Wyoming has 63,791 fewer people than Washington DC has. What is the population of Washington DC? Wyoming has 582,658 people total.​

The inner product of two vectors A = (2, -3,0) and B = (-1,0,5) is -2 / √(13×26).

Solving the given system of equations using Gaussian elimination:

2x + 3y + z = 2 y + 5z = 20 -x+2y+3z = 13

Matrix form of the system is

[A] = [B] 2 3 1 | 2 0 5 | 20 -1 2 3 | 13

Divide row 1 by 2 and replace row 1 by the new row 1: 1 3/2 1/2 | 1

Divide row 2 by 5 and replace row 2 by the new row 2: 0 1 1 | 4

Divide row 3 by -1 and replace row 3 by the new row 3: 0 0 1 | 5

Back substitution, replace z = 5 into second equation to solve for y, y + 5(5) = 20 y = -5

Back substitution, replace z = 5 and y = -5 into the first equation to solve for x, 2x + 3(-5) + 5 = 2 2x - 15 + 5 = 2 2x = 12 x = 6

The solution is (x,y,z) = (6,-5,5)

Therefore, the solution to the given system of equations using Gaussian elimination is (x,y,z) = (6,-5,5).

The given two vectors are A = (2, -3,0) and B = = (-1,0,5). The inner product of two vectors A and B is given by

A·B = |A||B|cosθ

Given,A = (2, -3,0) and B = (-1,0,5)

Magnitude of A is |A| = √(2²+(-3)²+0²) = √13

Magnitude of B is |B| = √((-1)²+0²+5²) = √26

Dot product of A and B is A·B = 2(-1) + (-3)(0) + 0(5) = -2

Cosine of the angle between A and B is

cosθ = A·B / (|A||B|)

cosθ = -2 / (√13×√26)

cosθ = -2 / √(13×26)

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The shortest total distance for the route from Anglemouth to Doncatry is 15 units.

On the table, we can see that there is a dash in the section of:

"Anglemouth to Doncatry"

So there is not a direct route, so we need to try another way.

If we go from Anglemouth to Covenham, we have a distance of 10 units.

If now we go from Covenham to Doncatry, we have a distance of 5 units.

Adding these two distances we get:

Total distance = 10 + 5 = 15 units.

This is also the shortest total distance between the two towns.

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Answer:

Yes, because -18/6 is -3, which is a higher value than -4 :)

Answer:| -17|

Step-by-step explanation: the lines represent the absolute value which is 17 out of the rest it has the smallest value

Answer:

a is the answer to this question but if I am wrong sorry

Answer:

4

Step-by-step explanation:

Solving:

Checking:

Answer:

Step-by-step explanation:

Remark

What the question means is wherever you see an x on the right, you put in 12 and solve it. I'm going to assume you mean (2/3)*x + 3 on the right.

Solution

f(12) = (2/3) * 12 + 3

f(12) = 2 * 12 / 3 + 3

f(12) = 24/3 + 3

f(12) = 8 + 3

f(12) = 11

Answer:  A

Step-by-step explanation: common sense

Answer:

its a -2 because its a negative and when u count u dont start with a negative do u?

Step-by-step explanation:

Answer:

90 i think :)

Step-by-step explanation:

Answer:

90

Step-by-step explanation:

By reasoning, we can say 50% of 200 is 100

We can say 10% of 200 is 20

We divide 20 by 2 to get 5%

20/2

= 10

Subtract 100 by 10

100 - 10

= 90

45% of 200 is 90

Answer:

Step-by-step explanation:

2a + (10 - 4) = 2a + 6

2a + 6 = 6 + 2a

Step-by-step explanation:

<3° +116 = 180 (linear pair)

<3° = 180-116 = 64°

<1° + <3° + 52 = 180 ( angle sum property of a triangle)

<1° +64+52=180

<1°= 180-64-52

<1°= 64°

Answer:

3.451, 3.452, 3.453, 3.454, 3.455, 3.456, 3.457, 3.458, 3.459, 3.460

Answer:

12.6

Step-by-step explanation:

f(-4.5) means "what is the y-value when x equals -4.5?"

