i uhm eeeeeeeeeeeeeeeeeeeeeeeeee
2.5.1 Characterization Theorem
If S is a subset of R that contains at least two points and has the property
(1)
if x, y ES and
then S is an interval.
Proof. There are four cases to consider: (i) S is bounded, (ii) S is bounded above but not below, (iii) S is bounded below but not above, and (iv) S is neither bounded above nor below.
Case (i): Let a = inf S and b = sup S. Then SC[a, b] and we will show that (a, b)C S.
If a < z
Now if a S and b S, then S =[a, b]. (Why?) If a S and b S, then S=(a, b). The other possibilities lead to either S = (a, b) or S = [a, b).
Case (ii): Let b = sup S. Then SC (-[infinity]o, b] and we will show that (-oo, b)C S. For, if z
Cases (iii) and (iv) are left as exercises.
Cases (iii) and (iv) are left as exercises, meaning the proof for those cases is not provided in the given information. To fully establish the Characterization Theorem, the proof for these remaining cases needs to be completed.
Theorem 2.5.1 (Characterization Theorem):
If S is a subset of R that contains at least two points and has the property that if x, y ES and x < y, then (x, y)C S, then S is an interval.Proof.
There are four cases to consider:
(i) S is bounded,
(ii) S is bounded above but not below,
(iii) S is bounded below but not above, and
(iv) S is neither bounded above nor below.
Case (i): Let a = inf S and b = sup S.
Then SC[a, b] and we will show that (a, b)C S. If a < z < b, then there exist x, y
ES such that x < z < y. Since x < y and S has property (1), we have (x, y)C S.
Since zEP(x, y), it follows that zES.
Thus (a, b)C S.
Now if a S and b S, then S =[a, b].
If a S and b S, then S=(a, b).
The other possibilities lead to either S = (a, b) or S = [a, b].
Case (ii): Let b = sup S.
Then SC (-[infinity]o, b] and we will show that (-oo, b)C S. For, if z < b, then there exists y
ES such that z < y < b.
Since b is the least upper bound of S and yES, it follows that y 6S. But then (z, y)C (-oo, b) and (z, y)C S.
Thus (-oo, b)C S. Now if S contains its smallest element a, then S = [a, b]. Otherwise, S=(a, b).
Cases (iii) and (iv) are left as exercises.
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One option in a roulette game is to bet on the color red or black. (There are 18 red compartments, 18 black compartments and two compartments that are neither black nor red.) If you bet on a color you get to keep your bet and win that same amount if the color occurs. If that color does not occur you will lose the amount of money you wagered on that color to appear. What is the expected payback for this game if you bet $6 on red?
The expected payback for betting $6 on red in this roulette game is approximately -$0.32. This means, on average, you can expect to lose about $0.32 per $6 wagered.
To calculate the expected payback for the game, we need to consider the probabilities and payouts associated with the bet on red.
In a standard roulette wheel, there are 18 red compartments, 18 black compartments, and two green compartments (neither black nor red) representing the 0 and 00. This means there are 38 equally likely outcomes.
If you bet $6 on red, there are 18 favorable outcomes (the red compartments) and 20 unfavorable outcomes (the black and green compartments). Therefore, the probability of winning is 18/38, and the probability of losing is 20/38.
If the color red occurs, you get to keep your bet of $6 and win an additional $6.
To calculate the expected payback, we multiply the probability of winning by the payout for winning and subtract the probability of losing multiplied by the amount wagered:
Expected Payback = (Probability of Winning * Payout for Winning) - (Probability of Losing * Amount Wagered)
Expected Payback = ((18/38) * $6) - ((20/38) * $6)
Expected Payback = ($108/38) - ($120/38)
Expected Payback = -$12/38
The expected payback for betting $6 on red in this roulette game is approximately -$0.32. This means, on average, you can expect to lose about $0.32 per $6 wagered.
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Find the period and the amplitude of the periodic function. I'm awful with graphs :(
A period is the difference in x over which a sine function returns to its equivalent state and the amplitude is A/5.
