a) evaluate the sum b) Prove the formula (2-1) = N². i=0

Answer:

x = 1

Step-by-step explanation:

6(x - 2) = 3 - 9x

We want to find x so that LHS = RHS/

6x - 12 = 3 - 9x

6x + 9x = 3 + 12

15x = 15

x = 1

Not 100% sure!

The value of x that makes the equation true is x = 1.

An expression in mathematics is a combination of numbers, variables, and mathematical operations (such as addition, subtraction, multiplication, and division) that represents a value or quantity.

We can solve for x by simplifying the equation using the distributive property and combining like terms:

6(x - 2) = 3 - 9x

6x - 12 = 3 - 9x (distribute 6)

6x + 9x = 3 + 12 (add 9x and 12 to both sides)

15x = 15 (combine like terms)

x = 1 (divide both sides by 15)

Therefore, the value of x that makes the equation true is x = 1.

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Answer:

Step-by-step explanation:

A

y = 7 - x

y = 7 - 2

y = 5

B

y = x^2 - 1

y = (2)^2 - 1

y = 2*2 - 1

y = 4 - 1

y = 3

C

y = x + 14

I'm going to assume that you mean (x + 14)^3

y = (x + 14)^3

y = (2 + 14)^3

y = 16^3

y = 4096

If you really do mean what it says, then

y = 2 + 14^3

y = 2744 + 2

y = 2746

Answer:

q = - 5 , q = \(\frac{7}{5}\)

Step-by-step explanation:

5q² + 18q = 35 ( subtract 35 from both sides )

5q² + 18q - 35 = 0 ← in standard form

consider the factors of the product of the coefficient of the q² term and the constant term which sum to give the coefficient of the q- term

product = 5 × - 35 = - 175 and sum = + 18

the factors are + 25 and - 7

use these factors to split the q- term

5q² + 25q - 7q - 35 = 0 ( factor the first/second and third/fourth terms )

5q(q + 5) - 7(q + 5) = 0 ← factor out (q + 5) from each term

(q + 5)(5q - 7) = 0 ← in factored form

equate each factor to zero and solve for q

q + 5 = 0 ( subtract 5 from both sides )

q = - 5

5q - 7 = 0 ( add 7 to both sides )

5q = 7 ( divide both sides by 5 )

q = \(\frac{7}{5}\)

solutions are q = - 5 , q = \(\frac{7}{5}\)

The most precise classification of BCDE is a rhombus.

To determine the most precise classification of BCDE, we need to determine its properties, such as parallel sides, congruent sides, and right angles.

First, let's find the lengths of sides AB and CD:

AB = √((6-(-1))² + (-2-(-1))²) = √((7²) + (1²)) = √(49 + 1) = √50

CD = √((5-(6))² + (-9-(-2))²) = √((-1²) + (7²)) = √(1 + 49) = √50

Next, let's find the lengths of sides BC and AD:

BC = √((6-(-1))² + (-2-(-9))²) = √((7²) + (7²)) = √(49 + 49) = √98

AD = √((5-(-2))² + (-9-(-1))²) = √((7²) + (8²)) = √(49 + 64) = √113

Since AB and CD are equal, we can conclude that BCDE is a parallelogram.

To determine if BCDE is a rectangle, rhombus, or square, we need to determine if it has right angles. If a parallelogram has right angles, then it is either a rectangle or a square.

To determine if BCDE has right angles, we can use the fact that the diagonals of a parallelogram bisect each other. So if the diagonals of a parallelogram are equal in length, then it is a rhombus. And if the diagonals of a parallelogram are equal in length and the parallelogram has right angles, then it is a square.

Let's find the lengths of the diagonals BD and AC:

BD = √((5-(-1))² + (-9-(-1))²) = √((6²) + (8²)) = √(36 + 64) = √100

AC = √((6-(-2))² + (-2-(-8))²) = √((8²) + (6²)) = √(64 + 36) = √100

Since the diagonals BD and AC are equal in length, BCDE is a rhombus.

So, the most precise classification of BCDE is a rhombus.

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An equation of a line AC with the given coordinates is 3x+11y+34=0.

The point slope form is used to find the equation of the straight line which is inclined at a given angle to the x-axis and passes through a given point.

The equation of the point slope form is: (y - y₁) = m(x - x₁)

where, (x, y) is a random point on the line and m is the slope of the line.

