The dimensions of a rectangular field are 16x - 6 and 10x + 12 units. The value of x for which it would be square is______.

The budgets of Hong Kong, the United States of America, and Korea differ in contents, formats, advantages, and disadvantages. While each budget has its strengths and weaknesses, they all aim to provide a clear and transparent financial plan for their respective countries.

A budget is a financial plan that estimates expected income and expenditure for a specific period. It may include income, expenses, debts, and savings. Budgets may vary from country to country and can be analyzed by comparing their contents, formats, advantages, and disadvantages. Here are the budgets of Hong Kong, the United States of America, and Korea:

United States Budget:

Korean Budget:

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Answer:

2.6 kilometers

Step-by-step explanation:

To find the circumference of a circle, we can use the formula:

Circumference = π * diameter

Given that the diameter of the volcanic crater is 840 meters, we can substitute this value into the formula:

Circumference = π * 840

Using the approximate value of π as 3.14159, we can calculate the circumference:

Circumference = 3.14159 * 840

Circumference ≈ 2643.1796 meters

To convert the circumference to kilometers, we divide the value by 1000:

Circumference in kilometers = 2643.1796 / 1000

Circumference ≈ 2.6432 kilometers

Therefore, the circumference of the rim of the volcanic crater is approximately 2.6 kilometers (rounded to 1 decimal place).

The radius of convergence of the series ∑(cn + dn)Xⁿ  is at least 5.

Thus, we can say that both series converge absolutely for |x| < 5 and |x| < 6, respectively.The radius of convergence of a series is defined as the distance from the center of the series to the closest point where the series converges.

The radius of convergence for the series

∑(cn + dn)Xⁿ

can be determined using the following formula:

R = \(\frac{1}{\lim\limits_{n\to\infty} \sup \sqrt[n]{|c_n + d_n|}}\)

Here, cn and dn are the nth terms of the respective series. The limit superior is taken as n approaches infinity.To simplify the calculation, we can take the larger of the two radii of convergence.

∑(cn + dn)Xⁿ

is at least 5 since it is less than or equal to the radius of convergence of the series ∑dn^xⁿ .

Therefore, we can say that the radius of convergence of the series ∑(cn + dn)Xⁿ is at least 5.

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Answer:

pls dont kill my dad.. i cant help but please. hes the only thing i have left man

Step-by-step explanation:

i would so help if i could but i just really dont want shrek dead

Answer:

3/8

Step-by-step explanation:

3/4 / 2/1

3/4 * 1/2=3/8

3/8

Answer:

\(\frac{3}{8}\)  

I hope this helps!

Answer:

8x+60

Step-by-step explanation:

4(2x+15)

=4×2x+4×15

=8x+60

expand brackets ;)

The population of each country will become double in 47 years.

Given that,

The population of the Dominican republic is, n = 10.7 million.

The growth rate of the Dominican republic is, p = 1.5 %.

The population of Paraguay is, n' = 6.0 million.

The growth rate of Paraguay is p' = 1.5 %.

The doubling time of population growth depends on the rate of population growth.

Here,

n is the final population and n0 is the initial population and doubling the value in the future, n= 2*n0.

Solving this, we get:

t= ln (2*n0/n0)/(1.5/100) = 47 years.

Thus, we can conclude the population of each country will become double in 47 years.

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The average value of both f(x) and g(x) on 0≤x≤2 is 1/4. The average value of (f.g) on 0≤x≤2 is 0 and the statement avg(f) . avg(g) = avg(f . g) is false.

avg value of a function = 1/(b - a) ∫f(x) with limts a and b. Here a and b are the constraints under which the average has to be calculated.

a)

Hence average value of f(x) on 0≤x≤2

= 1/2 ∫f(x)  with 0 and 2 as intervals

Since integration is basically the area under the curve we get

avg of f(x) = 1/2[area under curve from 0 to 1 + Area under the curve from 1 to 2]

Since from 0 to 1, the figure is a triangle and beyond that a straight line we get

1/2[1/2 X 1 X 1 + 0]

= 1/4 sq units

b)

Similarly, the average value of g(x) on 0 ≤ x ≤ 2

1/2[area from 0 to 1 + area from 1 to 2]

= 1/2[0 + 1/2]

= 1/4 sq units

c) here we need to find the average of f(x) . g(x)

Here we see that f(x) is 0 from x = 1 to x = 1 while g(x) id 0 from x = 0 from x = 1

Hence we see that on multiplying the functions, the resultant has to be a 0 function.

