What is the domain and range of y = log(-x + 3) - 1?

The two statements that are correct include the following:

B. s is inversely proportional to t.

C. s is directly proportional to 1/t.

In Mathematics, a proportional relationship can be defined as a type of relationship that generates equivalent ratios and it can be modeled or represented by the following mathematical expression:

y = kx

Where:

Additionally, an inverse variation can be modeled by this mathematical expression:

s ∝ 1/t

s = k/t

Where:

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No, it is not true that every pyramid is a prism, because they have different properties.

A pyramid is a solid shape that has a base and triangular faces that meet at a point called the apex. The base of a pyramid can be any polygon, such as a square, triangle, or rectangle. A pyramid is named according to the shape of its base. For example, a pyramid with a square base is called a square pyramid.

A prism, on the other hand, is a solid shape that has two identical bases that are parallel to each other and rectangular faces that connect the bases. The bases of a prism can also be any polygon, and a prism is named according to the shape of its bases. For example, a prism with a rectangular base is called a rectangular prism.

So, while both pyramids and prisms are three-dimensional shapes with bases and faces, they have different properties and are not the same. Therefore, it is not true that every pyramid is a prism.

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Yes, if u1, u2, and u3 are linearly independent, then v1, v2, and v3 will also be linearly independent.  


To show this, assume that v1, v2, and v3 are linearly dependent. This means that there are scalars a,b, and c, such that:

a*v1 + b*v2 + c*v3 = 0

Since v1 = u1 + u2, v2 = u1 + u3, and v3 = u2 + u3, the equation above can be rewritten as:

a*(u1 + u2) + b*(u1 + u3) + c*(u2 + u3) = 0


Simplifying, this gives us:

(a + b + c)*u1 + (a + c)*u2 + (b + c)*u3 = 0


But since u1, u2, and u3 are linearly independent, the coefficients (a + b + c), (a + c), and (b + c) must all be equal to 0. This implies that a = b = c = 0, meaning that the original equation must be equal to 0. This means that v1, v2, and v3 are linearly independent.

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We deduced the following from the given phrase:

1) The supplied expression is a sum with the four terms a, b, l, and c.

2) 2c is the result of the factors 2 and c on its own.

A function is a relationship between a number of inputs and outputs. Simply described, a function is an association between inputs in which each input is coupled to exactly one output. For each function, there is a corresponding range, codomain, and domain.

What follows is:

A + (b+1) + 2c is the function that has been discovered and written in the question.

As we can see, three distinct terms—a, b+1, and 2c—have been demonstrated to be a part of this function.

As a result, we deduced the following from the above formula:

1) With the four terms a, b, 1 and 2c, the complete equation is a sum.

2) 2c is the result of the factors 2 and c on its own.

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The complete question is:

On its own 2c is a product with

The final answer is:

4C+2D = [28 28]
       [14 26]

To find 4C+2D, we first need to multiply the matrices C and D by their respective scalars, 4 and 2. Then, we add the resulting matrices together.

First, let's multiply matrix C by 4:

4C = 4[5 3] = [20 12]
   [1 2]   [ 4  8]

Next, let's multiply matrix D by 2:

2D = 2[4 8] = [ 8 16]
   [5 9]   [10 18]

Now, we can add the resulting matrices together:

4C+2D = [20 12] + [ 8 16] = [28 28]
       [ 4  8]   [10 18]   [14 26]

So, the final answer is:

4C+2D = [28 28]
       [14 26]

I hope this helps! Let me know if you have any further questions.

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To solve this problem, we can use a system of equations. Let's represent the amount invested in stocks as x, the amount invested in bonds as y, and the amount invested in CDs as z.