Given that, ΔABC with the coordinates A(-4, -2), B(4, 4), and C(18, -8).

Here, the slope of AC is A(-4, -2) and C(18, -8)

So slope m=(-8+2)/(18+4)

m= -6/22

m= -3/11

Substitute m=-3/11 and (x₁, y₁)=A(-4, -2) in (y - y₁) = m(x - x₁), we get

(y+2)=-3/11 (x+4)

11y+22=-3x-12

3x+11y+34=0

Therefore, an equation of a line AC with the given coordinates is 3x+11y+34=0.

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Answer:

6

Step-by-step explanation:

add all of them divided by how many numbers there are

Step-by-step explanation:

mean=sum of numbers/no.of numbers

=12+8+6+3+1+6/6

=6

mean=6

The amount that you would tip someone if the total cost of the meal is 13.40$ is: $2.01.

In the United States, the standard tip for good service is 15%. So, assuming that the meal service offered could be classified as a good service, we can say that 15% of  13.40$ will be the tip to provide.

15% of  13.40$ is equal to  $2.01.

Therefore, the amount that the person who received the service is expected to pay is  $2.01. Also, note that the tip for delayed service is 10% and the tip for excellent service is 20%. Bad service requires no tip.

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x^2+y^2-12x+6y+36=0

Top Point: (6,0)

Left Point: (3,-3)

Right Point: (9,-3)

Bottom Point: (6,-6)

Answer:

\( x^2 +y^2 -12x +6y +36 =0\)

And we can complete the squares like this:

\( (x^2 -12x +6^2) + (y^2 +6y +3^2) = -36 +6^2 +3^2\)

And we got:

\( (x-6)^2 + (y+3)^2 = 9\)

And we have a circle with radius r =3 and the vertex would be;

\( V= (6,-3) \)

The graph is on the figure attached.

Step-by-step explanation:

For this case we have the following expression:

\( x^2 +y^2 -12x +6y +36 =0\)

And we can complete the squares like this:

\( (x^2 -12x +6^2) + (y^2 +6y +3^2) = -36 +6^2 +3^2\)

And we got:

\( (x-6)^2 + (y+3)^2 = 9\)

And we have a circle with radius r =3 and the vertex would be;

\( V= (6,-3) \)

The graph is on the figure attached.

Step-by-step explanation:

To solve one step equations you have to do the opposite of whatever operation is being performed on the variable so you have to get the variable by itself

The most important thing to remember is that whatever you do to one side of the equation, you have to do the same thing to the other side.

Answer:

58.03 ft

Step-by-step explanation:

To solve for the total circumference of circle F, we can create a ratio of section angle measure to circumference. We know that these two attributes of a circle have a linear relationship because the formula for arc length (\(S = 2\pi r \cdot \frac{\theta}{360\°}\)) relies proportionately on the radius and angle measure of the section.

angle measure : circumference

               290°   :   46.75 ft

We can multiply this ratio by \(\frac{360}{290}\) to get the corresponding circumference for a 360° section (which is the entire circle).

\(\frac{360}{290}(290\° : 46.75 \text{ ft})\)

\(= 360\° : \boxed{58.03 \text{ ft}}\)

Therefore, the circumference of circle F is approximately 58.03 ft.

According to the equation we have After simplifying, the equation in spherical coordinates is: 5ρ^2 - 3ρ sin(θ) cos(φ) = 0 .

To write the given equation in spherical coordinates, we first need to express x, y, and z in terms of rho (ρ), theta (θ), and phi (φ), which are the spherical coordinates.

We know that:

x = ρsinφcosθ
y = ρsinφsinθ
z = ρcosφ

Substituting these values in the given equation, we get:

5(ρsinφcosθ)² - 3(ρsinφcosθ) + 5(ρsinφsinθ)² + 5(ρcosφ)² = 0

Simplifying further, we get:

5ρ²sin²φcos²θ + 5ρ²sin²φsin²θ + 5ρ²cos²φ - 3ρsinφcosθ = 0

Now, we can use the trigonometric identities:

sin²θ + cos²θ = 1
sin²φ + cos²φ = 1

Substituting these in the equation, we get:

5ρ²sin²φ + 5ρ²cos²φ - 3ρsinφcosθ = 0

To rewrite the given equation 5x^2 - 3x + 5y^2 + 5z^2 = 0 in spherical coordinates, we need to use the conversions:

x = ρ sin(θ) cos(φ)
y = ρ sin(θ) sin(φ)
z = ρ cos(θ)

Substitute these conversions into the equation:

5(ρ sin(θ) cos(φ))^2 - 3(ρ sin(θ) cos(φ)) + 5(ρ sin(θ) sin(φ))^2 + 5(ρ cos(θ))^2 = 0

After simplifying, the equation in spherical coordinates is:

5ρ^2 - 3ρ sin(θ) cos(φ) = 0

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Answer:

810!