Hence its average value will be 0.

d)

Average(f) . Average(g) = 1/4 X 1/4

= 1/16

Average of (f.g) = 0

Hence the statement is false

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Complete Question

The figure attached to the left is a graph of f(x), and below to the right is g(x).

The figure below to the left is a graph of f(x), a

(a) What is the average value of f(x) on 0≤x≤2? avg value = __________

(b) What is the average value of g(x) on 0≤x≤2? avg value = __________

(c) What is the average value of f(x) . g(x) on 0≤x≤2? avg value = _________

(d) Is the following statement true?

Average(f) . Average(g)=Average(f.g)

A. Yes

B. No

Answer:

x = 65

Step-by-step explanation:

Answer:

B. x = 65

Step-by-step explanation:

Angles ∠PTU and ∠VTU are supplementary, meaning they equal 180° when added together.

180 - 115 = 65

∠VTU = 65°

All angles in a triangle must add to equal 180°, so you use the equation:

50 + 65 = 115

180 - 115 = 65

Therefore x = 65

Answer: y-5=-3(x-10)

Step-by-step explanation:

The probability that all of the resulting pieces have lengths of at least 8.5 cm. is 0.0625

We can think of the probabilities as direct areas because the distribution is uniform (as it is along a straight line).

A square with an area of 34² can be used to represent it.

Total stick area = length x width = 34 x 34 = 1156 cm².

This area has a probability of 1.

When two points are chosen at random, they can now be represented as X₁ and X₂.

There will be three pieces of the stick after breaking from two points.

The length of 1 piece = 8.5 cm

Then the length of 3 pieces = 8.5 x 3 = 25.5 cm

Now the area of pieces with a minimum length of 8.5 cm

= (length of whole stick - length of 3 pieces)² cm²

= (34 - 25.5)² cm²

= 8.5²  cm²

= 72.25 cm²

Probability of obtaining pieces of at least 8.5 lengths is

P(8.5 lengths)

= Area of pieces with 8.5 lengths/Area of stick

= 72.25/1156

= 0.0625

Therefore the probability that all of the resulting pieces have lengths of at least 8.5 cm. is 0.0625

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Answer:

230 cm²

Step-by-step explanation:

Split the shape into a rectangle and a triangle to make it easier to solve.

A(rectangle) = l · w

A(triangle) = 1/2bh

Let's find the area of the rectangle first. The length is 20 and the width is 7. Substitute those values into the equation.

A(rectangle) = 20 · 7 = 140 cm²

Next, find the area of the triangle. The base is 20 but in order to find the height, you need to subtract 7 from 16. This means the height is 9. Substitute those values into the equation.

A(triangle) = 1/2(20)(9) = 90 cm²

Finally, in order to find the area of the entire shape, we need to add the two areas we evaluated.

A(shape) = 140 + 90 = 230 cm²

Therefore, the area of the shape is 230 cm².

Substitute x with -1/2 and y with 1/2.

So the equation will look like this:

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

= -3/ -2.5 + 1/2

= -3/ -2

= 1.5

Therefore, the answer is 3/2 or 1.5.

Using mathematical induction, we have proved that 6ⁿ + 4 is divisible by 5 for n≥0. This result has important applications in various areas of mathematics and science. The proof demonstrates the power and usefulness of mathematical induction in proving statements for all natural numbers.

To prove that 6ⁿ + 4 is divisible by 5 for n≥0 using induction, we need to show that the statement is true for the base case, and then assume that the statement is true for n=k, and prove that it is also true for n=k+1.

Base case: For n=0, we have 6⁰+ 4 = 5, which is divisible by 5. Therefore, the statement is true for the base case.

Assume that the statement is true for n=k, which means that 6ᵃ+ 4 is divisible by 5.

Proof: Now we need to prove that the statement is also true for n=k+1, which means that we need to show that 6ᵃ⁺¹ + 4 is divisible by 5. (LET k=a)

Using the assumption that 6^k + 4 is divisible by 5, we can write:

6ᵃ⁺¹ + 4 = 6 * 6ᵃ + 4 = 5 * 6ⁿ + 6^k + 4 = 5 * 6ᵃ + (6ᵃ + 4)

Since 6ᵃ + 4 is divisible by 5 (by the assumption), and 5 * 6ᵃis also divisible by 5, we can conclude that 6ᵃ⁺¹+ 4 is divisible by 5.

Therefore, by mathematical induction, we can conclude that 6ⁿ + 4 is divisible by 5 for n≥0.