We see that when x = -4.5, our y or f(x) value is 12.6

The second solution is: y2(x) = -1 / x¹⁸ + 29x sin(5lnx) ∫ e^(29u) / sin(u) du/5 + Cx sin(5lnx) where C is a constant of integration.

To find a second solution y2(x) for the given differential equation x²y'' - xy' + 26y = 0 with the function y1(x) = x sin(5 ln x), we'll use the reduction of order formula:y2(x) = y1(x) * e^(-∫P(x)dx) * ∫(e^(∫P(x)dx) / y1(x)^2 dx)
First, rewrite the given differential equation in the standard form:
y'' - (1/x)y' + (26/x²)y = 0
From this, we can identify P(x) = -1/x.
Now, calculate the integral of P(x):
∫(-1/x) dx = - ln|x|
Now, apply the reduction of order formula:
y2(x) = x sin(5 ln x) * e^(ln|x|) * ∫(e^(-ln|x|) / (x sin(5 ln x))² dx)
Simplify the equation:
y2(x) = x sin(5 ln x) * x * ∫(1 / x² (x sin(5 ln x))² dx)
y2(x) = x² sin(5 ln x) * ∫(1 / (x² sin²(5 ln x)) dx)
Now, you can solve the remaining integral to find the second solution y2(x) for the given differential equation.

To find the second solution y2(x), we will use the reduction of order method. Let's assume that y2(x) = v(x) y1(x), where v(x) is an unknown function. Then, we can find y2'(x) and y2''(x) as follows:
y2'(x) = v(x) y1'(x) + v'(x) y1(x)
y2''(x) = v(x) y1''(x) + 2v'(x) y1'(x) + v''(x) y1(x)
Substituting y1(x) and its derivatives into the differential equation and using the above expressions for y2(x) and its derivatives, we get:
x^2 (v(x) y1''(x) + 2v'(x) y1'(x) + v''(x) y1(x)) - x(v(x) y1'(x) + v'(x) y1(x)) + 26v(x) y1(x) = 0
Dividing both sides by x^2 y1(x), we obtain:
v(x) y1''(x) + 2v'(x) y1'(x) + (v''(x) + (26/x^2) v(x)) y1(x) - (1/x) v'(x) y1(x) = 0
Since y1(x) is a solution of the differential equation, we have:
x^2 y1''(x) - x y1'(x) + 26y1(x) = 0
Substituting y1(x) and its derivatives into the above equation, we get:
x^2 (5v'(x) cos(5lnx) + (25/x) v(x) sin(5lnx)) - x(v(x) cos(5lnx) + v'(x) x sin(5lnx)) + 26v(x) x sin(5lnx) = 0
Dividing both sides by x sin(5lnx), we obtain:
5x v'(x) + (25/x) v(x) - v'(x) - 5v(x)/x + v'(x) + 26v(x)/x = 0
Simplifying the above expression, we get:
v''(x) + (1/x) v'(x) + (1/x² - 31/x) v(x) = 0

