How do I solve a Pythagorean triangle of 7 squared + 2 squared and then the number after what would it be when u square root it

Answer:

one

Step-by-step explanation:

y=1

hope this helps

Answer:

one

Step-by-step explanation:

Solution:

The cost of the Camera is $540

The sales tax is 7.2%

To find the tax charge, the formula is

Substitute into the formula above

Hence, the tax charged is $38.88.

The total cost of the Camera will be

Hence, the total cost of the Camera is $578.88

Answer:

Step-by-step explanation:

Plug in 5 for h

6(5)+7(5)

30+35=65

65

Answer:

\( \sf \: 6h + 7h = 65\)

Step-by-step explanation:

Given information,

→ 6h + 7h

→ h = 5

Now the final value will be,

→ 6h + 7h

→ 6(5) + 7(5)

→ 30 + 35

→ 65 => final value

Hence, the answer is 65.

Main Answer:The linear combination of v = (13/14)u1 + (2/7)u2 + (47/14)u3  

Supporting Question and Answer:

How can we express a vector as a linear combination of  vectors using a system of equations?

To express a vector as a linear combination of  vectors using a system of equations, we need to find the coefficients that multiply each given vector to obtain the desired vector. This can be done by setting up a system of equations, where each equation corresponds to the components of the vectors involved.

Body of the Solution:

(a) To show that the vectors u1 = (2, 0, 3), u2 = (-3, 0, 2), and u3 = (0, 7, 0) form an orthogonal basis for R^3, we need to demonstrate two conditions: orthogonality and linear independence.

u1 · u2 = (2)(-3) + (0)(0) + (3)(2) = -6 + 0 + 6 = 0

u1 · u3 = (2)(0) + (0)(7) + (3)(0) = 0 + 0 + 0 = 0

u2 · u3 = (-3)(0) + (0)(7) + (2)(0) = 0 + 0 + 0 = 0

Since the dot product of every pair of vectors is zero, they are orthogonal.

   2.Linear Independence: We need to show that the vectors u1, u2, and u3 are linearly independent, meaning that no vector can be written as a linear combination of the other vectors.

We can determine linear independence by forming a matrix with the vectors as its columns and performing row operations to check if the matrix can be reduced to the identity matrix.

[A | I] = [u1 | u2 | u3 | I] =

[2 -3 0 | 1 0 0]

[0 0 7 | 0 1 0]

[3 2 0 | 0 0 1]

Performing row operations:

R3 - (3/2)R1 -> R3

R1 <-> R2

[1 0 0 | -3/2 1 0]

[0 1 0 | 0 1 0]

[0 0 7 | 0 0 1]

Since we can obtain the identity matrix on the left side, the vectors u1, u2, and u3 are linearly independent.

Therefore, the vectors u1 = (2, 0, 3), u2 = (-3, 0, 2), and u3 = (0, 7, 0) form an orthogonal basis for R^3.

(b) To write v = (1, 2, 3) as a linear combination of u1, u2, and u3, we need to find the coefficients x, y, and z such that:

v = xu1 + yu2 + z*u3

Substituting the given vectors and coefficients:

(1, 2, 3) = x(2, 0, 3) + y(-3, 0, 2) + z(0, 7, 0)

Simplifying the equation component-wise:

1 = 2x - 3y

2 = 7y

3 = 3x + 2y

From the second equation, we can solve for y:

y = 2/7

Substituting y into the first equation:

1 = 2x - 3(2/7)

1 = 2x - 6/7

7 = 14x - 6

14x = 13

x = 13/14

Substituting the found values of x and y into the third equation

3 = 3(13/14) + 2(2/7)

3 = 39/14 + 4/7

3 = 39/14 + 8/14

3 = 47/14

Therefore, we have determined the values of x, y, and z as follows:

x = 13/14

y = 2/7

z = 47/14

Thus, we can write the vector v = (1, 2, 3) as a linear combination of u1 = (2, 0, 3), u2 = (-3, 0, 2), and u3 = (0, 7, 0) as:

v = (13/14)u1 + (2/7)u2 + (47/14)u3

Therefore, v can be expressed as a linear combination of the given vectors.

Final Answer:Therefore,the linear combination of v = (13/14)u1 + (2/7)u2 + (47/14)u3  

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The linear combination of v = (13/14)u1 + (2/7)u2 + (47/14)u3  

To express a vector as a linear combination of  vectors using a system of equations, we need to find the coefficients that multiply each given vector to obtain the desired vector. This can be done by setting up a system of equations, where each equation corresponds to the components of the vectors involved.

Body of the Solution:

(a) To show that the vectors u1 = (2, 0, 3), u2 = (-3, 0, 2), and u3 = (0, 7, 0) form an orthogonal basis for R^3, we need to demonstrate two conditions: orthogonality and linear independence.

Orthogonality: We need to show that each pair of vectors is orthogonal, meaning their dot product is zero.

u1 · u2 = (2)(-3) + (0)(0) + (3)(2) = -6 + 0 + 6 = 0

u1 · u3 = (2)(0) + (0)(7) + (3)(0) = 0 + 0 + 0 = 0

u2 · u3 = (-3)(0) + (0)(7) + (2)(0) = 0 + 0 + 0 = 0

Since the dot product of every pair of vectors is zero, they are orthogonal.

  2.Linear Independence: We need to show that the vectors u1, u2, and u3 are linearly independent, meaning that no vector can be written as a linear combination of the other vectors.

We can determine linear independence by forming a matrix with the vectors as its columns and performing row operations to check if the matrix can be reduced to the identity matrix.

[A | I] = [u1 | u2 | u3 | I] =

[2 -3 0 | 1 0 0]

[0 0 7 | 0 1 0]

[3 2 0 | 0 0 1]

Performing row operations:

R3 - (3/2)R1 -> R3

R1 <-> R2

[1 0 0 | -3/2 1 0]

[0 1 0 | 0 1 0]

[0 0 7 | 0 0 1]

Since we can obtain the identity matrix on the left side, the vectors u1, u2, and u3 are linearly independent.

Therefore, the vectors u1 = (2, 0, 3), u2 = (-3, 0, 2), and u3 = (0, 7, 0) form an orthogonal basis for R^3.

(b) To write v = (1, 2, 3) as a linear combination of u1, u2, and u3, we need to find the coefficients x, y, and z such that:

v = xu1 + yu2 + z*u3

Substituting the given vectors and coefficients:

(1, 2, 3) = x(2, 0, 3) + y(-3, 0, 2) + z(0, 7, 0)

Simplifying the equation component-wise:

1 = 2x - 3y

2 = 7y

3 = 3x + 2y

From the second equation, we can solve for y:

y = 2/7

Substituting y into the first equation:

1 = 2x - 3(2/7)

1 = 2x - 6/7

7 = 14x - 6

14x = 13

x = 13/14

Substituting the found values of x and y into the third equation

3 = 3(13/14) + 2(2/7)

3 = 39/14 + 4/7

3 = 39/14 + 8/14

3 = 47/14

Therefore, we have determined the values of x, y, and z as follows:

x = 13/14

y = 2/7

z = 47/14

Thus, we can write the vector v = (1, 2, 3) as a linear combination of u1 = (2, 0, 3), u2 = (-3, 0, 2), and u3 = (0, 7, 0) as:

v = (13/14)u1 + (2/7)u2 + (47/14)u3

Therefore, v can be expressed as a linear combination of the given vectors.

Therefore, the linear combination of v = (13/14)u1 + (2/7)u2 + (47/14)u3  

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To use logarithmic differentiation to find the derivative of y = 3√x(x −2) / x^2, we first take the natural logarithm of both sides:

ln(y) = ln(3√x(x −2) / x^2)

Then we use the logarithmic differentiation rule, which states that if y = f(x) is a function of x, then

y' / y = (ln(f(x)))'

Using this rule, we can find the derivative of ln(y) and simplify it:

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

ln(y)' = 0 + (1/2)(1/(x(x-2)))(2x-2) - 2*(1/x)

ln(y)' = (x-1)/(x(x-2))

Now we can find y' by multiplying both sides of the original equation by y and substituting in the expression we just found for ln(y)':

y = 3√x(x −2) / x^2

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

y' / y = (x-1)/(x(x-2))

y' = y*(x-1)/(x(x-2))

Substituting the original expression for y, we have:

y' = (3√x(x −2) / x^2)*((x-1)/(x(x-2)))

Therefore, the derivative of y = 3√x(x −2) / x^2 is y' = (3√x(x −2) / x^2)*((x-1)/(x(x-2))).

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Answer:

C. 4/27

Step-by-step explanation:

Let's use the multiplication rule of probability to calculate the probability that both balls drawn are white:

P(white ball from Bag 1) = 2/6 = 1/3

P(white ball from Bag 2) = 4/9

Therefore, the probability of drawing a white ball from each bag is:

P(white from Bag 1 and white from Bag 2) = P(white from Bag 1) * P(white from Bag 2)

= (1/3) * (4/9)

= 4/27

So, the answer is C. The probability that both balls are white is 4/27.

Answer:

To figure out your average, you add them together then divide by2

Step-by-step explanation:

After calculating and analyzing the given question, the bank officer should be inclined to take a sample of at least 133 under the condition of within $200 (MOE) of the actual average with 99% confidence.

In the event of determining the size sample needed for understanding average total monthly deposits by implementing the formula

n = (z x Σ / E)²

here,

n = sample size,

z = z-score involving  the desired level of confidence,

Σ = population standard deviation,

E = margin of error

Staging the values in the formula

n = (2.576 * 1000 / 200)² = 132.71

≈ 133

After calculating and analyzing the given question, the bank officer should be inclined to take a sample of at least 133 under the condition of within $200 (MOE) of the actual average with 99% confidence.

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Answer:

.125

Step-by-step explanation:

Answer:

Im guessing the X is supposed to be multiplication.

-0.10416

Exact Form = -5/48

Step-by-step explanation:

Answer:

y=-7x-2

Step-by-step explanation:

I assume you need the equation for the line, so that's what I'm solving for here.

1. Start by putting the slope and the coordinates into point slope form, which is y-y1=m(x-x1)

y+30=-7(x-4)

2. Distribute -7 to (x-4) (or multiply x and -4 by -7).

y+30=-7x+28

3. Subtract 30 from both sides to get y by itself.

y=-7x-2

Answer: 23 kg

Step-by-step explanation:

Let's begin by using algebra to solve the problem.

Let x be the number of kilograms of salmon the fish-shop owner bought at the market.

We know that the total cost of the salmon was $400, so we can write:

400 = x * c

where c is the cost per kilogram of salmon.

We also know that all except for 2 kg of the fish were sold at a price per kg that was $10 more than what the owner paid at the market. So the price per kilogram of salmon at the fish shop was c + 10.

The total revenue from the sale of the fish was $540, so we can write:

540 = (x - 2) * (c + 10)

Now we can use these two equations to solve for x.

First, we can use the first equation to solve for c:

c = 400 / x

Then we can substitute this expression for c into the second equation:

540 = (x - 2) * (400/x + 10)

Simplifying this equation:

540 = 4000/x + 10x - 20 - 80/x

Multiplying both sides by x:

540x = 4000 + 10x^2 - 20x - 80

10x^2 - 20x - 4600 = 0

Dividing both sides by 10:

x^2 - 2x - 460 = 0

We can solve for x using the quadratic formula:

x = [2 ± sqrt(4 + 4*460)] / 2

x = [2 ± 44] / 2

Discarding the negative solution, we get:

x = (2 + 44) / 2

x = 23

Therefore, the fish-shop owner bought 23 kilograms of salmon at the market.

Using a trigonometric identity, since in the first quadrant and in the third quadrant the sine and the cosine have the same sign, \(\sin{2\theta}\) is always positive.

It is given by:

\(\sin{2\theta} = 2\sin{\theta}\cos{\theta}\)

In the first quadrant(0° < θ < 90°) and in the third(180° < θ < 270°), the sine and the cosine have the same sign, hence the multiplication is positive and \(\sin{2\theta}\) is always positive.

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Answer:

Side length = 5 root 2

perimeter is (5 root 2)*3

Step-by-step explanation:

Use pythagoras

a^2 = b^2 + c^2

a^2 = 5 root 2

(5 root 2)^2 = (c^2)/2 + c^2

75 = (c^2)/2 + c^2

150 = c^2 + 2c^2

150 = 3c^2

50=c^2

root of 50 = 5 root 2

as it is equiliateral triangle all sides are the same

Answer:

Side: 10

Perimeter: 30

Step-by-step explanation:

An equilateral triangle has a height of 5√3. What is the length of each side in the equilateral triangle? What is the perimeter of the equilateral triangle?

In triangles with angles with 30°, 60°, and 90°, the hypotenuse (the angle opposite to the 90° angle) is twice as long as the base, and the height is √3 times as long as the base. To make it easier, this is a list of the sides:

x = base

√3 * x = height

2x = hypotenuse.

Look at the drawing I have attached below

If AD is the base of the triangle ADC, then CD, the height is √3 times AD. If we set AD as x, CD = √3*x = 5√3

√3*x = 5√3

Divide both sides by √3.

x = 5

Then, because altitudes in equilateral triangles bisect the base (CD cuts AB in half), then AB = 10.

The sides in equilateral triangles are equal, so each side is 10.

Then, the perimeter must be 30.

I hope this helps! Feel free to ask any questions!

Answer:

between 9 and 10. it is closer to 10

Answer:

b / 3

Step-by-step explanation:

2br = 2r * b

6r = 2r * 3

A = 2br ÷ 6r

  = ( 2r * b ) / ( 2r * 3 )

A = b / 3

Answer:

edge lines

Step-by-step explanation:

To draw the image of quadrilateral ABCD under a translation by 1 unit to the right and 4 units up, we will move each point of the quadrilateral in the specified direction.

Let's assume the coordinates of the original quadrilateral ABCD are as follows:

A(x₁, y₁), B(x₂, y₂), C(x₃, y₃), D(x₄, y₄)

To perform the translation, we will add the given values to the x-coordinates and y-coordinates of each point:

A'(x₁ + 1, y₁ + 4), B'(x₂ + 1, y₂ + 4), C'(x₃ + 1, y₃ + 4), D'(x₄ + 1, y₄ + 4)

Now, plot the original quadrilateral ABCD and then move each point to its corresponding new position.

For example, if point A had coordinates (2, 3), after the translation, it will move to (2 + 1, 3 + 4) = (3, 7). Similarly, you can calculate the new coordinates for points B, C, and D using the same process.

Once you have the new coordinates for each point, connect them to form the image of the quadrilateral ABCD under the translation.

The new quadrilateral A'B'C'D' will be a shifted version of the original quadrilateral, 1 unit to the right and 4 units up.

It's important to note that the scale and proportions of the quadrilateral will remain the same after the translation. Only its position in the coordinate plane will change.

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The best statistical method to use for studying the relationship between the income of people living in a neighborhood and the number of sales made at the franchise company's store in that neighborhood would be regression analysis.

Regression analysis would be the best statistical method to use in this situation.

It would help to determine the relationship between the income of people living in a neighborhood and the number of sales made at the franchise company's store in that neighborhood.

The regression analysis would provide a model that would help to predict the expected number of sales based on the income levels of the neighborhood.

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Answer:it is 9 because you subtract 6 from the 8 and then you add 2 and 7 to get 9

Step-by-step explanation:

The correct option C.4 square root 13 units; is the obtained perimeter of the rhombus WXYZ.

The congruence of the sides is one of the characteristics of rhombuses.

As a result, we only need to use the distance formula to get the length with one side.

Using the distance formula, find one side as;

d = √(x₂ - x₁)² + (y₂ - y₁)²

The distance at line YZ is:

YZ = √(5 - 3)² + (5 - 2)²

YZ = √13

Perimeter = 4 x (length of one side)

Perimeter =  4 √13

Thus, the obtained perimeter of the rhombus WXYZ is 4√13 units.

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The correct question is-

What is the perimeter of rhombus wxyz?

A.square root 13 units

B.12 units

C.4 square root 13 units

D.20 units

Answer:

the answer is equal to 90%of 11.3921 which is 1.25313= 1.253

Answer:

$3.43

Step-by-step explanation:

Cost per pound means how much you are paying for one pound of the item. In this question it says a pound of cheese costs 3.43, therefore each pound of cheese costs 3.43. We can also use the equation 3.43x where x represents the amount of pounds you are purchasing. Just multiply the two and you will get a cost for any amount (pounds) of cheese.

Answer: In mathematics, the method of equating the coefficients is a way of solving a functional equation of two expressions such as polynomials for a number of unknown parameters. It relies on the fact that two expressions are identical precisely when corresponding coefficients are equal for each different type of term.

.

Answer:

Angles 2 and 7 are opposite exterior angles.

Step-by-step explanation:

Angles 2 and 7 are on the outside so they are exterior,  They are also on the opposite sides of the transversal so they are opposite.

Angles 2 and 7 are opposite exterior angles.

The value of b = -3/2 and c = -5/4

To write the quadratic x² - 3x + 1 in the form (x + b)² + c, we can expand (x + b)² and compare it to the given expression:

(x + b)² = x² + 2bx + b²

Comparing this to the given expression x² - 3x + 1, we see that we need:

2bx = -3x, so b = -3/2

b² + c = 1, so substituting b = -3/2 gives:

(9/4) + c = 1

so c = 1 - 9/4

= 4/4 - 9/4

= -5/4

The quadratic x² - 3x + 1 can be written in the form (x - 3/2)² + ( - 5/4).

Therefore, the value of b = -3/2 and c = -5/4

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Given question is incomplete, the complete question is below

the quadratic x²-3x + 1 can be written in the form (x +b)² + c, where b and c are constants. what is b, c?

Answer:

d. 20

Step-by-step explanation:

28 ÷ (100%+40%)

= 28 ÷ 140%

= 28 ÷ 1.4 = 20

Answer:

option d

Step-by-step explanation:

Let the number be x

40% of x = 0.40x

Increased by 40% = 28

That is ,

           x + 0.40x = 28

               1.40x = 28

                   \(x = \frac{28}{1.40}\\\)

                  \(x = \frac{28 \times 100}{1.40 \times 100 } = \frac{28 \times 100}{140} =\frac{4 \times 100}{20} = 4 \times 5 = 20\)

Therefore, the number is 20

Answer:

it's 1

Step-by-step explanation:

when one is multiplied by three times.it gives us three and its difference result negative five 3–8 = -5