To prove that 6ⁿ + 4 is divisible by 5 for n≥0 using induction, we need to show that the statement is true for the base case, and then assume that the statement is true for n=k, and prove that it is also true for n=k+1. The base case is n=0, and we can see that 6⁰ + 4 = 5, which is divisible by 5. Assuming that the statement is true for n=k, we can use this to prove that it is also true for n=k+1. By the mathematical induction, we can conclude that 6ⁿ + 4 is divisible by 5 for n≥0.


Using mathematical induction, we have proved that 6ⁿ + 4 is divisible by 5 for n≥0. This result has important applications in various areas of mathematics and science. The proof demonstrates the power and usefulness of mathematical induction in proving statements for all natural numbers.

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Answer:

l

Step-by-step explanation:

;

Answer:

390 minutes I do believe.

Step-by-step explanation:

a.  √2 ∉ Q(√3).

b. The function does not exist.

(a) Proof:

Given x = a + b√2 where x is a non-zero number. We need to prove that x¯ = a² - 26² - a² - 2b²√2.

Let us take the conjugate of x. That is x¯ = a - b√2.

Now, let us multiply x and x¯:

x·x¯ = (a + b√2)(a - b√2) = a² - 2b².

Now, take the square of 2. That is 2² = 4 = 26 - 22.

Therefore, we can write the above equation as:

a² - 2b² - 22 = a² - 26² - a² - 2b²√2.

Thus, the proof is complete.

(b) Proof:

Given a prime number k, we define Q(√k) = {a + b√k : a,b ≤ Q} ≤ R. This set becomes a field when equipped with the usual addition and multiplication operations inherited from R.

We need to show that √2 ∈ Q(√3).

Let us take an element x = a + b√2 such that x ∈ Q(√2).

Therefore, a, b ∈ Q or they are rational numbers. √2 is an irrational number, but the square root of 3 is also an irrational number.

Therefore, the product of √2 and √3 is also an irrational number. Hence, it will be impossible to express the value in the form of p + q√2 where p and q are rational numbers. Hence, it can be concluded that √2 ∉ Q(√3).

(c) Proof:

We need to prove that there cannot be a function: Q(√2) → Q(√3) so that: (Q(√2) - {0}, ×) → (Q(√3) − {0}, ×) and: (Q(√2), +) → (Q(√3), +) are both group isomorphisms.

Let us assume that there exists a function: Q(√2) → Q(√3) such that: (Q(√2) - {0}, ×) → (Q(√3) − {0}, ×) and: (Q(√2), +) → (Q(√3), +) are both group isomorphisms.

Now, we can say that, (√2 × √2) = 2 ∈ Q(√2) and (√3 × √3) = 3 ∈ Q(√3).

As per the given function, φ(2) = a + b√3 and φ(3) = c + d√3, where a, b, c, and d are all rational numbers.

Now, as per the homomorphism property, φ(√2 × √2) = φ(2 + 2) = φ(2) + φ(2) = 2(a + b√3).

And, φ(√2 × √2) = φ(√2) × φ(√2) = a - b√3.

Thus, 2(a + b√3) = a - b√3.

That is, 3b + √3a = 0.

However, it contradicts the fact that √3 is irrational and 3b and a are rational numbers. Hence, the function does not exist.

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To solve the equation 10x dy/dx - 2y = x-3, we will use the method of separation of variables, we get 5x ln(2y - x + 3) + (5/2) x^2 - (1/2) (2y - x + 3)^2 = x + C

This method involves rearranging the equation so that all terms involving x are on one side and all terms involving y are on the other side. Then, we can integrate both sides of the equation to find the general solution. Here are the steps:

Rearrange the equation to separate the variables:

10x dy/dx = 2y + x - 3

10x dy = (2y + x - 3) dx

Separate the variables:

10x dy = 2y dx + x dx - 3 dx

10x dy - 2y dx = x dx - 3 dx

(10x dy - 2y dx)/(2y - x + 3) = dx

Integrate both sides of the equation:

∫(10x dy - 2y dx)/(2y - x + 3) = ∫dx

Use the substitution method to solve the integral on the left side of the equation. Let u = 2y - x + 3, then du = 2 dy - dx:

∫(10x (du/2 + dx) - 2u du)/(u) = ∫dx

5x ∫du + 5 ∫x dx - ∫u du = ∫dx

5x ln(u) + (5/2) x^2 - (1/2) u^2 = x + C

Substitute back for u and simplify:

5x ln(2y - x + 3) + (5/2) x^2 - (1/2) (2y - x + 3)^2 = x + C

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Answer:

Option C

hope this helps you. Do mark me as brainliest.

