Use the fact that the vector product is distributive over addition to show that (a - b) x (a + b) = 2(axb) By considering the definition of a Xb prove that k(a X b) = (ka) × b = ax (kb). 7 If a, b and c form the triangle shown, prove that axb=bXc=cXa [Hint: consider the obvious relation between a, b and c then construct suitable vector products.]

Answer:

9/35.............,..........

Answer:

1/5

Step-by-step explanation:

2/5 - 1/7 = ???

find the least common denominator!

45 would be the least common demoninator!

so...

2 (7) / 5(7) - 1 (5) / 7 (5) = ?

14/ 45 - 5 /45 = ?

14 - 5 = 9

9/45. Simplify!

9/45 divide 9 from both sides

9/9 /  45/9

= 1/5, one fifths is your answer!

Symmetric cryptography algorithm uses a single shared key for both encryption and decryption, such as the Advanced Encryption Standard (AES). Asymmetric cryptography uses a pair of public and private keys for encryption and decryption, such as the RSA algorithm.

For secure communication between 10 users:

a. Asymmetric cryptography requires 10 public keys and 10 private keys.

b. Symmetric cryptography requires 45 keys (10 users choose a common shared key for each pair of communication).

Symmetric cryptography algorithm:

It is a cryptography algorithm that uses the same key for both encryption and decryption. The sender and receiver share a common secret key, and the sender encrypts the message with this key. The recipient decrypts the message using the same key. Symmetric algorithms have high speed and are used to encrypt data, but key distribution is difficult.

Advanced Encryption Standard (AES) is an example of a symmetric cryptography algorithm.

Asymmetric cryptography algorithm:

Asymmetric cryptography algorithm, also known as public-key cryptography, uses two keys: a public key and a private key. The sender encrypts the message using the recipient's public key, and the recipient decrypts the message using his or her private key. As a result, only the recipient has the private key and can read the message.

RSA (Rivest-Shamir-Adleman) is an example of an asymmetric cryptography algorithm.

For secure communication between ten users:

a. In asymmetric cryptography: It requires ten public and ten private keys. Each user needs to have one public key and ten private keys. When one user wants to send a message to another, they use the recipient's public key to encrypt the message and send it to the recipient. The recipient will then use his or her private key to decrypt the message.

b. In symmetric cryptography: In symmetric cryptography, each user will need to share a common secret key with the other nine users.

In total, there will be 45 keys (10*(10-1)/2) required for secure communication between ten users using a symmetric cryptography algorithm.

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Answer:

The discriminant equates to 0. (the expression underneath the square root sign will equal 0) This means that the curve will not cross the x-axis in two places.

Answer:

b²-4ac=0

Step-by-step explanation:

where

b²-4ac <0 it has no solution

b²-4ac >0 it has two solution

The value of the mean will always change by changing the value of one score.

Mean:

The sum of all values divided by the total number of values determines the mean (also known as the arithmetic mean, which differs from the geometric mean) of a dataset. The term "average" is frequently used to describe this measure of central tendency.

The mean can be calculated in two steps:

Add up all of the data set's values.

By the total number of values, divide this number.

With a test data set, we'll go over these procedures.

The value of the mean will always change by changing the value of one score.

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Answer:

67 degrees

Step-by-step explanation:

the shape is a tryangle so it will have the same angle measurements, just make sure you look if it has the slash next to the letter or not in the future

Hope this helps girly!!

Answer:

\(\angle{C}=54\)

Step-by-step explanation:

Let's first start by establishing that when it comes to a reflection, side lengths and angle measurements remain the same. With that being said, let's identify our angle measurements:

\(\angle{A=}\\\angle{B}= 67\\\angle{C}=\\\angle{A'}=59\\\angle{B'}=\\\angle{C'}=\\\)

As mentioned earlier, angle measurements will remain the same, so we can go ahead and identify the values of \(\angle{A}\) & \(\angle{B'}\)

\(\angle{A=59}\\\angle{B}= 67\\\angle{C}=\\\angle{A'}=59\\\angle{B'}=67\\\angle{C'}=\\\)

The sum of the angles in a triangle will always be equal to 180°.

Add the two identified angles of the original figure.

\(59+67=126\)

Subtract the sum from 180:

\(180-126=54\)

Therefore:

\(\angle{C}=54\)

_

Check your work by adding the three identified angle measurements to see if they measure to 180°:

\(59+67+54\)

\(=180\)

The answer is correct!