This is a second-order linear homogeneous differential equation with variable coefficients. We can use formula (5) in Section 4.2 to find the second linearly independent solution:
y2(x) = y1(x) ∫ e^(-∫P(x) dx) / y1^2(x) dx
where P(x) = 1/x - 31/x^2. Substituting y1(x) and P(x) into the above formula, we get:
y2(x) = x sin(5lnx) ∫ e^(-∫(1/x - 31/x²) dx) / (x sin(5lnx))² dx
Simplifying the exponent and the denominator, we get:
y2(x) = x sin(5lnx) ∫ e^(31lnx - ln(x)) / x^2sin²(5lnx) dx
y2(x) = x sin(5lnx) ∫ x^30 / sin²(5lnx) dx
Let u = 5lnx, then du/dx = 5/x, and dx = e^(-u)/5 du. Substituting u and dx into the integral, we get:
y2(x) = x sin(5lnx) ∫ e^(30u) / sin²(u) e^(-u) du/5
y2(x) = x sin(5lnx) ∫ e^(29u) / sin²(u) du/5
Using integration by parts, we can find that:
∫ e^(29u) / sin^2(u) du = -e^(29u) / sin(u) - 29 ∫ e^(29u) / sin(u) du + C
where C is a constant of integration. Substituting this result into the expression for y2(x), we get:
y2(x) = -x sin(5lnx) e^(29lnx - 5lnx) / sin(5lnx) - 29x sin(5lnx) ∫ e^(29u) / sin(u) du/5 + Cx sin(5lnx)
Simplifying the first term and using the substitution u = 5lnx, we get:
y2(x) = -x⁶ e^(24lnx) + 29x sin(5lnx) ∫ e^(29u) / sin(u) du/5 + Cx sin(5lnx)
y2(x) = -x⁶ / x^24 + 29x sin(5lnx) ∫ e^(29u) / sin(u) du/5 + Cx sin(5lnx)
y2(x) = -1 / x¹⁸ + 29x sin(5lnx) ∫ e^(29u) / sin(u) du/5 + Cx sin(5lnx)
Therefore, the second solution is: y2(x) = -1 / x¹⁸ + 29x sin(5lnx) ∫ e^(29u) / sin(u) du/5 + Cx sin(5lnx) where C is a constant of integration.

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Answer:

  $132,400

Step-by-step explanation:

You want to find the principal amount of a loan needed to pay for a home costing $165,500 after a 20% down payment has been made.

The loan amount will be for the remaining 80% of the price of the home:

  0.80 × $165,500 = $132,400

The amount to be borrowed is $132,400.

__

Additional comment

In these simplistic problems, the other costs of the transaction are usually ignored. Home loans often include fees for loan origination, taxes, agent commissions, and points for rate reduction, among others. The borrower may elect to finance some or all of these extra fees, adding to the loan value.

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The pattern is attached in the image provided with the work.

I have started off listing 4 terms and then 3 blanks

so we can study the pattern and find the next few terms.

Here, notice that the difference between -5 and 1/2 and -5 is +1/2.

The difference between -5 and -4 and 1/2 is +1/2

and the difference between -4 and 1/2 and -4 is +1/2.

Continuing the same pattern, -4 + 1/2 will be equal to -3 and 1/2.

-3 and 1/2 + 1/2 will be equal -3

and -3 + 1/2 will be equal to -2 and 1/5.

Answer:

The answer is below

Step-by-step explanation:

Which statements are true about the parallelograms? Check all that apply.

The length of side MN is 2 units.

The length of side M'N' is 5 units.

The image is smaller than the pre-image.

Sides MQ and M'Q' both have the same slope, 1.

The scale factor is 2/5

a) The length of side MN is determined using the formula:

\(|MN|=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}=\sqrt{(4-2)^2+(-2-(-2))^2}=\sqrt{2^2}=2\\ \\ |MN|=2\)

The first option is correct

b) The length of side M'N' is determined using the formula:

\(|M'N'|=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}=\sqrt{(10-5)^2+(-5-(-5))^2}=\sqrt{5^2}=2\\ \\ |M'N'|=5\)

The second option is correct

c) From the coordinates of parallelogram MNPQ and M'N'P'Q', we can see that parallelogram MNPQ is dilated by a factor of 5/2 to produce parallelogram M'N'P'Q' , hence parallelogram M'N'P'Q'  is bigger that parallelogram MNPQ. This means that The image is bigger than the pre-image.

The third option is wrong

d) The slopes are given as:

\(Slope\ of\ MQ=\frac{Change\ in\ y}{Change\ in\ x}=\frac{1-2}{-3-(-2)} =1\\ \\Slope\ of\ M'Q'=\frac{Change\ in\ y}{Change\ in\ x}=\frac{3-5}{-7-(-5)} =1\\\)

Option four is correct

e) From the coordinates of parallelogram MNPQ and M'N'P'Q', we can see that parallelogram MNPQ is dilated by a factor of 5/2 to produce parallelogram M'N'P'Q', hence the scale factor is 5/2

Option 5 is wrong

The length of MN and M'N' is 2 and 5 respectively and parallelogram MNPQ is dilated by a factor of 5/2 to produce parallelogram M'N'P'Q', hence parallelogram M'N'P'Q' is bigger than parallelogram MNPQ.