Answer:

approximately 7.5265in

Step-by-step explanation:

Area = length x width

2.75 x 2.75 = 7.5265in

The graph of the inequality x - 6y > 18 is plotted and attached

Inequality are graphed considering the table of values formed by assigning several values for x

x - 6y > 18

rearranging the equation will result to

x - 18 > 6y

y < x/6 - 3

for x = -6, y < -6 / 6 - 3 = -4

for x = 0, y < 0 / 6 - 3 = -3

for x = 6, y < 6 / 6 - 3 = -2

Table of value

x      y

-6    -4

0      -3

6      -2

the equation: y < x/6 - 3 will have a dashed line and shading is below the line because it has a less than sign

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Answer:

Step-by-step explanation: I got 14.4 but I might be wrong and im sorry if I am

Answer: 85

Step-by-step explanation:

51 / 3 = 17

17 x 2 = 34

51 + 34 = 85

z1 = (4 - 8.35) / 2.5 = -1.74
z2 = (12 - 8.35) / 2.5 = 1.46
P(-1.74 < z < 1.46) = 0.8711 - 0.0428 = 0.8283
Therefore, the probability that a household views television between 4 and 12 hours a day is 0.8283 (or 82.83% when expressed as a percentage).

To find the probability that a household views television between 4 and 12 hours a day, we will use the normal probability distribution.
1. To solve this problem, we can use the normal probability distribution formula:
z = (x - μ) / σ
where z is the z-score, x is the value we are interested in (in this case, between 4 and 12 hours), μ is the mean (8.35 hours), and σ is the standard deviation (2.5 hours).

2. We will find the Z-scores for the lower and upper bounds (4 and 12 hours, respectively) using the following formula: Z = (X - µ) / σ.

For the lower bound (4 hours):
Z1 = (4 - 8.35) / 2.5 = -1.74

For the upper bound (12 hours):
Z2 = (12 - 8.35) / 2.5 = 1.46

3. Now, we will use a Z-table or a calculator with a normal distribution function to find the probabilities corresponding to these Z-scores.

P(Z1) = P(Z < -1.74) ≈ 0.0409
P(Z2) = P(Z < 1.46) ≈ 0.9222

4. Finally, to find the probability that a household views television between 4 and 12 hours a day, subtract P(Z1) from P(Z2).

P(4 < X < 12) = P(Z2) - P(Z1) = 0.9222 - 0.0409 = 0.8813

So, the probability that a household views television between 4 and 12 hours a day is approximately 0.8813, or 88.13% (rounded to four decimal places).

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Answer:

A

Step-by-step explanation:

plz give brainliest

The perimeter of the book marker is 22cm

Perimeter is the outside boundary of a shape.

Analysis:

Length = x + 1

Width = x+1 - 5= x - 4

Area = 24 square centimeters = length x width

(x-4)(x+1) = 24

x2 -3x -4 = 24

x2 -3x -28 = 0

x2 -7x + 4x - 28 = 0

x(x-7) + 4(x - 7) = 0

(x+4)(x-7) = 0

since dimension cannot be negative x = 7

Length = 7 + 1 = 8 cm

Width = 7 - 4 = 3cm

Perimeter = 2(8 + 3 ) = 2 x 1 1 = 22cm

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To find all of the cube roots of ii and write the answers in rectangular form, we need to first express ii in polar form. To do this, we can convert ii to its polar form by writing it as a complex number in the form r(cosθ + isinθ), where r is the magnitude and θ is the argument.

In this case, we have ii = 1(cos(π/2) + isin(π/2)).  The magnitude of ii is 1, and the argument is π/2.  Now, to find the cube roots, we need to find the numbers that, when raised to the power of 3, give us ii. To find the cube roots, we can use De Moivre's theorem, which states that for any complex number z = r(cosθ + isinθ), the nth roots of z can be found by taking the nth root of the magnitude and dividing the argument by n.

In this case, we have n = 3, r = 1, and θ = π/2.  Taking the cube root of the magnitude 1 gives us 1^(1/3) = 1. Dividing the argument π/2 by 3 gives us (π/2) / 3 = π/6. So, the first cube root is 1(cos(π/6) + isin(π/6)). To find the other cube roots, we can add multiples of 2π/3 to the argument. Adding 2π/3 to π/6 gives us π/6 + 2π/3 = π/2. So, the second cube root is 1(cos(π/2) + isin(π/2)), which is equal to ii. Adding another 2π/3 gives us π/2 + 2π/3 = 7π/6. So, the third cube root is 1(cos(7π/6) + isin(7π/6)). Therefore, the cube roots of ii in rectangular .

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Explanation:

Using expontia

Answer:

Im pretty sure its f(0) = g(0)

Step-by-step explanation: