what does domain and what does range mean in algebra :(​

The following parts can be solved by the concept of Sets.

(a) KnF is definitely compact and closed.

(b) Fc U Kc is definitely closed, but not necessarily compact.

(c) K\F is definitely closed, but not necessarily compact.

(d) KnFc is definitely neither compact nor closed.

(a) KnF:

Since K is compact and F is closed, their intersection KnF is also closed, as the intersection of any finite number of closed sets is closed. Moreover, since K is compact, every open cover of K has a finite subcover, and thus, KnF is compact by the finite intersection property.

(b) Fc U Kc:

Fc is closed since the complement of a closed set is open, and Kc is closed since K is compact (and thus, closed) and the complement of a closed set is open. The union of two closed sets is also closed, so Fc U Kc is closed. However, Kc may not be compact, so Fc U Kc is not necessarily compact.

(c) K\F:

K\F is closed because it is the complement of the open set F. However, K\F may not be compact, as K itself may not be compact. For example, if K is the real line and F is the open interval (0,1), then K\F is not compact.

(d) KnFc:

KnFc is neither compact nor closed. To see that it is not compact, consider the sequence {x_n} in K given by x_n = (1 + 1/n, 0). This sequence converges to the point (1, 0), which is outside of K, but every term of the sequence is in K. Thus, K is not closed. On the other hand, since F is closed, Fc is open and contains K, so KnFc is not closed either.

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The ladder reaches a height of 5.6 feet on the house when the angle with the ground is 62 degrees

Given the following parameters

Angle with the ground = 62 degrees

Length of the ladder = 12 foot

The above parameters mean that the height of the ladder on the ladder can be calculated using the following trigonometry ratio from right triangles

cos(62) = h/12

Make h the subject of the formula

So, we have

h = 12 * cos(62)

Evaluate the equation

h = 5.6

Hence, the height is 5.6 feet

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Answer:

Step-by-step explanation:

From the graphs attached,

Let the coordinates of the two points given on the black line in the first graph are (-4, 2) and (-1, 10).

When these points have been rotated by 90° about the origin,

Rule for the rotation will be,

(x, y) → (y, -x)

Therefore, coordinates of the image points will be,

(-4, 2) → (2, 4)

(-1, 10) → (10, 1)

Therefore, red line given given in graph (1) and black line (After rotaion of 90° clockwise) in graph (2) will be same.

Answer:

yes they are the SAME.

Step-by-step explanation:

h = 60, x = 25 (option B)

x/leg 1 =leg 1/ (x + 144)

leg 1 = 65

144/leg 2 = leg 2/(x + 144)

leg 2 = 156

To avoid a quadratic equation, we will go with the equation having leg 2

To get height (h), apply geometric mean:

h = 60, x = 25 (option B)

Answer:

I hope this helps!

Step-by-step explanation:

1. M is .25

b is 20

so

y= .25x+20

2. y= 3x+2

Answer:

0.324 inch

Step-by-step explanation:

When asked to write two hundred thousandths as a decimal, three students gave three different answers as shown below. so you have to find by decimals..

Answer:

34 degrees

Step-by-step explanation:

If ABD = 64, and CBD is 30, we can use PWP( Part Whole Postulate)

Step 1.CBD + ABC = ABD

Step 2. Substitute

30 + ABC = 64

Step 3. Isolate ABC

34 = ABC

ABC is 34 degrees

9514 1404 393

Answer:

  34°

Step-by-step explanation:

It should be fairly intuitive that the two smaller angles add to give the value of the larger one. (Even if it's not, the angle sum theorem tells you this is true.)

  ∠ABC + ∠CBD = ∠ABD

  ∠ABC + 30° = 64°

  ∠ABC = 34° . . . . . . . . . subtract 30° from both sides of the equation

The series diverges with an integral of 1/ln(16) and the series converges with an integral of 1/4 and a sum of 1/2.

We can use the integral test to determine the convergence of the series ∑n=1∞ 1/6n. The integral of the function f(x) = 1/6x is:

\(∫f(x) dx = (1/6) ln(x) + C\)

Using the limits of integration from 1 to ∞, we get:

∫1∞ f(x) dx = (1/6) ln(∞) - (1/6) ln(1) = ∞

Since the integral diverges, the series also diverges.

We can use the integral test to determine the convergence of the series ∑n=1∞ \((n+4)/(n^2+8n+4\)). The integral of the function f(x) = \((x+4)/(x^2+8x+4)\) is:

∫f(x) dx = (1/2) ln(x^2 + 8x + 4) + 3 ln|x + 4| + C

Using the limits of integration from 1 to ∞, we get:

∫1∞ f(x) dx = (1/2) ln(∞) + 3 ln(∞ + 4) - (1/2) ln(13) - 3 ln(5) = ∞

Since the integral diverges, the series also diverges.

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Answer:

=-26.7

Step-by-step explanation:

=-13.9+(-12.8)

=-13.9-12.8

=-26.7

Answer:

13.9+(−12.8)= 1.1 gggggggg

Answer: Y=1/5x-2

Step-by-step explanation:

Answer:

In the PDF. All the answers should be there. Let me know if I'm missing any.

Answer:

Answers are below

Step-by-step explanation:

Answer:

31.2

Step-by-step explanation:

4(5 + (- 3.5 × - 0.8)

4(5 + 2.8)

4(7.8)

31.2

The fractions order from least to greatest is 1/2, 8 5/3

Fractions are mathematical expressions that represent a part of a whole or a division of quantities. They consist of a numerator and a denominator, separated by a slash (/) or a horizontal line. The numerator represents the number of equal parts being considered, while the denominator represents the total number of equal parts that make up a whole.

For example, in the fraction 3/4, the numerator is 3, indicating that we have three parts, and the denominator is 4, indicating that the whole is divided into four equal parts. This fraction represents three out of four equal parts or three-quarters of the whole.

To order the fractions from least to greatest, we have:

8 5/3, 1/2

To compare these fractions, we can convert them to a common denominator.

The common denominator for 3 and 2 is 6.

Converting the fractions:

8 5/3 = (8 * 3 + 5)/3 = 29/3

1/2 = (1 * 3)/6 = 3/6

Now, we can compare the fractions:

3/6 < 29/3

Therefore, the order from least to greatest is: 1/2, 8 5/3

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Answer:

14units

Step-by-step explanation:

Given

Initial point A = -2 (since it is on negative 2)

Other point B = 12 (lying in positive 12)

To get the distance between point A and B, we will use the expression:

AB = point B - point A

Substitute the given point in the expression

AB = 12-(-2)

AB = 12+2

AB = 14

Hence the distance between points A and B in the number line is 14units

The diameter of Earth in kilometers is approximately 12,682 km, making option D the correct answer.

To convert the diameter of Earth from miles to kilometers, we can multiply the given diameter in miles by the conversion factor of 1.6 kilometers per mile.

Given that Earth's diameter is 7,926 miles, we can calculate its diameter in kilometers as follows:

Diameter in kilometers = Diameter in miles × Conversion factor

Diameter in kilometers = 7,926 miles × 1.6 kilometers/mile

Diameter in kilometers = 12,681.6 kilometers

Rounding this value to the nearest whole number, we get 12,682 kilometers.

Therefore, the correct answer is option D: 12,682 km.

Option A: 49,553 km is not the correct answer. It is not consistent with the given diameter of Earth.

Option B: 120,586 km is also not the correct answer. It is not consistent with the given diameter of Earth.

Option C: 1,392,650 km is significantly larger than the actual diameter of Earth and is not a plausible value.

In conclusion, the diameter of Earth in kilometers is approximately 12,682 km, making option D the correct answer.

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In linear equation,75.78  is the equivalent decimal value for the dog's weight .

What in mathematics is a linear equation?

A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.

                         Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

Andrews Labrador retrievers weight 75 7/9 lb.

      \(75\frac{7}{9}\)  =  75 + 7/9

the fraction 7/9 and using the long division will be

    7/9 = 0.777777....  = 0. 7

This means the digit 7 will be repeated to infinity

      \(75\frac{7}{9}\) = 75.7.......  ≈ 75.78

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Hicksian demand functions are:x1** = 2P₁x₂ ; x₂** = P₂²

Utility function: u(x1+x2) = .5ln(x1) + .25ln(x₂) .The Marshallian demand functions are: x1* = - and x₂* = P₂.

The indirect utility function is found by substituting Marshallian demand functions into the utility function and solving for v(P₁, P₂, Y).u(x1*,x2*) = v(P₁,P₂,Y) ⇒ u(-, P₂) = v(P₁,P₂,Y) ⇒ .5ln(-) + .25ln(P₂) = v(P₁,P₂,Y) ⇒ v(P₁,P₂,Y) = - ∞ (as ln(-) is not defined)

Thus the indirect utility function is undefined.

Minimum expenditure function can be derived from the Marshallian demand function and prices of goods:

Exp = P₁x1* + P₂x2* = P₁(-) + P₂P₂ = -P₁ + P₂²

Minimum expenditure function is thus:

Exp = P₁(-) + P₂²

Hicksian demand functions can be derived from the utility function and prices of goods:

H1(x1, P1, P2, U) = x1*H2(x2, P1, P2, U) = x2*

Hicksian demand functions are:

x1** = 2P₁x₂

x₂** = P₂²

If there are no restrictions on the amount of money the consumer can spend, the Hicksian demand functions for x1 and x2 coincide with Marshallian demand functions.

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The asymptotic notation relationship between the functions \(f(n) = n^3 (8 + 2 cos 2n)\) and \(g(n) = n^2 + 2n^3 + 3n\) is f(n) ∈ Θ(g(n)). Therefore, the growth rates of f(n) and g(n) are primarily determined by the cubic terms, and they grow at the same rate within a constant factor.

To determine the asymptotic notation relationship between the functions \(f(n) = n^3 (8 + 2 cos 2n)\) and \(g(n) = n^2 + 2n^3 + 3n\), we need to compare their growth rates as n approaches infinity.

Θ (Theta) Notation: f(n) ∈ Θ(g(n)) means that f(n) grows at the same rate as g(n) within a constant factor. In other words, there exists positive constants c1 and c2 such that c1 * g(n) ≤ f(n) ≤ c2 * g(n) for sufficiently large n.

o (Little-o) Notation: f(n) ∈ o(g(n)) means that f(n) grows strictly slower than g(n). In other words, for any positive constant c, there exists a positive constant n0 such that f(n) < c * g(n) for all n > n0.

ω (Omega) Notation: f(n) ∈ ω(g(n)) means that f(n) grows strictly faster than g(n). In other words, for any positive constant c, there exists a positive constant n0 such that f(n) > c * g(n) for all n > n0.

Now let's analyze the given functions:

\(f(n) = n^3 (8 + 2 cos 2n)\\g(n) = n^2 + 2n^3 + 3n\)

Since both functions have the same dominant term, we can say that f(n) ∈ Θ(g(n)) because they grow at the same rate within a constant factor. The other notations, o and ω, are not applicable here because neither function grows strictly faster nor slower than the other.

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A demand function is an equation or formula that represents the relationship between the quantity demanded of a good or service and the various factors that influence it, such as price, income, and other relevant variables.

The given demand and supply functions are given below: Demand function: \(\( P=8-Q_{D} \\)) Supply function:\(\( P=2+Q_{S} \)\) The graph of demand and supply functions are shown below:

Graph of demand and supply functions The demand curve has a negative slope since when the price of a good increases the quantity demanded decreases. The supply curve has a positive slope since when the price of a good increases the quantity supplied increases.At the equilibrium point, the price and quantity supplied and demanded are equal. The equilibrium point is at the point where the demand and supply curves intersect.

In this case, the equilibrium price is equal to 5 and the equilibrium quantity is equal to 3. At the equilibrium point, there is neither excess demand nor excess supply.

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We can write the the area of the trapezoid as 132 square inches.

Area is a collection of two - dimensional points enclosed by a single dimensional line. Mathematically, we can write -

V = ∫∫F(x, y) dx dy

Given is a trapezoid that has been divided into two right triangles and a rectangle.

We can write the area of the trapezoid as -

A{trapezoid} = 2 x Area{Δ} + Area{Rectangle}

A{trapezoid} = 2 x 1/2 x 3 x 12 + 12 x 8

A{trapezoid} = 36 + 96

A{trapezoid} = 132 square inches

Therefore, we can write the the area of the trapezoid as 132 square inches.

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Answer: 31.39%

Step-by-step explanation:

Given: The ages of rocks in an isolated area are known to be approximately normally distributed with a mean of 7 years and a standard deviation of 1.8 years.

i.e. \(\mu = 7 \ \ \ \ \sigma= 1.8\)

Let X be the age of rocks in an isolated area .

Then, the probability that rocks are between 5.8 and 7.3 years old :

\(P(5.8<X<7.3)=P(\dfrac{5.8-7}{1.8}<\dfrac{X-\mu}{\sigma}<\dfrac{7.3-7}{1.8})\\\\=P(-0.667<Z<0.167)\ \ \ [z=\dfrac{X-\mu}{\sigma}]\\\\=P(Z<0.167)-P(z<-0.667)\\\\=P(Z<0.167)-(1-P(z<0.667))\\\\=0.5663-(1-0.7476)\\\\=0.3139\)

\(=31.39\%\)

Hence, the percent of rocks are between 5.8 and 7.3 years old = 31.39%

Step-by-step explanation:

I think that 10m/s is equal to 36km/h

I hope this helped! ☆☆

Answer:

(-14, 4)

Step-by-step explanation:

I graphed it on Desmos Graphing calculator. This is a great resource. Hope this helps!

Step-by-step explanation:

( - 14, -4)

is a right answer

Answer:

w = 65

Step-by-step explanation:

What number that when divided by 5 the quotient can be added to 17?

65 :D (wish it was 69 though)

Answer:

65

Step-by-step explanation:

Usando el maximo comun divisor(MCD), tiene-se que lo máximo que mide el circuito es 4 km.

--------------------

Factorando por factores primos, simultáneamente:

20 - 36 - 44|2

10 - 18 - 22|2

5 - 9 - 11

O sea, MCD(20,36,44) = 2x2 = 4.

Así, lo máximo que mide el circuito es 4 km.

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Answer:

-6

Step-by-step explanation:

The pattern here is that you substract 15 every time you move a number (left to right) , therefore: 9-15 = -6

If you have any questions about the way I solved it, don't hesitate to ask me in the comments below =)

Answer:

27*10⁵ is basically 270000.