Amplitude:
The amplitude of a periodic variable is a measure of its change over a period of time, such as a temporal or spatial period. The amplitude of an aperiodic signal is its magnitude compared to a reference value. There are various definitions (see below) of amplitude, which is any function of the magnitude of the difference between the extreme values of a variable. In the previous text, the phase of a periodic function is called the amplitude.
X = A sin (ω[ t - K]) + b
A is the amplitude (or peak amplitude),
x is the oscillating variable,
ω is angular frequency,
t is time,
K and b are arbitrary constants representing time and displacement respectively.
According to the Question:
An equation does not have an amplitude. This "equation" represents the formula of a vibration, and was better written as:
X= A/5* sin(1000.t + 120)
These oscillations have a certain amplitude. X values can vary from minimum to maximum. Normally, the stop position of the oscillation is X=0. In this case, we can see that the maximum occurs when the sine is +1 and the minimum occurs when the sine is -1.
For theses cases X= A/5 respectively -A/5.
Therefore,
The amplitude is A/5.
For formulas of this type, the term in front of the sinus (or cosine) is equal to the amplitude.
Complete question:
Can I find the amplitude of this equation? A/5 *
Help please!!! retake question
PR / Sin(Q) = QR / Sin(P)
53 / Sin(90) = 45 / Sin(P)
53 / 1 = 45 / Sin(P)
Sin(P) = 45 / 53
Sin(P) = 0.8490566038
P = 58.11 degrees
Answer:
58.11°
Step-by-step explanation:
tan P = 45/28 = 1.607
< P = tan`¹ 1.607 = 58.11°
HELP ME OUT PLEASE! I WILL GIVE U A BRAINIEST! 15 POINTS!
Answer:
d. <6
e. <2
Step-by-step explanation:
hopefully this helps :)
Each student in a class recorded how many books they read during the summer. Here is a box plot that summarizes their data. What is the median number of books read by the students?
The median of the data is 6.
Looking at the box plot you provided, we can see that it's divided into four sections, or quartiles. The median, or the middle value of the data, is represented by the line that divides the box in half.
To find the median number of books read by the students, we need to look at the box plot and identify the median line. Then we can follow that line until it intersects with the y-axis, which represents the number of books read. The value at that point is the median number of books read by the students.
By looking through the box plot we have identified that te median is 6.
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System OT
W + b =13
6.5w + 2b = 57.5
Answer: w = 7, x = 6
Step-by-step explanation: Solve by substitution
W + b = 13
rewrite as b = 13 - w and substitute that value for b in the second equation
6.5w + 2b = 57.5 Then solve for w
6.5w + 2(13-w) = 57.5 . Distribute
6.5w + 26 - 2w = 57.5 . Subtract 26 from both sides. Combine like terms and simplify
6.5w - 2w = 57.5 - 26
4.5w = 31.5 Divide both sides by 4.65
w = 7 . Substitute 7 for w in the first equation and solve for b
7 + b = 13 . Subtract 7 from both sides
b = 6
Mr Altman class recycled 72 water bottles in march. The Numbers of juice was 1/4 One Fourth times as many. What is the total number of water bottles and juice cans they recycled in march?
Answer:
The answer is 90 altogether.
Step-by-step explanation:
1/4 of 72 or 0.25x72 is 18. When you add 72 water bottles with the juice you get 90 altogether.
What is a "gestalt"? How do the experimental examples provided in the text (Necker cube, visual cliff, etc.) help demonstrate principles of perceptual organization?; choose one example to discuss specifically.
The Kanizsa triangle illusion helps us understand that our perceptual experiences are not simply the sum of the individual sensory inputs, but rather the result of a complex and variable process of perceptual organization.
Gestalt is a German word meaning "shape" or "form," and in psychology, it refers to a set of principles that describe how people perceive and organize sensory information into meaningful wholes. These principles propose that the whole is greater than the sum of its parts, and that we tend to organize our perceptual experiences into coherent, holistic forms rather than isolated, unrelated sensations.
Experimental examples such as the Necker cube, visual cliff, and others help demonstrate principles of perceptual organization by highlighting how our minds naturally try to impose structure and order on sensory input. For example, the Necker cube is a two-dimensional drawing that can be perceived as a cube that can be viewed from different angles. However, as one stares at the image, it appears to flip back and forth between different possible interpretations. This phenomenon illustrates the Gestalt principle of figure-ground, which describes how we tend to perceive objects as being distinct from their surrounding context.