Answer:

The solution for the system of right triangles are, respectively: \(a = 2\sqrt{6}\), \(b = 4\sqrt{3}\), \(c = 4\sqrt{6}\), \(d = 6\sqrt{2}\)

Step-by-step explanation:

By Geometry, we get the following equivalencies:

\(a = 2\sqrt{6}\) (45 - 45 - 90 Theorem)

\(b = \sqrt{2}\cdot (2\sqrt{6})\) (45 - 45 - 90 Theorem)

\(b = 4\sqrt{3}\)

\(c = \frac{2\sqrt{6}}{\frac{1}{2} }\) (30 - 60 - 90 Theorem)

\(c = 4\sqrt{6}\)

\(d = \frac{2\sqrt{6}}{\frac{\sqrt{3}}{3} }\) (30 - 60 - 90 Theorem)

\(d = 6\sqrt{2}\)

Jamie's annual interest rate is 5%.

To find Jamie's annual interest rate, we need to consider the relationship between the quarterly interest payments and the loan amount. Let's break it down step by step:

1. We know that Jamie's quarterly interest payments are $150. Since there are four quarters in a year, the total annual interest payments can be calculated by multiplying the quarterly payments by four: $150 * 4 = $600.

2. Now, let's determine the interest rate. We have the annual interest payment, but we need to express it as a percentage of the loan amount. The formula to calculate interest rate is (Interest Payment / Loan Amount)  100.

3. Substituting the values into the formula, we have ($600 / $12,000)

100 = 0.05  100 = 5%.

Therefore, Jamie's annual interest rate is 5%.

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The expression in terms of logs of x, y, and z is:
(3/2) log (z) - (1/2) log (x) - (1/2) log (y)

The expression to be written in terms of logs of x, y, and z is:
(xyz)^3/2 / (xy)^2
To simplify this expression, we can use the properties of logarithms:
logb (xy) = logb (x) + logb (y)
logb (x^a) = a logb (x)
logb (x/y) = logb (x) - logb (y)
First, let's write the numerator and denominator separately:
Numerator: (xyz)^3/2
= (x^3/2 y^3/2 z^3/2)
= x^3/2 * y^3/2 * z^3/2
Denominator: (xy)^2
= x^2 * y^2
Now, we can rewrite the expression using the properties of logs:
logb [(x^3/2 * y^3/2 * z^3/2) / (x^2 * y^2)]
= logb (x^3/2) + logb (y^3/2) + logb (z^3/2) - 2 logb (x) - 2 logb (y)
Finally, we can simplify the expression:
logb [(x^3/2 * y^3/2 * z^3/2) / (x^2 * y^2)]
= (3/2) logb (x) + (3/2) logb (y) + (3/2) logb (z) - 2 logb (x) - 2 logb (y)
= (3/2) logb (z) - (1/2) logb (x) - (1/2) logb (y)
Therefore, the expression in terms of logs of x, y, and z is:
(3/2) log (z) - (1/2) log (x) - (1/2) log (y)

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The given mathematical expression is evaluated for the input values (2, 4). The result of the expression is calculated using various operations such as addition, multiplication, square root, natural logarithm, minimum, maximum, and function composition.

The expression f(x1, x2) involves several mathematical operations. Let's evaluate each part of the expression step by step:

1. The first term is 421 + 222, which equals 643.

2. The second term is 3x² + 213. Plugging in x1 = 2 and x2 = 4, we get 3(2)² + 213 = 3(4) + 213 = 12 + 213 = 225.

3. The third term is 5x11². Substituting x1 = 2 and x2 = 4, we have 5(2)(11)² = 5(2)(121) = 1210.

4. The fourth term is (√₁+√₂)². Replacing x1 = 2 and x2 = 4, we obtain (√2 + √4)² = (1 + 2)² = 3² = 9.

5. The fifth term is 10ln(₁). Plugging in x1 = 2, we have 10ln(2) = 10 * 0.69314718 ≈ 6.9314718.

6. The sixth term is (x₁+x₂)(x² + x3). Substituting x1 = 2 and x2 = 4, we get (2 + 4)(2² + 4³) = 6(4 + 64) = 6(68) = 408.

7. The seventh term is min(3r1, 10√2). As we don't have the value of r1, we cannot determine the minimum between 3r1 and 10√2.

8. The eighth term is max{5x1,2r2}. Since we don't know the value of r2, we cannot find the maximum between 5x1 and 2r2.

9. Finally, we have MP1(x1, x2), MP2(X1, X2), and TRS(x1, x2), which are not defined or given.

Considering the given expression, the evaluated terms for the input values (2, 4) are as follows:

- 421 + 222 = 643

- 3x² + 213 = 225

- 5x11² = 1210

- (√₁+√₂)² = 9

- 10ln(₁) ≈ 6.9314718

- (x₁+x₂)(x² + x3) = 408

The terms involving min() and max() cannot be calculated without knowing the values of r1 and r2, respectively. Additionally, MP1(x1, x2), MP2(X1, X2), and TRS(x1, x2) are not defined.

