step explanation:
please please Help me!!!!!
Answer:
19,23
Step-by-step explanation:
9+x-7≥ 21
Combine like terms
2+x≥21
Subtract 2 from each side
2+x-2 ≥21-2
x≥19
Any number greater than or equal to 19
For what values of x is the expression below defined?
Sqrt x+5 divided by sqrt 1-x
Answer:
D. - 5 ≤ x < 1
Step-by-step explanation:
The numerator cannot be the square root of a neg. no.
So, x + 5 ≥ 0 or x ≥ -5
The denominator cannot be a neg. no. or 0.
So, 1 - x > 0
1 > x or x < 1
So, altogether - 5 ≤ x < 1
Therefore, D is the correct answer.
Find the distance between each pair of points.
(7 1/2, -6) and (7 1/2, -2 1/2)
Answer:
7/2
Step-by-step explanation:
√(x2 - x1)² + (y2 - y1)²
√(7 1/2 - 7 1/2)² + [-2 1/2 - (-6)]²
√(0)² + (7/2)²
√49/4
= 7/2
Please help me I really need it..
Answer:
\(\frac{1}{8^{2} }\)
Step-by-step explanation:
What is the numerator called in a percent problem? What is the denominator called in a percent problem ?
PLEASE I NEED HELP NOW!!!
Answer:
A percentage or percent for short is a fraction; a fraction that always has the denominator as 100. Because the denominator of a percent is always a 100, no matter what the numerator is, we replace 100 with the percent symbol % after the number. By definition, for any number x, x% = x100.
Step-by-step explanation:
A vitamin tablet contains 120 milligrams of vitamin C. How many grams of vitamin C is this?
Answer:
0.12 grams of Vitamin C.
Step-by-step explanation:
tell me if i am right
Calculate the distance between the points (-6, 4) and (5, -1). Round to the nearest tenth.
What is the amperage capacity of a 240-v/24-v control transformer with a 40va rating?
The amperage capacity of the 240 V/24 V control transformer with a 40 VA rating is approximately 0.1667 A for the 240 V side and 1.6667 A for the 24 V side.
To determine the amperage capacity of a control transformer, we can use the formula:
Amperage (A) = Volt-Amperes (VA) / Voltage (V)
Given that the control transformer has a 40 VA rating, and two different voltages are mentioned (240 V and 24 V), we need to calculate the amperage capacity for both voltage levels separately.
For 240 V:
Amperage (A) = 40 VA / 240 V = 0.1667 A (rounded to four decimal places)
For 24 V:
Amperage (A) = 40 VA / 24 V = 1.6667 A (rounded to four decimal places)
Therefore, the amperage capacity of the 240 V/24 V control transformer with a 40 VA rating is approximately 0.1667 A for the 240 V side and 1.6667 A for the 24 V side.
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price level (p) value of money (1/p) quantity of money demanded (billions of dollars) 1.00 1.5 1.33 2.0 2.00 3.5 4.00 7.0
The relationship between price level (P), value of money (1/P), and quantity of money demanded (Q) is as follows:
As P increases, the value of money (1/P) decreases.
As P increases, the quantity of money demanded (Q) increases.
In macroeconomics, the quantity theory of money is a concept that states that the supply and demand for money determine the level of prices.
The concept is based on the assumption that the velocity of money (the rate at which money is exchanged in the economy) and real output are constant.
This theory is expressed mathematically as follows: MV = PQ, where M is the money supply, V is the velocity of money, P is the price level, and Q is real output.
The relationship between the price level, value of money, and quantity of money demanded can be explained through the quantity theory of money equation: MV = PQ
Where M is the money supply, V is the velocity of money, P is the price level, and Q is the quantity of goods and services produced in an economy.
We can rearrange this equation to solve for P:
P = MV/Q
Now, using the given data, we can find the relationship between price level (P), value of money (1/P), and quantity of money demanded (Q):
Price Level (P)Value of Money (1/P)
Quantity of Money Demanded (billions of dollars)1.001.5001.3312.003.504.007.0
To calculate the value of money (1/P), we need to take the reciprocal of each value of P. For example, if P = 1, then 1/P = 1/1 = 1.