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HELP WILL GIVE BRAINLIEST
Answer:
C
Step-by-step explanation:
Verify, give me brainliest, and rate, and say thank you
Answer:
log ( \(\frac{x^2-2x(x-1)}{(x-1)^2}\) )
Step-by-step explanation:
to find (f ◦ g)(x) , substitute x = g(x) into f(x)
= log ( ( \(\frac{x}{(x-1)^}\) )² - 2(\(\frac{x}{x-1}\) ) )
= log ( \(\frac{x^2}{(x-1)^2}\) - \(\frac{2x}{x-1}\) ) ← express as a single fraction
= log ( \(\frac{x^2-2x(x-1)}{(x-1)^2}\) )
The average daily high temperature in madrid peaks at 92°f in the summer and drops as low as 33°f in the winter. the temperature can be modeled by t (d) = 29.5 cosine (startfraction 2 pi over 365 endfraction (d minus 204) ) 62.5, where d represents the day number of the year (january 1 is 1, january 2 is 2, and so on). during which day is the high temperature expected to be closest to 75°f? 106 63 270 204
The day in Madrid at which the high temperature is expected to be closest to 75 degree Fahrenheit is 270.
What is linear function?Linear function is the function in which the highest power of the unknown variable is one. Linear functions are used to model the real life problem in the mathematical expressions.
The average daily high temperature in Madrid peaks at 92°f in the summer and drops as low as 33°f in the winter.
The temperature can be modeled by the following function,
\(t (d) = 29.5 \cos\left(\dfrac{2\pi}{365}(d-204)\right)+62.5\)
Here, d represents the day number of the year (january 1 is 1, january 2 is 2, and so on).
The day has to be find out when the temperature is at 75 degree Fahrenheit. Put the value of temperature 75 in the above equation as,
\(75 = 29.5 \cos\left(\dfrac{2\pi}{365}(d-204)\right)+62.5\)
On solving the above equation for cosine function, we get the two values of d as,
\(d\approx 138\\d\approx 270\)
From the given options, 270 is the correct one.
Thus, the day at which the high temperature is expected to be closest to 75 degree Fahrenheit is 270.
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Answer: Mann is correct
Step-by-step explanation:
EDGE
. use de morgan’s laws to find the negation of each of the following statementsMei will run or walk to the gym tomorrow.
Propositional logic : Step 1 : r : Mei will run to the gym tomorrow. w : Mei will walk to the gym tomorrow.
The negation of the given statement is ¬(r ∨ w) which is ¬r ∧ ¬w.
Given statement: Mei will run or walk to the gym tomorrow. Propositional logic:
Step 1: r: Mei will run to the gym tomorrow. w: Mei will walk to the gym tomorrow.
Step 2: The given statement can be rewritten in the form: r ∨ w.
Step 3: The negation of the given statement is ¬(r ∨ w). Using De Morgan's Laws, we can write the negation as ¬r ∧ ¬w.
Main Part: ¬(r ∨ w)
Explanation: We know that the negation of a disjunction is the conjunction of the negations of the disjuncts. So, the negation of the given statement r ∨ w is ¬r ∧ ¬w. The negation of the given statement "Mei will run or walk to the gym tomorrow" is "Mei will not run and will not walk to the gym tomorrow."
Conclusion: Therefore, the negation of the given statement is ¬(r ∨ w) which is ¬r ∧ ¬w.
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Joey has budgeted $125 for his family of four to go to the fair.
Admission is $8 per person and each ride costs $1.25.
Food for the family costs $27.
They each ride the same number of rides.
What is the maximum number of rides each person in the family can ride and not go over Joey’s budget?
Answer:
52 rides
Step-by-step explanation:
125 - 8 - 8 - 8 - 8 = 93
93 - 27 = 66
66 ÷ 1.25 = 52.8
Since 52.8 rides we have to use only the whole numbers, so in this case 52.