Given :

A) First, find the length of MN:

\(\rm |MN| = \sqrt{(4-2)^2+(-2-(-2))^2} =2\)

Therefore, this option is correct.

B) Now, find the length of M'N':

\(\rm |M'N'| = \sqrt{(10-5)^2+(-5-(-5))^2} =5\)

Therefore, this option is correct.

C) Parallelogram MNPQ is dilated by a factor of 5/2 to produce parallelogram M'N'P'Q', hence parallelogram M'N'P'Q' is bigger than parallelogram MNPQ. So the image is bigger than the pre-image. Therefore, this option is incorrect.

D) MQ slope is given by:

\(\rm m_1 = \dfrac{1-2}{-3-(-2)}=1\)

M'Q' slope is given by:

\(\rm m_2= \dfrac{3-5}{-7-(-5)}=1\)

So, the sides MQ and M'Q' both have the same slope, 1. Therefore, this option is correct.

E) Parallelogram MNPQ is dilated by a factor of 5/2 to produce parallelogram M'N'P'Q', hence parallelogram M'N'P'Q' is bigger than parallelogram MNPQ. Therefore, this option is incorrect.

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Answer:

d = 5 , a₂₅ = 112

Step-by-step explanation:

(a)

The nth term of an arithmetic sequence is

\(a_{n}\) = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Given a₁ = - 8 and a₁₆ = 67 , then

a₁ + 15d = 67

- 8 + 15d = 67 ( add 8 to both sides )

15d = 75 ( divide both sides by 15 )

d = 5

(b)

a₂₅ = - 8 + (24 × 5) = - 8 + 120 = 112

Answer:

16+n

Is this all? if yes 9+7=16 so 16+n is the simplified form o.o

16+n is the answer

9+7+n

=16+n

Answer:

6-4 = 2  -  -3 = 5

Step-by-step explanation:

Answer:

8-(2/x)

Step-by-step explanation:

Answer:

a₂₀ = 69

Step-by-step explanation:

The nth term of an arithmetic sequence is

\(a_{n}\) = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = 12 and d = 15 - 12 = 3 , then

a₂₀ = 12 + (3 × 19) = 12 + 57 = 69

Answer:

See Prove

Step-by-step explanation:

Given the expression: \(\dfrac{x^3-x^2}{x} -(x-1)(x+1)\)

To Prove: \(\dfrac{x^3-x^2}{x} -(x-1)(x+1)=1-x\)

Taking the Left-Hand side

\(\dfrac{x^3-x^2}{x} -(x-1)(x+1)\\=\dfrac{x(x^2-x)}{x} -[x(x+1)-1(x+1)]\\=x^2-x-[x^2+x-x-1]\\=x^2-x-x^2+1\\=-x+1\\=1-x\)

This is the right-hand side as required.

We have proved the given algebraic identity.

Answer: x = 34°

Step-by-step explanation:

180°-92°-54° = 34°

The percent increase in pipe footage sales is approximately 7%.

To find the percent increase in pipe footage sales, use the formula:

[(New Value - Old Value)/Old Value] × 100.

In this case, the new value is the amount of pipe sold in September (2,558 feet) and the old value is the amount of pipe sold in August (2,390 feet). Plugging these values into the formula, we get:

[(2,558 - 2,390)/2,390] × 100 = [168/2,390] × 100 = 0.0703 × 100 = 7.03%

Therefore, the correct answer is 7%, which is option A. The percent increase in pipe footage sales from August to September is 7%.