Hope this helped! Have a nice day!!

Answer:

30% of 2,700 is 810

Step-by-step explanation:

proportions

0.30×2,700

810

The x and y components of the total force exerted on this charge by the other two charges are 3.72 × 10⁻⁶ N and 8.87 × 10⁻⁶ N respectively. The magnitude of this force is 9.64 × 10⁻⁶ N. The direction of this force is 66.02° below the +x-axis.

The formula to calculate electric force is:

Electric force = (k*q1*q2)/r²

Where,k = Coulomb's constant = 9 × 10⁹ Nm²/C²

q1, q2 = Charges in Coulombs

r = Distance in meters

(a) The third charge q3 at (3.10, 3.95) experiences the force from q1 and q2.

Let's calculate the distance of q3 from q1 and q2.

Distance from q1 to q3 is = sqrt( (3.10-0)² + (3.95-0)² ) = 4.38 cm = 0.0438 m

Distance from q2 to q3 is = sqrt( (3.10-0)² + (3.95-3.95)² ) = 3.10 cm = 0.0310 m

Magnitude of electric force due to q1 = k*q1*q3/r1²Here, q1 = -3.20 nC and q3 = 5.00 nC

Thus, the electric force due to q1 = (9 × 10⁹) * (-3.20 × 10⁻⁹) * (5.00 × 10⁻⁹) / (0.0438)² = - 9.38 × 10⁻⁶ N ….. (i)

Here, r1 is the distance from q1 to q3.

Distance from q2 to q3 is = 3.10 cm = 0.0310 m.

Magnitude of electric force due to q2 = k*q2*q3/r2²Here, q2 = 1.60 nC and q3 = 5.00 nC

Thus, the electric force due to q2 = (9 × 10⁹) * (1.60 × 10⁻⁹) * (5.00 × 10⁻⁹) / (0.0310)² = 8.87 × 10⁻⁶ N ….. (ii)

Here, r2 is the distance from q2 to q3.

Total force in the x direction on q3 is: Fx = F1x + F2xFx = -F1 cos(θ1) + F2 cos(θ2)

Here, θ1 is the angle between r1 and the x-axis and θ2 is the angle between r2 and the x-axis

Let's calculate the angle θ1

tanθ1 = (3.95 - 0) / 3.10θ1 = tan⁻¹(3.95/3.10) = 51.04°

And the angle θ2

tanθ2 = (3.95 - 0) / 0θ2 = 90°

Now, the force in the x direction on q3:

Fx = - F1 cos(θ1) + F2 cos(θ2) = -(-9.38 × 10⁻⁶) cos(51.04) + 8.87 × 10⁻⁶ cos(90°) = 3.72 × 10⁻⁶ N

Total force in the y direction on q3: Fy = F1y + F2yFy = -F1 sin(θ1) + F2 sin(θ2)

Here, θ1 is the angle between r1 and the y-axis and θ2 is the angle between r2 and the y-axis. Let's calculate the angle θ1

tanθ1 = 0 / 3.10θ1 = tan⁻¹(0/3.10) = 0°

And the angle θ2

tanθ2 = 0 / 0θ2 = 90°

Now, the force in the y direction on q3:

Fy = - F1 sin(θ1) + F2 sin(θ2) = -(-9.38 × 10⁻⁶) sin(0°) + 8.87 × 10⁻⁶ sin(90°) = 8.87 × 10⁻⁶ N

Thus, the x and y components of the total force exerted on this charge by the other two charges are 3.72 × 10⁻⁶ N and 8.87 × 10⁻⁶ N respectively.

(b) The magnitude of this force = √(Fx² + Fy²) = √[(3.72 × 10⁻⁶)² + (8.87 × 10⁻⁶)²] = 9.64 × 10⁻⁶ N

The magnitude of this force is 9.64 × 10⁻⁶ N.