The first equation we can create is the total amount invested:

x + y + z = 85000

The second equation is the difference between the amount invested in bonds and CDs:

y - z = 20000

The third equation is the total interest earned:

0.064x + 0.052y + 0.055z = 4780

We can use substitution to solve this system of equations. Let's rearrange the second equation to solve for y:

y = z + 20000

We can then substitute this value of y into the first equation:

x + (z + 20000) + z = 85000

Simplifying gives us:

x + 2z = 65000

Now, let's substitute the value of y into the third equation:

0.064x + 0.052(z + 20000) + 0.055z = 4780

Simplifying gives us:

0.064x + 0.107z = 3780

We can now use the first and third equations to solve for x and z. Let's rearrange the first equation to solve for x:

x = 65000 - 2z

We can then substitute this value of x into the third equation:

0.064(65000 - 2z) + 0.107z = 3780

Simplifying gives us:

4160 - 0.128z + 0.107z = 3780

Combining like terms gives us:

-0.021z = -380

Solving for z gives us:

z = 18095.24

We can now use this value of z to solve for y:

y = z + 20000 = 18095.24 + 20000 = 38095.24

And finally, we can use the value of z to solve for x:

x = 65000 - 2z = 65000 - 2(18095.24) = 28809.52

So, Maricopa Success invested $28809.52 in stocks, $38095.24 in bonds, and $18095.24 in CDs.

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On a given day where the price of the stock is 2900AED, the stock broker should sell the stock.

The stock broker should sell the stock if the price is in the top 4% range. To determine if the price of 2900AED is in the top 4% range, we need to calculate the z-score and compare it to the z-score for the top 4% range.

The z-score formula is:
z = (x - μ) / σ

Where:
x = the value we are interested in (2900AED)
μ = the mean (2540AED)
σ = the standard deviation (150AED)

Plugging in the values, we get:
z = (2900 - 2540) / 150
z = 360 / 150
z = 2.4

The z-score for the top 4% range is 1.75. Since the z-score of 2.4 is greater than 1.75, the price of 2900AED is in the top 4% range. Hence, he should sell the stocks.

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The domain and range of the functions are:
1. \( f(x)=3 x^{2}+2 \) : Domain: all real numbers, Range: all real numbers
2. \( f(x)=\frac{1}{1-x} \) : Domain: all real numbers except x=1, Range: all real numbers except y=0
3. \( f(x)=\sqrt{x+2} \) : Domain: all real numbers greater than or equal to -2, Range: all real numbers greater than or equal to 0

The domain and range of a function are the set of possible inputs and outputs, respectively.

1. For the function \( f(x)=3 x^{2}+2 \), the domain is all real numbers because there are no restrictions on the input. The range is also all real numbers because the output can be any value.

2. For the function \( f(x)=\frac{1}{1-x} \), the domain is all real numbers except x=1, because when x=1, the denominator becomes 0 and the function is undefined. The range is also all real numbers except y=0, because the output can never equal 0.

3. For the function \( f(x)=\sqrt{x+2} \), the domain is all real numbers greater than or equal to -2, because the square root of a negative number is not a real number. The range is all real numbers greater than or equal to 0, because the square root of a number is always positive or 0.

In conclusion, the domain and range of the functions are:
1. \( f(x)=3 x^{2}+2 \) : Domain: all real numbers, Range: all real numbers
2. \( f(x)=\frac{1}{1-x} \) : Domain: all real numbers except x=1, Range: all real numbers except y=0
3. \( f(x)=\sqrt{x+2} \) : Domain: all real numbers greater than or equal to -2, Range: all real numbers greater than or equal to 0

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The area of the sign is 35 square feet. The solution has been obtained by using the area of the trapezoid.

The entire area occupied by the sides of a trapezoid is its area. A trapezoid's area is determined by how many unit squares fit inside of it.

We know that area of the trapezoid is

Area (A) = (a + b ) * h/ 2

Now, here we are given the following:

a = 8

b = 6

h = 5

Now, on substituting these values in the formula, we get

⇒A = (8 + 6 ) * 5 / 2

⇒A = (14 * 5) / 2

⇒A = 70 / 2

⇒A = 35 square feet

Hence, the area of the sign is 35 square feet.

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Elena plans on running a total of 5 miles.

Mile, any of several distance measurements, such as the statutory mile (5,280 ft) (1.609 km). It comes from of the Romans lire passus, also referred as the "1000 steps," which was equal to 5,000 Romans feet. Unit of length is a related topic. See all relevant material The "old London" mile was eight furlongs when it was first established in 1500.

The term mille passus, which translates to "a hundred paces" in Latin and meant a length of 1,000 rates of speed or 5,000 Rome feet, was originally used by the Romans. It is equivalent to around 1,480 metres, or 1,618 contemporary yards.