Using the formula P = MV/Q, we can calculate the value of M by rearranging the equation: M = PQ/V. Since we don't have data for V, we can assume that it is constant (i.e., V = 1).
Therefore, M = PQ.To calculate the quantity of money demanded (Q), we can use the formula Q = MV/P. Again, assuming that V is constant at 1, we get Q = M/P.So, using the data in the table, we can calculate:
M = PQ = 1.00 x 1.5 = 1.5Q = MV/P = 1.5 x 1.00 = 1.5 billion dollars
M = PQ = 1.33 x 2.00 = 2.66Q = MV/P = 2.66 x 1.33 = 3.54 billion dollars
M = PQ = 2.00 x 3.50 = 7.00Q = MV/P = 7.00 x 2.00 = 14.00 billion dollars
M = PQ = 4.00 x 7.00 = 28.00Q = MV/P = 28.00 x 4.00 = 112.00 billion dollars
Therefore, the relationship between price level (P), value of money (1/P), and quantity of money demanded (Q) is as follows:
As P increases, the value of money (1/P) decreases.
As P increases, the quantity of money demanded (Q) increases.
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The answer to the quantity of money demanded (billions of dollars) is shown in the table below.
Price level (p)Value of money (1/p)Quantity of money demanded (billions of dollars)1.001.55.001.333.52.007.04.0012.5
As per the table given above, the quantity of money demanded (billions of dollars) is as follows for the respective price level (p) given below:
When the price level is 1.00, the quantity of money demanded is $5 billion.
When the price level is 2.00, the quantity of money demanded is $3.5 billion.
When the price level is 4.00, the quantity of money demanded is $12.5 billion.
The table provided above shows the relationship between the price level and the quantity of money demanded.
It can be observed that as the price level increases, the value of money decreases and the quantity of money demanded increases.
This shows an inverse relationship between the value of money and the quantity of money demanded.
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2nd attempt Feedback Whee Periodic Table The radius of an exoplanet is \( 8.00 \) times larger than Earth's radius. What is the ratio of Earth's cooling time to the exoplanet's cooling time?
The ratio of the cooling time of Earth to the cooling time of the exoplanet is 16,777,216.
What is an exoplanet?An exoplanet, also known as an extrasolar planet, is a planet that orbits a star other than the Sun, which is part of our solar system. An exoplanet is one of many planets that might exist in the universe outside of our solar system.
The ratio of the cooling time of Earth to the cooling time of the exoplanet can be determined using Stefan-Boltzmann's Law and Wien's Law.
We first need to use the Stefan-Boltzmann Law in order to calculate the cooling time.
σT⁴ = L/(16πR²)
σ(5780)⁴ = (3.846 × 10²⁶ W)/(16π(6.3781 × 10⁶)² m²)
Ratio of the exoplanet's radius to the Earth's radius:
re/rE = 8.00
Ratio of the exoplanet's mass to the Earth's mass:
me/mE = (re/re)³ = 8³ = 512 (since density is assumed to be the same for both planets)
Ratio of the exoplanet's luminosity to the Earth's luminosity:
Le/LE = (me/mE)(re/rE)² = 512(8)² = 32768
Ratio of the exoplanet's temperature to the Earth's temperature:
Te/TE = (Le/LE)¹∕⁴ = 32768¹∕⁴ = 32.0
The Wien Law can now be used to determine the ratio of the cooling times of the two planets.
(T/wavelength max)E = 2.898 × 10⁻³ m K(5780 K) = 1.68 × 10⁻⁸ m (using Earth as the comparison planet)
(T/wavelength max)e = 2.898 × 10⁻³ m K(Te)(8.00) = wavelength max (using the exoplanet)
Ratio of the wavelengths:
wavelength max,e/wavelength max,E = (Te/TE)(re/rE) = 32.0 × 8.00 = 256
Ratio of the cooling times:
cooling time,e/cooling time,E = (wavelength max,e/wavelength max,E)³ = 256³ = 16,777,216
Hence, the ratio of Earth's cooling time to the exoplanet's cooling time is 16,777,216.