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Answer:

Step-by-step explanation:

Answer:

the answer is 2.6

Step-by-step explanation:

I just did it on edge just look at the photo

The correct choice is B

Let's solve the following triangle using the Law of Cosines for this given information, b = 10, c = 12, A = 59°. The Law of Cosines is expressed as;c² = a² + b² - 2ab cosCUsing the given values,

we can calculate the measure of the missing side of the triangle;a² = b² + c² - 2bc cosAa² = (10)² + (12)² - 2(10)(12) cos(59°)a² ≈ 144.1a ≈ 12 (rounded to one decimal place)Now we can use the Law of Sines to find the values of B and C.

The Law of Sines is expressed as;a/sinA = b/sinB = c/sinCa/sinA = b/sinBsinB = b (sinA / a)sinB = 10 (sin59° / 12)sinB ≈ 0.6914B ≈ sin⁻¹(0.6914)B ≈ 44.2°(rounded to one decimal place)C = 180° - A - BC = 180° - 59° - 44.2°C ≈ 76.8°(rounded to one decimal place),

the solution with the smaller angle B is;a ≈ 12, B ≈ 44.2°, C ≈ 76.8°.Hence, the correct choice is;B. There are two possible solutions for the triangle. The measurements for the solution with the smaller angle B are as follows. a ≈ 12, B ≈ 44.2°, C ≈ 76.8°.

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Isometric perspective refers to a system of diagonal lines that are parallel without converging. This perspective is commonly used in technical drawings and architectural illustrations to represent three-dimensional objects in a visually balanced and proportional manner.

Isometric perspective is a method of representing three-dimensional objects on a two-dimensional surface. It involves creating an illusion of depth and dimension by using a specific set of rules for drawing lines and angles. Isometric perspective is characterized by the use of parallel lines that remain parallel and do not converge, creating a sense of uniformity and stability in the representation.

In isometric perspective, the lines are typically drawn at a 30-degree angle from the horizontal plane. This angle creates a sense of depth and allows for accurate scaling of the object's dimensions. The vertical lines remain vertical, while the horizontal lines are drawn at a 30-degree angle to the horizontal plane.

Unlike other perspective techniques, such as linear perspective, isometric perspective does not include vanishing points or converging lines. Instead, it relies on the principle that all lines that are parallel in reality remain parallel in the isometric representation.

By following the rules of isometric perspective, an artist or designer can accurately depict the three-dimensional qualities of an object in a two-dimensional format. This technique is widely used in technical drawings, architectural illustrations, and engineering diagrams, as it provides a clear and consistent representation of objects from various angles.

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To determine whether a critical point is a relative minimum or maximum using concavity, we need to examine the second derivative of the function at the critical point.

If the second derivative is positive, then the function is concave up, meaning it is shaped like a bowl opening upwards. At a critical point where the first derivative is zero, this indicates a relative minimum, as the function is increasing on either side of the critical point.

On the other hand, if the second derivative is negative, then the function is concave down, meaning it is shaped like a bowl opening downwards. At a critical point where the first derivative is zero, this indicates a relative maximum, as the function is decreasing on either side of the critical point.

If the second derivative is zero, then the test is inconclusive and further analysis is needed, such as examining higher order derivatives or using other methods such as the first derivative test.

Therefore, the concavity test is a useful method for determining the nature of critical points and whether they represent a relative minimum or maximum.

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Complete question is:

What we need to examine for a method for determining whether a critical point is a relative minimum or maximum using concavity.

Answer:

63

Step-by-step explanation:

1/4 of 168 is 42 which is how many Boxes of Candy they sold

42 x 1.50 = 63

Answer:

From the sale of boxes of candy, the team made $63

Explanation:

We know that 3/4 of the sold items were chocolate bars. A fast trick to find 3/4ths, or 75%, of a number is to multiply it by 3 and divide by 4.

168 * 3 = 504

504 ÷ 4 = 126

Now, we do 168 - 126 to find the number of candy boxes.

168 - 126 = 42

So, the soccer team sold 42 boxes of candy. Since each box was $1.50, we just multiply

42 * 1.50 = 63

The soccer team made $63 dollars by selling candy boxes.

Note: This is just my way that I did quickly, there are many many other ways to do this. Try to find what's best for you.