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Answer:

Step-by-step explanation:

I think its A

Answer:

23

Step-by-step explanation:

The percentage increase of the number of seats is A = 33.3 %

A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, %

The difference between an exact value and an approximation to it is the approximation error in a data value. Either an absolute error or a relative error might be used to describe this error.

Percentage change is the difference between the measured value and the true value , as a percentage of the true value

Percentage change =( (| Measured Value - True Value |) / True Value ) x 100

Given data ,

Let the percentage increase in the number of seats be A

And , the total number of initial seats = 117 seats

The increased number of seats = 156 seats

Percentage change =( (| Measured Value - True Value |) / True Value ) x 100

On simplifying , we get

Percentage change P = [ ( 156 - 117 ) / 117 ] x 100

Percentage change P = ( 39/117 ) x 100

Percentage change P = 0.333 x 100

Percentage change P = 33.3 %

Hence , the percentage increase is 33.3 %

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Answer:

Step-by-step explanation:

The five-number summary is:

Minimum: 9

First Quartile: 16.5

Median: 25.5

Third Quartile: 39

Maximum: 51

3. Range = 42

4. Interquartile range = 22.5

Given the data for the lengths as, 36, 15, 9, 22, 36, 14, 42, 45, 51, 29, 18, 20, to find the five-number summary of the data set, we would follow the steps below:

1. The numbers in ordered from the smallest to the largest would be:

9, 14, 15, 18, 20, 22, 29, 36, 36, 42, 45, 51

2. The five-number summary for the lengths in minutes would be:

3. Range of the data = max - min = 51 - 9 = 42

4. The interquartile range for the data set = Q3 - Q1 = 39 - 16.5

Interquartile range for the data set = 22.5

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The coordinate of the centroid of the given triangle will be at (-2.33,5).

A triangle is a 3-sided shape that is occasionally referred to as a triangle. There are three sides and three angles in every triangle, some of which may be the same.

The given triangle with vertices has been drawn.

The midpoint of H( – 6, 3) and F(1, 5) will be as,

x = (-6 + 1)/2 = -2.5

y = (3 + 5)/2 = 4 so D(-2.5,4)

The coordinate of the centroid will intersect 2:1 of the median from the vertex side.

Thus by intercept formula,

x = (2 × -2.5 + 1 × -2)/(2 + 1) and y = (2 × 4 + 1 × 7)/(2 + 1)

x = -2.33 and y = 5

So the coordinate of vertices will be (-2.33,5).

Hence "The specified triangle's centroid's coordinate will be at (-2.33,5)".

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Solving by factoring in steps shown below

Answer:

\(\textsf{1. \quad $x=1, \quad x=-\dfrac{2}{5}$}\)

\(\textsf{2. \quad $x=1, \quad x=3$}\)

Step-by-step explanation:

Solving quadratic equations by factoring

Given equation:

\(5x^2=3x+2\)

Subtract (3x + 2) from both sides:

\(\implies 5x^2-(3x+2)=3x+2-(3x+2)\)

\(\implies 5x^2-3x-2=0\)

Find two numbers that multiply to \(ac\) and sum to \(b\), and rewrite \(b\) as the sum of these two numbers:

\(\implies ac=5 \cdot -2=-10\)

\(\implies b=-3\)

Therefore, the two numbers are -5 and 2.

Rewrite \(b\) as the sum of the two numbers:

\(\implies 5x^2-5x+2x-2=0\)

Factor the first two terms and the last two terms separately:

\(\implies 5x(x-1)+2(x-1)=0\)

Factor out the common term (x - 1):

\(\implies (5x+2)(x-1)=0\)

Apply the zero-product property:

\(\implies 5x+2=0 \implies x=-\dfrac{2}{5}\)

\(\implies x-1=0 \implies x=1\)

Therefore, the solutions are:

\(\boxed{x=1, \quad x=-\dfrac{2}{5}}\)

Given equation:

\(\implies x^2-4x+3=0\)

Find two numbers that multiply to \(ac\) and sum to \(b\), and rewrite \(b\) as the sum of these two numbers:

\(\implies ac=1 \cdot 3=3\)

\(\implies b=-4\)

Therefore, the two numbers are -3 and -1.

Rewrite \(b\) as the sum of the two numbers:

\(\implies x^2-3x-x+3=0\)

Factor the first two terms and the last two terms separately:

\(\implies x(x-3)-1(x-3)=0\)

Factor out the common term (x - 3):

\(\implies (x-1)(x-3)=0\)

Apply the zero-product property:

\(\implies x-1=0 \implies x=1\)

\(\implies x-3=0 \implies x=3\)

Therefore, the solutions are:

\(\boxed{x=1, \quad x=3}\)

Answer:

I would say the last one

Step-by-step explanation:

Answer:

42/45

Step-by-step explanation:

Answer:

w

Step-by-step explanation:

The amount of water they need to bring depends on how long they will be hiking.

divide 799 by 9 then multiply by 10 equals 887.7

Type I error (also called a false positive) occurs when a null hypothesis is rejected when it is actually true. The probability of committing a Type I error is denoted by the symbol alpha (α), and is typically set at a certain level (e.g., 0.05 or 0.01) depending on the significance level desired for the hypothesis test.