We are aware that she has covered 2 miles, or 40% of a total distance, in her run thus far:

[tex]2=0.4x[/tex]

To find x,

[tex]2=0.4x[/tex]

[tex]x=\frac{2}{0.4}[/tex]

[tex]x=5[/tex]

Therefore, Elena plans to run a total distance of 5 miles.

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Answer:

9/10

Step-by-step explanation:

Find a common denominator

4/5 × 2 = 8/10

8/10 + 1/10 = 9/10

Hey there!

4/5 + 1/10

= 4 × 2 / 5 × 2 + 1/10

= 8/10 + 1/10

= 8 + 1 / 10 + 0

= 9/10

Therefore, your answer should be:

9/10

Good luck on your assignment \& enjoy your day!

~Amphitrite1040:)

Answer: 90

Step-by-step explanation:

Answer:

90

Step-by-step explanation:

(1, 7) and (10, 1) would be the two points that a line of fit would go through to best fit the data.

What is Scatter Plot ?

A scatter plot is a graph that shows the relationship between two sets of data. Each dot on the plot represents a single data point, and the position of the dot corresponds to the values of the two variables being plotted.

In this specific scatter plot, we have 10 data points represented by dots. To find the two points that a line of best fit would go through, we want to look for a pattern or trend in the data. Ideally, the line of best fit should pass as close as possible to all of the data points, but this is not always possible.

One common method for finding the line of best fit is to choose two points that seem to be close to the middle of the data and that the line passes through. This is because we want the line to be a good representation of the overall trend in the data.

Looking at the scatter plot provided, we can see that there is a general trend of the data points sloping downward from left to right. If we draw a line that passes through the points (3, 7) and (9, 1), we can see that it closely follows the trend of the data points. Therefore, these are the two points that a line of best fit would go through to best fit the data.

Therefore, (1, 7) and (10, 1) would be the two points that a line of fit would go through to best fit the data.

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The equation are: x = -1 radians (-57.3°) and x = 11 radians (626.9°).

To solve this equation, use the identity sin2x + cos2x = 1 and apply it to the left side of the equation.

2 sin2x + 20 cos x = 6

2 (1 - cos2x) + 20 cos x = 6

2 - 2 cos2x + 20 cos x = 6

2 cos2x - 20 cos x + 2 = 6

cos2x - 10 cos x + 1 = 0

Next, solve the resulting quadratic equation using the quadratic formula: x = [-b ± √(b2 - 4ac)]/2a. In this case:

x = [-(-10) ± √((-10)2 - 4(1)(1))]/2(1)

x = [10 ± √(100 - 4)]/2

x = [10 ± √(96)]/2

x = (10 ± 4√6)/2

x = (10 ± 12)/2

x = 5 ± 6

We then use the interval [0,2π) to calculate the exact radian values for x. The two solutions in this interval are:

x = 5 - 6 = -1

x = 5 + 6 = 11

For reference, the angle corresponding to -1 radians is -57.3° and the angle corresponding to 11 radians is 626.9°.
To check the solution, graph the two sides of the equation on Desmos, with the interval [0,2π). The graph will show the two points of intersection (marked with circles) which correspond to the two solutions.

In conclusion, the exact values of x which satisfy the equation are: x = -1 radians (-57.3°) and x = 11 radians (626.9°).

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The fraction amount of pizza eaten is given by A = ( 5/6 ) of the pizza

The amount of pizza left over B = ( 1/6 ) of the pizza

An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.

Given data ,

Let the fraction of pizza eaten be represented as A

Now , the value of A is

Let the amount of pizza eaten by Tyler be p = ( 1/2 ) of the pizza

Let the amount of pizza eaten by Dean be q = ( 1/3 ) of the pizza

Now , the fraction of pizza eaten A = p + q

On simplifying , we get

The fraction of pizza eaten A = ( 1/2 ) + ( 13 )

The fraction of pizza eaten A = ( 3 + 2 ) / 6

The fraction of pizza eaten A = ( 5/6 ) of the pizza

And , the amount of pizza left B = 1 - A

On simplifying , we get

The amount of pizza left = 1/6 of the total pizza

Hence , the fractions are solved

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The linear velocity of the bicycle is approximately 6.68 miles per hour.