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The ratio of the sides of the triangle is 3:8:7 if the perimeter of the triangle is 162 meters what's the length of the longest side
The longest side of the triangle is equal to 72.
The perimeter of a triangle is equal to the sum of the sides and is the total boundary of the shape. So because of ratios, the three sides become -
= 3x + 8x + 7x
The perimeter totals out to be -
= 3x + 8x + 7x = 162
= 18x = 162
= x = 162/ 18
= x = 9
Now, we have the sides -
= 3*9 = 18
= 8*9 = 72
= 7*9 = 63
From this, it is evident that the length of the longest side is 72.
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What is domain? What is domain?
Answer:
wait I don't understand is this suppose to be a definition, City, or anything?
Answer:
ARN
Step-by-step explanation:
Describe the slope of the line then find the slope plzzz help I’m bad at math
question is attached
f ( x ) = x² + 144
=> x² + 144 = 0
=> ( x + 12 ) ( x - 12 ) = 0
=> x + 12 = 0 and x - 12 = 0
=> x = -12 and x = 12
So,the zeroes of f are -12 and 12 .
Which of the following is true about the diagonals of a rectangle? Select all that are true.
Diagonals bisect each other.
Diagonals are congruent.
Diagonals are perpendicular.
Diagonals bisect the angles.
Answer:
Diagonals bisect each other.Diagonals are congruent.Diagonals are perpendicular.Diagonals bisect the anglesan urn contains 6 blue balls and 4 red balls. 6 balls are chosen at random and without replacement from the urn. if x is the number of red balls chosen, find the standard deviation of x.
The standard deviation of the number of red balls chosen, x, is 1.2.
In probability theory, the standard deviation is a measure of the amount of variation or dispersion in a set of values. It helps us understand how spread out the values are from the mean. In this scenario, we have an urn containing blue and red balls, and we are randomly selecting 6 balls without replacement. We want to determine the standard deviation of the number of red balls chosen, denoted by x.
To find the standard deviation of x, we need to calculate the variance first. The variance represents the average of the squared differences between each value and the mean. The standard deviation is then the square root of the variance.
Step 1: Finding the probability of selecting a red ball
In the given urn, there are a total of 6 blue balls and 4 red balls. To determine the probability of selecting a red ball, we divide the number of red balls by the total number of balls:
P(red) = 4 / (6 + 4)
= 0.4
Step 2: Calculating the mean of x
The mean of x, denoted as μx, represents the expected value or average number of red balls chosen. Since the probability of selecting a red ball is 0.4, we can calculate the mean as follows:
μₓ = (Number of trials) × P(red)
= 6 × 0.4
= 2.4
Step 3: Determining the variance of x
The variance, denoted as Var(x), is calculated by finding the average of the squared differences between each value of x and the mean:
Var(x) = (Number of trials) × P(red) × P(blue)
= 6 × 0.4 × 0.6
= 1.44
Step 4: Finding the standard deviation of x
Finally, the standard deviation, denoted as σx, is the square root of the variance:
σₓ = √Var(x)
= √1.44
= 1.2
Therefore, the standard deviation of the number of red balls chosen, x, is 1.2.
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The mean of {6,8,2,12,5}
Answer:
6.6
Step-by-step explanation:
Answer:
6.6
Step-by-step explanation:
6 + 8 + 2 + 12 + 5 = 33
33 / 5 = 6.6
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The population of a city increases by 2.3% per year. If this year's population is
157,000, what will next year's population be, to the nearest individual?
Answer:
16011 people
I hope this helps
19-3 as a verbal expression
Answer:
I think it would be "nineteen minus three equals sixteen"?
Step-by-step explanation:
Answer:
Nineteen minus three.
Step-by-step explanation:
9=Nineteen -Minus 3=Three
How many solutions do 3y-6x=15 have?
Answer:
infinite
Step-by-step explanation:
Review Worksheet:
What is the Intermediate Value Theorem (IVT)? What has to be true about the function in order to use the IVT?
The Intermediate Value Theorem (IVT) is a theorem in calculus that states that if a continuous function f(x) takes on values of opposite signs at two points a and b, then there exists at least one point c between a and b such that f(c) = 0.
In order to use the IVT, the function f(x) must be continuous on the closed interval [a, b]. This means that the function must be defined at every point in the interval, and that there are no gaps or jumps in the graph of the function on that interval. In addition, the function must not have any asymptotes or vertical lines of discontinuity on the interval, as these would prevent the function from being continuous.
If the function satisfies these conditions, then we can use the IVT to show that there exists at least one point in the interval where the function takes on a particular value, such as zero. The IVT is a powerful tool in calculus, as it allows us to prove the existence of solutions to equations and inequalities without actually finding those solutions.
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Swapping the contents of two variables requires a third variable that can serve as a temporary storage location. True False.
Answer:
True.
Step-by-step explanation:
True.
Let's say A = 5, and B = 10.
We need to swap the contents of A and B, so A will end up with 10 and B will end up with 5.
A = 5
B = 10
Introduce variable C.
C = A (now C contains 5)
A = B (now A contains 10)
B = C (now B contains 5)
In the last two steps above, you see that the values of A and B were swapped.
Ram Purchased a flat at ₹1. 1 lakh and Prem purchased aplot of land worth ₹ 1. 1 lakh. The respective annual rates at which the prices of the flat and the plot increases were 10% and 5%. After two years they exchanged their belongings and one paid the other the difference. Then who paid to whom by how much?
Prem purchased a plot for ₹1.1 lakh and its price increased at an annual rate of 5%.Ram's flat had a higher value than Prem's plot, Prem paid Ram the difference, which was ₹0.118 lakh or ₹11,800. Ram's flat is more valuable than Prem's plot of land
After two years, the value of Ram's flat would be ₹1.1 lakh + (10% of ₹1.1 lakh × 2 years) = ₹1.43 lakh.
Similarly, the value of Prem's plot of land would be ₹1.1 lakh + (5% of ₹1.1 lakh × 2 years) = ₹1.21 lakh.
Therefore, the difference in value between Ram's flat and Prem's plot of land is ₹1.43 lakh - ₹1.21 lakh = ₹22,000.
Ram would have to pay ₹22,000 to Prem as Ram's flat is more valuable than Prem's plot of land.
Ram purchased a flat for ₹1.1 lakh and its price increased at an annual rate of 10%. After two years, the flat's value would be:
1.1 lakh * (1 + 0.1)^2 = 1.1 lakh * 1.21 = ₹1.331 lakh
Prem purchased a plot for ₹1.1 lakh and its price increased at an annual rate of 5%. After two years, the plot's value would be:
1.1 lakh * (1 + 0.05)^2 = 1.1 lakh * 1.1025 = ₹1.213 lakh
After exchanging their properties, the difference in value is:
₹1.331 lakh (flat) - ₹1.213 lakh (plot) = ₹0.118 lakh
Since Ram's flat had a higher value than Prem's plot, Prem paid Ram the difference, which was ₹0.118 lakh or ₹11,800.
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The diagram shows ten identical squares inside a rectangle.
length-
15 cm
The width of the rectangle is 15 cm.
Work out the length of the rectangle.
Optional working
Answer: length =
+
cm
Please attached a diagram drawn with MS Word based on the question parameters, and from a diagram from a similar question.
The length of the rectangle that contains 10 identical squares and has a width of 15 centimeters is 21 centimeters
What is a square?A square is a quadrilateral that has four sides of the same length and the the four interior angles are each equal to 90°.
Some parts of the question appear missing, please find attached the design of a rectangle based on a similar GCSE question online. The width of the rectangle = 15 cm
The number of squares = 10
The number of squares that make up the width from the drawing = 5
The number of squares that make up the length of the rectangle are more than the number that makes up the width.The side length of the square is therefore; 15 cm ÷ 5 = 3 cm
The number of squares that make up the length of the rectangle = 7
The length of the rectangle is therefore, L = 7 × 3 cm = 21 cm
The length of the rectangle = 21 centimeters
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