(c) Calculation of the direction of this force.

θ = tan⁻¹(Fy/Fx)θ = tan⁻¹(8.87 × 10⁻⁶ / 3.72 × 10⁻⁶) = 66.02°

The direction of this force is 66.02° below the +x-axis.

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zw in polar form is zw = 24√2(cos(75°) + i*sin(75°)).

z/w in polar form is z/w = (4√2/3)(cos(-15°) + i*sin(-15°)).

1/z in polar form is 1/z = (1/8)(cos(-30°) + i*sin(-30°)).

Now that we have z and w in polar form, we can find the polar forms for the products and reciprocal of these complex numbers.

Product (zw): To multiply two complex numbers in polar form, we multiply their magnitudes and add their arguments. Applying this to z and w, we have: zw = 8(cos(30°) + isin(30°)) * 3√2(cos(45°) + isin(45°))

Multiplying the magnitudes: |zw| = 8 * 3√2 = 24√2

Adding the arguments: θzw = 30° + 45° = 75 degrees

Therefore, zw in polar form is zw = 24√2(cos(75°) + i*sin(75°)).

Division (z/w): To divide two complex numbers in polar form, we divide their magnitudes and subtract their arguments. Applying this to z and w, we have: z/w = 8(cos(30°) + isin(30°)) / 3√2(cos(45°) + isin(45°))

Dividing the magnitudes: |z/w| = 8 / (3√2) = 8 / 3√2 = 8 / (3 * √(2)) = (8 / 3) * (1 / √(2)) = (8 / 3) * (√(2) / 2) = (4√2) / 3

Subtracting the arguments: θz/w = 30° - 45° = -15 degrees

Thus, z/w in polar form is z/w = (4√2/3)(cos(-15°) + i*sin(-15°)).

Reciprocal (1/z): To find the reciprocal of a complex number in polar form, we take the reciprocal of its magnitude and negate its argument. Applying this to z, we have: 1/z = 1 / [8(cos(30°) + i*sin(30°))]

Taking the reciprocal of the magnitude: |1/z| = 1 / 8 = 1/8

Negating the argument: θ1/z = -30°

Hence the 1/z in polar form is 1/z = (1/8)(cos(-30°) + i*sin(-30°)).

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Answer:

The answer is 36.

Step-by-step explanation:

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First, divide 108 by 12.

The result is 9.

Now square root 9.

The result is 3.

Now, multiply 12 by 3.

The result is 36.

To check that this is the pattern, we multiply 36 by 3, and we indeed see that 3 times 36 is equal to 108.

*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^*^

#teamtrees #WAP (Water And Plant)

Answer:

cosθ = \(\frac{5}{13}\)

Step-by-step explanation:

This is a 5- 12- 13 right triangle then

cosθ = \(\frac{adjacent}{hypotenuse}\) = \(\frac{5}{13}\)

Answer: the answer is 10

Step-by-step explanation: used a caculator

The rotation matrices must have their signs switched from positive to negative in order to retain the same definition of a positive rotation in a left-handed system.

In a left-handed system, the rotation matrices must be changed to their negative counterparts in order to retain the same definition of a positive rotation. This means that the matrices must have their signs switched from positive to negative. For example, in the 3D rotation matrix, the elements of the matrix must be changed from (1, 0, 0; 0, cosθ, -sinθ; 0, sinθ, cosθ) to (1, 0, 0; 0, -cosθ, sinθ; 0, -sinθ, -cosθ). This is done to ensure that the rotations in the left-handed system are in the opposite direction than the rotations in the right-handed system. This change will retain the same definition of a positive rotation, but the direction of the rotation will be inverted.

The rotation matrices must have their signs switched from positive to negative in order to retain the same definition of a positive rotation in a left-handed system.

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The slope of the line passing through the points (7,-6) and (7,6) is undefined.

The slope of a line is the steepness of the line. It is represented as a ratio of the vertical change between two points on the line to the horizontal change between the same points. The slope of the line passing through the points (7,-6) and (7,6) can be found using the slope formula.Slope formula: Slope (m) = (y₂ - y₁) / (x₂ - x₁)Given points: (7,-6) and (7,6)Substituting the values in the slope formula, we get:Slope (m) = (y₂ - y₁) / (x₂ - x₁)Slope (m) = (6 - (-6)) / (7 - 7)Slope (m) = 12 / 0Since the denominator of the slope formula is zero, we cannot divide by zero. Therefore, the slope of the line passing through the points (7,-6) and (7,6) is undefined.An undefined slope indicates that the line is vertical. This means that the line is parallel to the y-axis and has no horizontal change. The slope of a vertical line is always undefined.