Type II error (also called a false negative) occurs when a null hypothesis is not rejected when it is actually false. The probability of committing a Type II error is denoted by the symbol beta (β). The power of a statistical test is equal to 1 minus the probability of a Type II error (i.e., power = 1 - β).

Therefore, the statement that is true regarding the probability of Type I and Type II errors is that they are complementary to each other. That is, as the probability of a Type I error decreases (by setting a lower significance level), the probability of a Type II error generally increases (i.e., the power of the test decreases). Conversely, as the probability of a Type II error decreases (by increasing the sample size or effect size), the probability of a Type I error generally increases. It is important to strike a balance between controlling these two types of errors, depending on the specific goals and context of the research or hypothesis test.

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The benefit value of the widget on the books of abc is $8

The given parameters are:

Cost price = $5 cash

Selling price = $8 account

The benefit value of the widget is the same as their selling price on account

Hence, the benefit value of the widget is $8

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The measure of ∠POX  = 160°  The length of XOA = 16.95 mm ,We know that PM¯, PN¯, and PO¯ are angle bisectors of triangle MNO, so they divide the opposite sides in two equal parts. Let x = MY, y = NY, and z = OY. Then, we have:

MX / NO = MY / NY (by the angle bisector theorem)

MX / (MX + XO) = x / (x + y)

MX(x + y) = x(MX + XO)

MXy = XOx

NO / OX = NY / OY (by the angle bisector theorem)

(OX + XO) / OX = y / z

1 + XO/OX = y/z

XO/OX = (z - y)/y

Now, we can use these equations to solve the problem:

To find PX¯, we need to find MX. Using the angle sum property of triangles, we have:

m∠M = 180 - m∠MON = 140°

m∠PMX = m∠M/2 = 70°

m∠PMO = m∠MON/2 = 20°

m∠XMO = m∠PMX + m∠PMO = 70° + 20° = 90°

Therefore, PX¯ is the altitude from M to XO¯, so we have:

tan(30°) = PX / MX

MX = PX / tan(30°)

= 23 / √(3)

= 13.31 mm

To find m∠PMX, we can use the fact that PM¯ is an angle bisector:

m∠PMX = m∠M + m∠PMO

= 140° + 20°

= 160°

To find m∠POX, we can use the fact that PO¯ is an angle bisector:

m∠POX = m∠O + m∠PNO

= 180° - m∠MON + m∠PNO

= 180° - 40° + 20°

= 160°

To find XO¯, we need to find y and z. Using the fact that PX¯ is an angle bisector, we have:

PY / OY = PM / OM

23 / z = 52 / (x + y + z)

y + z = 52z / 23

z = 23y / (52 - 23)

Using the equation XO/OX = (z - y)/y, we have:

XOA / 52 = (23y / (52 - 23) - y) / x

XOA= 52 * 23y / ((52 - 23) * x - 23y)

Substituting MX = 23/√(3) - PX = 23/√(3) - 13.31, we get:

y = NO * PY / (PM + PN + PO) = 56.17 mm

z = OY + PY = 79.17 mm

XOA = 16.95 mm

Therefore, the answers are:

Length of PX¯: 13.31 mm

Measure of ∠PMX: 160°

Measure of ∠PO

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Answer:

Step-by-step explanation:

Equation:

-3k = 108

We need to separate -3 from k. So we must do the inverse operation.

Divide both sides by -3

k = -36

Hope this helps :)

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Answer:

here to help!

Step-by-step explanation:

The final solution is: y(x) = x + v(x) = x + 1/w(x) or y(x) = x +. 5x c − x5 . 4. Solve the following differential equations. (a) xy′ = √x2 + y2;. (b)

The measure of the value of 'x' from the expression is 8.8712

The given image is a triangle with the following parameters:

Opposite = 8

Hypotenuse = x

acute angle = 46 degrees

Required

The measure of the angle 'x'

Applying the rule of trigonometry

sin theta = opposite/hypotenuse

sin 46 = 8/x

x = 8/sin46

x = 8.8713

Hence the value of x from then given triangle is 8.8712

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Answer:

10

Step-by-step explanation:

200\20 you divide 200 over 20

Answer:

200 kilometers and used 20 liters/100km and 40litre = fuel price $1.30 Journey cost $52.00

Step-by-step explanation:

Step-by-step explanation:

4m =16

divide both sides by 4

m = 4

he has 4 model trains

Answer:

4

Step-by-step explanation:

Shown using number line and simple math