a) The angular velocity of the wheel can be found by using the formula:
ω = v / r
where ω is the angular velocity, v is the linear velocity, and r is the radius of the wheel.
In this case, v = 115 m/sec and r = (8 cm / 2) = 4 cm = 0.04 m.
So, the angular velocity of the wheel is:
ω = (115 m/sec) / (0.04 m) = 2875 radian per second.

b) The linear velocity of the bicycle can be found by using the formula:
v = ω * r
where v is the linear velocity, ω is the angular velocity, and r is the radius of the wheel.
In this case, ω = 125 revolutions per minute = (125 * 2π) / 60 = 13.09 radian per second and r = (18 inches / 2) = 9 inches = 0.75 feet.
So, the linear velocity of the bicycle is:
v = (13.09 radian per second) * (0.75 feet) = 9.82 feet per second.
To convert this to miles per hour, we can use the conversion factor 5280 feet = 1 mile:
v = (9.82 feet per second) * (60 seconds / 1 minute) * (60 minutes / 1 hour) * (1 mile / 5280 feet) = 6.68 miles per hour.
So, the linear velocity of the bicycle is approximately 6.68 miles per hour.

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The fraction of the flowers in the bouquet are daffodils is   6/ 9f + 6

A fraction can be defined as the part of a whole number or variable.

The different types of fractions in mathematics are;

Ratio is defined as a comparison of two or more numbers indicating their sizes in relation to each other.

It shows the number of times one number contains another.

From the information given, we have that;

The ratio of lilies to daffodils to marigolds in a bouquet is 7f:6:2f.

Then, thte number of daffodils would be;

= 6/7f + f+ 2f

= 6/ 9f + 6

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Answer:

y=2x+3

Step-by-step explanation:

Using the point-slope form of the equation of a line, we can write:

y - 9 = 2(x - 3)

Simplifying, we get:

y - 9 = 2x - 6

y = 2x + 3

Therefore, the equation of the line that is parallel to y=2x+1 and goes through the point (3,9) is y=2x+3.

parallel → the same slope

slope: y = 2x +1 → m = 2

y=2x+3 ⇔ 2(3)+3=6+3=9

y=2x+9 ⇔ 2(3)+9=6+9=15≠9

⇒ answer: y=2x+3

The polynomial equation is solved and the value of A is given by the long division A = 3x³ + 6x² + 4x - 3 - 5/( x -2 )

Polynomials are mathematical expressions involving variables raised with non-negative integers and coefficients(constants who are in multiplication with those variables) and constants with only operations of addition, subtraction, multiplication and non-negative exponentiation of variables involved.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the polynomial equation be represented as A

Now , let the first equation be p

p = 3x⁴ - 8x² - 11x + 1

Let the second equation be q

q = ( x - 2 )

And , the value of A = p/q

On simplifying , we get

A = ( 3x⁴ - 8x² - 11x + 1 ) / ( x - 2 )

From the long division of polynomials , we get

Step 1 :

A = 3x³ + [ ( 6x³ - 8x² - 11x + 1 ) / ( x - 2 ) ]

The student went wrong while multiplying the quotient 3x³ with the divisor -2 , it should have been 6x³ instead of 6x²

Step 2 :

A = 3x³ + 6x² + [ ( 4x² - 11x + 1 ) / ( x - 2 ) ]

Step 3 :

A = 3x³ + 6x² + 4x + [ ( -3x + 1 ) / ( x - 2 ) ]

Step 4 :

A = 3x³ + 6x² + 4x - 3 - [ 5/( x -2 ) ]

Therefor , the long division is solved , A = 3x³ + 6x² + 4x - 3 - [ 5/( x -2 ) ]

Hence , the polynomial is A = 3x³ + 6x² + 4x - 3 - [ 5/( x -2 ) ]

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Answer:

Step-by-step explanation:

To graph the equation 3(x - 2) = 5(x + 1), we can first simplify it by expanding the brackets:

3x - 6 = 5x + 5

Next, we can isolate the variable on one side of the equation. We can do this by subtracting 3x from both sides and adding 6 to both sides:

-11 = 2x

x = -11/2

Now we have the x-coordinate of the point where the graph of the equation intersects the x-axis. To find the y-coordinate of this point, we can substitute x = -11/2 into one of the original equations and solve for y:

3(x - 2) = 5(x + 1)

3(-11/2 - 2) = 5(-11/2 + 1)

-33/2 - 6 = -55/2 + 5

-33/2 - 6 + 55/2 = 5

-33/2 + 44/2 = 5

11/2 = 5

The probability that fewer than 3 of the selected consumers believe that cash will be obsolete in the next 20 years is 0.478

This probability problem can be solved using the binomial distribution. In this case, the probability of success is 0.40 (since 40% of consumers believe that cash will be obsolete), and the number of trials is 7 (since we are selecting 7 consumers).

To find the probability that fewer than 3 of the selected consumers believe that cash will be obsolete, we need to find the probability of getting 0, 1, or 2 successes. We can use the binomial probability formula to calculate each of these probabilities and then add them together:

P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)

Where X is the number of consumers who believe that cash will be obsolete, and P(X) is the probability of getting X successes.

The probability of getting exactly X successes in a binomial distribution with probability of success p and number of trials n is given by the formula:

P(X) = (n CX) * p^X * (1 - p)^(n - X)

Where (nCX) represents the number of ways to choose X successes from n trials, and is calculated using the binomial coefficient formula:

(nCX) = n! / (X! * (n - X)!)

Where n! represents the factorial of n, which is the product of all positive integers up to and including n.

Using this formula, we can calculate the probabilities of getting 0, 1, and 2 successes as follows:

P(X = 0) = (7C0) * 0.40^0 * 0.60^7 = 0.028

P(X = 1) = (7C1) * 0.40^1 * 0.60^6 = 0.15

P(X = 2) = (7C2) * 0.40^2 * 0.60^5 = 0.30

Thus, the probability of getting fewer than 3 successes is:

P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.028 + 0.15 + 0.30 = 0.478

Hence, the probability is 0.478.

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The wind generator will produce 2744W of power in a 35mph wind.

To find the power generated by the wind generator in a 35mph wind, we can use the formula P = kV³, where P is the power generated, k is a constant, and V is the wind's speed.

First, we need to find the value of k. We can do this by plugging in the given values of P and V into the formula and solving for k:

1000W = k(25mph)³ 1000W = k(15625mph³)

k = 1000W/15625mph³

k = 0.064W/mph³

Now that we have the value of k, we can plug it back into the formula along with the new wind speed of 35mph to find the power generated:

P = (0.064W/mph³)(35mph)³

P = (0.064W/mph³)(42875mph³)

P = 2744W

Therefore, the wind generator will produce 2744W of power in a 35mph wind.

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The fraction (4[tex]s^{(6)[/tex])(([tex]t^{(6)[/tex])[tex])^{3}[/tex]  in its simplest form is C. 64[tex]s^{(18)[/tex][tex]t^{(18)[/tex].  

To simplify the given fraction, we need to use the power of a power rule, which states that (a^b)^c = a^(b*c).

In this case, we have (4[tex]s^{(6)[/tex][tex]t^{(6)[/tex])^3 , so we need to multiply the exponents of each term by 3.

For the first term, [tex]4^{(3)[/tex] = 64. For the second term, [tex]s^{(6*3)[/tex] = [tex]s^{(18)[/tex]. And for the third term, [tex]t^{(6*3)[/tex]= [tex]t^{(18)[/tex].

Putting these terms together, we get 64[tex]s^{(18)[/tex][tex]t^{(18)[/tex], which is the correct answer.

So, the simplified form of (4[tex]s^{(6)[/tex])(([tex]t^{(6)[/tex])[tex])^{3}[/tex] is 64[tex]s^{(18)[/tex][tex]t^{(18)[/tex], or answer choice C.

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Answer:

Step-by-step explanation:

[tex]-\frac{1}{2}[/tex] x ≤ 17

( [tex]-\frac{2}{1}[/tex] )( [tex]-\frac{1}{2}[/tex] ) x ≤ 17( [tex]-\frac{2}{1}[/tex] )

x ≥ - 34

The correct statement about the functions f(x) and g(x) include the following: B. f(x) has a steeper slope than g(x).

In Mathematics, the slope of any straight line can be determined by using this mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Substituting the given points into the slope formula, we have the following;

Slope, m of g(x) = (1 - (-3))/(0 - (-2))

Slope, m of g(x) = 4/2

Slope, m of g(x) = 2.

Slope of f(x) = 3. Therefore, 3 is greater than 2.

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Zach still has to save 1/12 of the total amount after this month.

To find out how much of the total amount Zach still has to save after this month, we need to calculate how much he has already saved and how much he will save from this month's paycheck.

First, we know that Zach has already saved 2/3 of the money he will need for his trip. So, if we let x be the total amount he needs for the trip, we can write this as:
Already saved = 2/3 * x

Next, we know that Zach plans to put aside 3/4 of what he has left to save from this month's paycheck. Since he has already saved 2/3 of the total amount, he has 1/3 of the total amount left to save. So, the amount he will save from this month's paycheck is:
Amount from paycheck = 3/4 * (1/3 * x) = 1/4 * x

Now, we can add these two amounts to find out how much Zach has saved in total:
Total saved = Already saved + Amount from paycheck
Total saved = (2/3 * x) + (1/4 * x) = (8/12 * x) + (3/12 * x) = 11/12 * x

Finally, we can subtract this amount from the total amount he needs to find out how much he still has to save:
Amount still to save = Total amount - Total saved
Amount still to save = x - (11/12 * x) = (12/12 * x) - (11/12 * x) = 1/12 * x

So, Zach still has to save 1/12 of the total amount after this month.  

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[tex]\cfrac{1}{3}(9x+12)=15\implies \cfrac{9x+12}{3}=15\implies 9x+12=45 \\\\\\ 9x=33\implies x=\cfrac{33}{9}\implies x=\cfrac{3}{3}\cdot \cfrac{11}{3}\implies x=\cfrac{11}{3}\implies x=3\frac{2}{3}[/tex]

We have the following response after answering the given question: As a equation result, Country A saw more erratic weather throughout the summer, with a 6°C difference in temperatures.

In a mathematical equation, the equals sign (=), which connects two claims and denotes equality, is utilised. In algebra, an equation is a mathematical statement that proves the equality of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign separates the numbers by a space. Mathematical expressions can be used to describe the relationship between the two sentences on either side of a letter. The logo and the particular piece of software frequently correspond. like, for instance, 2x - 4 = 2.

Which nation experienced the hottest summer?

We may examine the average temperature for each nation throughout the observed weekends to determine which nation experienced the hottest summer.

Country A: (21.4°C) (18+20+22+23+24)/5

(24+26+28+29+27)/5 = 26.8°C for Country B.

The summer was therefore hotter in Country B, with an average temperature of 26.8°C.

b) Over the summer, which nation saw more erratic weather?

We may examine the temperature ranges recorded for each nation to determine which experienced more erratic weather during the summer.

24°C - 18°C equals 6°C in Country A.

29°C - 24°C equals 5°C in country B.

As a result, Country A saw more erratic weather throughout the summer, with a 6°C difference in temperatures.

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The correct interval for the area of triangle PQR is 2 <= A < 4.

To find the correct interval for the area of triangle PQR, we first need to calculate the area using the given points. We can do this by using the formula for the area of a triangle in three dimensions:

A = (1/2) * sqrt((x2*y3 - x3*y2)^2 + (x3*y1 - x1*y3)^2 + (x1*y2 - x2*y1)^2)

Plugging in the given points for P, Q, and R, we get:

A = (1/2) * sqrt((1*3 - 3*0)^2 + (3*0 - 0*1)^2 + (0*0 - 1*3)^2)

Simplifying, we get:

A = (1/2) * sqrt(9 + 9)

A = (1/2) * sqrt(18)

A = (1/2) * 3 * sqrt(2)

A = (3/2) * sqrt(2)

A = 2.12

Therefore, the correct interval for the area of triangle PQR is 2 <= A < 4. The correct answer is option b. 2 <= A < 4.

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The value of x and y are 40° and 40° respectively

A circle is a special kind of ellipse in which the eccentricity is zero and the two foci are coincident.

These are the few theorems of circle geometry

1. The angle at the centre is twice the angle at the circumference.

2. The angle in a semicircle is a right angle.

Angles in the same segment are equal.

3. Opposite angles in a cyclic quadrilateral sum to 180°

4. The angle between the chord and the tangent is equal to the angle in the alternate segment.

from triangle AOB,

angle 0 = 60° (opposite angles)

x = 180-( 80+60)

x = 180-140

x = 40°

x= y ( angle in the same segment are equal)

y = 40°

therefore the value of x and y are 40°

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