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Answer: n=7

Step-by-step explanation:

First distribute the numbers to get 5n+10=3+6n

Next Subtract 6n from both sides to get -n=10=3

Finally divide both sides my -1 to get rid of the -n to get n=7

Hope this helps :)

The 50th term is 290.

It is a sequence where there is a common difference between each consecutive term.

Example:

12, 14, 16, 18, 20 is an arithmetic sequence.

We have,

-4, 2, 8, 14,

This is an arithmetic sequence.

First term = a = - 4

Common difference.

d = 2 - (-4) = 6

d = 8 - 2 = 6

Now,

The nth term = a + (n -1)d

So,

n = 50

a = -4

d = 6

50th term.

= -4 + (50 - 1) 6

= - 4 + 49 x 6

= - 4 + 294

= 290

Thus,

The 50th term is 290.

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The complete question:

What is the 50th term of the sequence that begins −4, 2, 8, 14, ...?

Answer: 12,000 lbs is equal to 6 tons

Answer:

If a scatter plot shows a linear association, then there is a line that describes the relationship between the two measured quantities reasonably well. This means that there is a clear pattern in the data, and that the data points tend to follow a straight line when plotted on a graph. This does not necessarily mean that there is a line that passes through all of the plotted data points or that there is a tendency for relatively high values for one measured quantity to be paired with relatively high values for the other measured quantity.

Step-by-step explanation:

Answer:

A scatter plot shows a linear association.

Step-by-step explanation:

Answer:

Answer:

It's a (space) lot,... haha na I just kidding,... you're good,... I mean I'm not kidding cause it is correct,... but you are good,... like totally cool,... anyway,...

Step-by-step explanation:

By x the just mean what number,... so,...

what number + 6 = 7,

6 + what number = 7,

2 + what number + 5 = 7,

1 + what number = 7,

what number + 4 + what number = 7,

So that is what it mean,... hope it helps, alot LOL,... and,... Chow

To calculate the reliability of the bank loan processing system with backup components, we can use the concept of series-parallel system reliability.

In the original system, the three components are connected in series. To calculate the overall reliability of the system, we multiply the reliabilities of the individual components:

R_system = R_1 * R_2 * R_3 = 0.82 * 0.991 * 0.98 ≈ 0.801

So, the reliability of the bank loan processing system without backup components is approximately 0.801.

Now, if each of the three components has a backup with a reliability of 0.80, we have a parallel configuration between the original components and their backups. In a parallel system, the overall reliability is calculated as 1 minus the product of the complement of individual reliabilities.

Let's calculate the reliability of each component with the backup:

R_1_with_backup = 1 - (1 - R_1) * (1 - 0.80) = 1 - (1 - 0.82) * (1 - 0.80) ≈ 0.984

R_2_with_backup = 1 - (1 - R_2) * (1 - 0.80) = 1 - (1 - 0.991) * (1 - 0.80) ≈ 0.9988

R_3_with_backup = 1 - (1 - R_3) * (1 - 0.80) = 1 - (1 - 0.98) * (1 - 0.80) ≈ 0.9992

Now, we calculate the overall reliability of the system with the backups:

R_system_with_backup = R_1_with_backup * R_2_with_backup * R_3_with_backup ≈ 0.984 * 0.9988 * 0.9992 ≈ 0.981

Therefore, the reliability of the bank loan processing system with backup components is approximately 0.981.

Comparing the two scenarios, we can see that introducing backup components with a reliability of 0.80 has improved the overall reliability of the system. The total reliability increased from 0.801 (without backups) to 0.981 (with backups). Having backup components in a parallel configuration provides redundancy and increases the system's ability to withstand failures, resulting in higher reliability.

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Answer:

cos 0° = 1, because the cosine and sine are complements

Step-by-step explanation:

Here is the formula: sin 0 = cos (90°- 0) or cos 0 = sin (90°- 0)

So it would be: cos 0° = sin (90° - 0°) = sin 90° = 1