Hope this helps!
write 26:30 as a fraction in simplest form
Answer: 13/15
Step-by-step explanation:
26/30
Simple by 2
13/15
Answer:
26/30 = 13/15
Evaluate the function f(x) = 5x2 - 7x + 3 a. f(-4) = ___________________ b. f(4) =_____________________ c. f(0)= ______________________ d. f(12)= _____________________ e. f(-12)= ___________________ f. f(-5) =____________________ g. f(-3) = ____________________ h. f(6) = _____________________ i. f(-6) = ___________________ j. f(-3) = __________________
Answer:
say what
Step-by-step explanation:you + your = answer ( ask your teacher )
write brackets () in this statement to make it correct 6 + 4 x 5 - 3 = 14
Answer:
6+4*(5-3)
Step-by-step explanation:
Because of PEMDAS l, we first solve in the parantheses. So 5-3 would be 2, then we multiply 2 by 4 which would be 8 obviously. Then we do the final step, add 6 and 8 which would be 14. Cheers!
Answer: 6 + 4 × (5-3)
Explanation:
6 + 4 × (5-3) = 14
6 + 4 × 2 = 14
6 + 8 = 14
14 = 14
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When Beth buys 4 chocolates, she gets 8 free game tokens. Write the equation for the relationship between x and y. *
Answer:
y= 2x
y= x+4
Step-by-step explanation:
I am confused here.
since one data is given, the equation could be any of the two.
Using the manning's equation for the trapezoidal channel. Given
n=.1157, S=0.006. b=7, z= 2.
Find yn for Q=1070,1369,1624,1829,2171,2331
The values of yn for the given flow rates Q can be calculated using the Manning's equation for a trapezoidal channel with the given parameters n, S, b, and z.
The Manning's equation relates flow rate (Q) in a channel to its parameters: n (Manning's roughness coefficient), S (channel slope), b (bottom width), and z (side slope). The equation is given by Q = (1.49/n) * (b/z) * (A * R^(2/3)) * S^(1/2), where A is the cross-sectional area and R is the hydraulic radius.
To find yn (depth of flow), we rearrange the Manning's equation as A = (Q * n * z) / (1.49 * (b/z) * R^(2/3) * S^(1/2)). We then substitute the given values of n, S, b, and z, and calculate the values of A for each flow rate Q using the equation. Finally, we solve for yn by dividing A by the bottom width b.
Performing these calculations for each given flow rate Q (1070, 1369, 1624, 1829, 2171, and 2331), we can determine the corresponding values of yn for each flow rate using the Manning's equation and the provided parameters.
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the definition of the "moment of inertia for an area" involves an integral of the form:
The moment of inertia for an area is a measure of an object's resistance to rotational forces and is calculated using an integral involving the distance of small area elements from a reference axis.
Moment of inertia for an area, also known as the second moment of area or area moment of inertia, is a fundamental geometric property of a shape that reflects how its mass is distributed relative to a specific reference axis. It plays a crucial role in mechanics, as it is directly related to an object's resistance to bending and torsion.
In mathematical terms, the moment of inertia for an area is calculated using an integral of the form:
I = ∫(y^2 + z^2) dA
Where I represents the moment of inertia, y and z are the distances of a small area element dA from the reference axis (usually the centroid of the shape), and the integral is computed over the entire area of the shape.
The moment of inertia has units of length to the fourth power (L^4), and its value depends on both the shape's geometry and the axis around which it is calculated. For simple shapes like rectangles, circles, and triangles, the moment of inertia can be calculated using standard formulas. However, for more complex shapes, numerical methods like finite element analysis or integral calculus might be required.
In summary, the moment of inertia for an area is a measure of an object's resistance to rotational forces and is calculated using an integral involving the distance of small area elements from a reference axis. It plays a crucial role in mechanics and is essential in understanding an object's behavior under bending and torsion.
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produce a rough sketch of a graph of a rational function that has the following characteristics: Vertical Asymptotes at x = -3 and x = 4 with a Horizontal Asymptote at y = 2. The rational function also has intercepts of (-6,0), (7,0), and (0,7).
Create a rational function h(x) that has these characteristics h(x) = ___ Please describe how you designed h(x) to fulfill each of the listed characteristics.
Use Desmos to graph your created function as a final check. Does it fit?
To design a rational function with vertical asymptotes at x = -3 and x = 4, a horizontal asymptote at y = 2, and intercepts at (-6,0), (7,0), and (0,7), we can use the characteristics of these points and asymptotes to construct the function.
By considering the vertical asymptotes and the intercepts, we can determine the linear factors of the numerator and denominator. The horizontal asymptote guides us in determining the degree of the numerator and denominator. The resulting rational function is h(x) = (2(x + 6)(x - 7))/(x + 3)(x - 4).
To design the rational function, we start by noting that since the vertical asymptotes are at x = -3 and x = 4, the denominator should have factors of (x + 3) and (x - 4) to create these vertical asymptotes.
Next, we consider the intercepts at (-6,0), (7,0), and (0,7). From these points, we can determine the linear factors of the numerator: (x + 6) and (x - 7).
To ensure that the rational function has a horizontal asymptote at y = 2, the degree of the numerator should be equal to or less than the degree of the denominator. Since the numerator has a degree of 1 and the denominator has a degree of 2, we have fulfilled this requirement.
Combining these factors, the rational function h(x) = (2(x + 6)(x - 7))/(x + 3)(x - 4) satisfies all the given characteristics.
Using a graphing tool like Desmos, we can plot the function to verify if it fits the desired characteristics.
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what are two numbers that multiply to the value of 27and add to the value of -12
Answer:
\(-9\) and \(-3\)
right triangle abc is shown. triangle a b c is shown. angle a c b is a right angle and angle c b a is 50 degrees. the length of a c is 3 meters, the length of c b is a, and the length of hypotenuse a b is c. which equation can be used to solve for c? sin(50o)
The equation that can be used to solve for c in the given right triangle is the sine function: c = (3 meters) / sin(50°).
In the given right triangle ABC, we are given that angle ACB is a right angle (90°) and angle CBA is 50°. We also know the length of side AC, which is 3 meters. The length of side CB is denoted by "a," and the length of the hypotenuse AB is denoted by "c." To solve for c, we can use the trigonometric function sine (sin). In a right triangle, the sine of an acute angle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse. In this case, we can use the sine of angle CBA (50°) to find the ratio between side CB (a) and the hypotenuse AB (c).
The equation c = (3 meters) / sin(50°) represents this relationship. By dividing the length of side AC (3 meters) by the sine of angle CBA (50°), we can find the length of the hypotenuse AB (c) in meters. Using the given equation, we can calculate the value of c by evaluating the sine of 50° (approximately 0.766) and dividing 3 meters by this value. The resulting value will give us the length of the hypotenuse AB, completing the solution for the right triangle.
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Find the difference between points M(6, 16) and Z(-1, 14) to the nearest tenth.
The distance between points M(6, 16) and Z(-1, 14) is approximately 7.1 units.
We can use the distance formula to find the distance between two points in a coordinate plane. The distance formula is:
d = √((x2 - x1)² + (y2 - y1)²)
where (x1, y1) and (x2, y2) are the coordinates of the two points. Substituting the coordinates of M(6, 16) and Z(-1, 14), we get:
d = √((-1 - 6)² + (14 - 16)²) = √(49 + 4) = √53 ≈ 7.1
Therefore, the distance between points M(6, 16) and Z(-1, 14) is approximately 7.1 units.
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the perimeters of two squares are in the ratio 2 : 7. What is the ratio of the area of the smaller square to the area of the larger square
The ratio of the area of the smaller square to the area of the larger square = 4 : 49
Finding the area of a square from the perimeterLet the perimeter of the small square be \(P_1\)
Lethe the perimeter of the large square be \(P_2\)
Perimeter of a square = 4 Length
\(P_1=4L_1\\\\P_2=4L_2\)
The ratio of the perimeters = 2:7
\(\frac{4L_1}{4L_2} =\frac{2}{7} \\\\\frac{L_1}{L_2} =\frac{2}{7}\)
The area of a square = L^2
\((\frac{L_1}{L_2} )^2=(\frac{2}{7} )^2\\\\\frac{L_{1} ^{2} }{L_{2} ^{2}} =\frac{2^2}{7^2} \\\\\frac{L_{1} ^{2} }{L_{2} ^{2}} =\frac{4}{49}\)
Therefore, the ratio of the area of the smaller square to the area of the larger square = 4 : 49
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Please solve it quickly!
2. The exit poll of 10,000 voters showed that 48.4% of voters voted for party A. Calculate a 95% confidence level upper bound on the turnout. [2pts]
A 95% confidence level upper bound on the turnout is c) 0.487 (or 48.7%). Hence, option c) is the correct answer. Confidence interval (CI) formula is given by :`CI = X ± Z* (s/√n)
Given that the exit poll of 10,000 voters showed that 48.4% of voters voted for party A.
`Where, X = Sample Mean, Z = Z-Score S = Standard Deviation, n = Sample Size
We have X = 48.4%,
Z-score at 95% confidence level = 1.96 (from Z-table), and n = 10,000
Now, to find the Standard deviation,
we have: p = 0.484 (proportion of voters who voted for party A),
q = 1 - p
= 0.516
Standard deviation, `s = √(pq/n)
= √((0.484×0.516)/10,000)
= 0.0158`
Now, putting the values in the formula, we get :
CI = 0.484 ± 1.96 (0.0158/√10,000)CI
= 0.484 ± 0.003CI
= (0.487, 0.481)
Thus, a 95% confidence level upper bound on the turnout is 0.487 (or 48.7%). Hence, the correct option is (c) 0.487.
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Please help asap it's going to go overdue if I don't get an answer ):
Question 1 Consider the Markov chain whose transition probability matrix is: P= ⎝
⎛
0
0
0
3
1
1
0
0
0
0
3
1
0
2
1
1
0
0
3
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
2
1
⎠
⎞
(a) Classify the states {0,1,2,3,4,5} into classes. (b) Identify the recurrent and transient classes of (a).
A. Class 1: {0,1,2}Class 2: {3,4,5}
B. it is recurrent.
Using the definition of communication classes, we can see that states {0,1,2} form a class since they communicate with each other but not with any other state. Similarly, states {3,4,5} form another class since they communicate with each other but not with any other state.
Therefore, the classes are:
Class 1: {0,1,2}
Class 2: {3,4,5}
(b)
Within Class 1, all states communicate with each other so it is a closed communicating class. Therefore, it is recurrent.
Within Class 2, all states communicate with each other so it is a closed communicating class. Therefore, it is recurrent.
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Enter the value for x that makes the equation 13x+22=x-34+5x true
Answer: -8
Step-by-step explanation:
13x+22=x-34+5x
13x+22=6x-34 (combine like terms)
13x-6x+22=6x-6x-34 (subtract 6x on each side)
7x+22=-34
7x-22+22=-34-22 (subtract 22 on each side)
7x=-56
7x/7x = -56/7 (divide 7 on each side)
x=-8
The garden in the scale drawing is 0.75 inch long.
What is the actual length of the garden?
Garden
Lawn
Scale: 1 in. = 10ft
1. Write the scale as a ratio:
Answer:
7.5 feet
Step-by-step explanation:
Hello there.
1. We know that the scale drawing is 0.75 inches long.
2. If 1 whole inch on the map is equivalent to 10 feet in real life, then how much feet in real life would be 0.75 inches on the map?
0.75 is equivalent or equals to 3/4 as a fraction.
Multiply 3/4 with 10 feet to get 7.5 feet.
Hope this helped!
- Angelo
I figured x equals a specific number in every single question involving something like this. X is on all sides, there's no given number.
The angle x of the triangle is 60 degrees.
How to find the angles in a triangle?A triangle is a polygon with three sides. The sum of angles in a triangle is equals to 180 degrees.
A triangle can be classified base on the sides and angles. For example equilateral triangle, scalene triangle and isosceles triangle.
Therefore, the angle x of the triangle can be found as follows:
x + x + x = 180
3x = 180°
divide both sides of the equation by 3
3x / 3 = 180 / 3
x = 180 / 3
x = 60 degrees.
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Answer:
the person below or above me is the answer. Yeah
Step-by-step explanation: