Consider the two-node circuit shown below:


The node voltages V₁ and V₂ (in volts) satisfy the following system of equations:

15V₁ = 7V₂ + 60

3V₂ + 10 = 3V₁

a) Write the system of equations in the matrix form AV-B, where V = [V1, V2]

b) Find V₁ and V₂ using the matrix algebra method. Perform all matrix computations and show all steps.

Answer: option (a) and option (e).

Step-by-step explanation:

Answer:

(a) and (e) are correct

Step-by-step explanation:

(a) x² + (y - 3)² = 6²

(b) x² + (y - 5)² = (√6)²

(c) (x - 4)² + y² = 6²

(d) (x + 6)² + y² = 12²

(e) x² + (y + 8)² = 6²

The general equation of a circle is:

(x - a)² + (y - b)² = r², where (a, b) represents the x-y coordinates of the centre, and r represents the radius.

Hence, by process of elimination, the options that have a diameter of 12 units and therefore, a radius of 6 units, are (a), (c), and (e).

Therefore, the correct choices are (a), and (e), as (c) has a circle centre of (4,0) and does not lie on the y-axis.

The formula for the surface area of a triangular prism is

Surface Area(SA) = (b*h) + [(a+b+c) * l]

Where, b = length of the base of the triangular face,

             h = height of the triangular face,

             a, b, c = length of the three sides of the triangular face           respectively, and

             l = length of the rectangular face.

Here, b = 7.2 cm, a = 7.1 cm, c = 7.1 cm, h = 6.9 cm and l = 7.3 cm

Therefore, SA = (7.2*6.9) + [(7.1 + 7.2 + 7.1) * 7.3]

                        = 49.68 + (21.4*7.3)

                        = 49.68 + 156.22

                        = 205.9 cm² (Answer)

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Answer:

The surface area is 720 in^2

In still air, the jet's speed is 1030 mph, while the wind's speed 240 miles per hour.

It is the rate of change of an object's position with regard to time and a frame of reference. Although it may appear difficult, velocity is essentially speeding in a particular direction. Due to the fact that it is a vector quantity, velocity must be defined in terms of both magnitude (speed) and direction. It has a metre per second SI unit (ms-1).

The distance travelled in relation to the time it took to travel that distance is how speed is defined. As speed simply has a direction and no magnitude, it is a scalar quantity.

Jet's velocity against wind is 2370/3=790 mile per hour and flying with wind it is 10160/8= 1270 miles per hour.

According to question,

Let the velocity of jet in still air be x miles per hour and velocity of wind be y miles per hour.

As such its velocity against wind is x−y and with wind is x+y and therefore

x−y=790 and x+y=1270

Adding the two 2x= 2060 and x=1030

and y=240

Hence velocity of jet in still air is 1030 miles per hour and velocity of wind is 240 miles per hour.

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Answer: To solve the problem, we can use the formula for exponential decay:

N(t) = N0 * (1/2)^(t/T)

where:

N(t) is the amount of the radioactive element at time t

N0 is the initial amount of the radioactive element

t is the time that has elapsed

T is the half-life of the radioactive element

Let's assume that the initial amount of carbon-14 in the bones was N0. After the bones were discovered, they had lost 60.1% of their carbon-14, which means that only 39.9% of the original carbon-14 remained. Therefore, we can write:

N(t) = 0.399 * N0

We want to find the time t that has elapsed since the mastodon died. We can rearrange the formula for exponential decay to solve for t:

t = T * log( N(t) / N0 ) / log(1/2)

Substituting the given values, we get:

t = 5750 * log( 0.399 ) / log(1/2)

Using a calculator, we find that t is approximately 16060 years. Therefore, the bones were approximately 16060 years old at the time they were discovered.

Step-by-step explanation:

Using division we know that per pound the loose sweets have a better value which is £0.0089 per pound.

The division is one of the four basic arithmetic operations or the process by which two numbers are added together to produce a new number.

Multiplication, addition, and subtraction make up the remaining operations.

We may examine the quotient and the division's remainder using the division formula Dividend = (Divisor Quotient) + Remainder.

We can multiply our quotient by the divisor to check its accuracy if the remainder is 0.

If the product and dividend are equal, the quotient is correct.

So, the price per gram when pre-packed:

1.49/120 = £0.012

Now, the price per gram when the product is loose:

0.89/100 = £0.0089

Now, we know that per pound the loose sweets are better.

Therefore, using division we know that per pound the loose sweets have a better value which is £0.0089 per pound.

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On the x-axis use a scale of 2 units for each grid square. on the y-axis use a scale of 10 units of each grid square. The x-coordinates range from -5 to 5. y-coordinates range from -40 to 50.

In mathematics, points and functions are represented and graphed on the coordinate plane, commonly known as the Cartesian plane. The x-axis and y-axis are two perpendicular number lines that meet at the origin to form the plane (0,0).

On the coordinate plane, points are denoted by ordered pairs (x, y), where x denotes the point's separation from the y-axis and y denotes its separation from the x-axis.

For the given coordinates the range of x and y coordinates are:

x-coordinates range from -5 to 5

y-coordinates range from -40 to 50.

Thus, we use a scale of 2 on the x-axis and 10 units on the y axis.

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Answer:

b)

Step-by-step explanation:

The value of

m∠GHJ = (3(20°)+50)° = 110°.

m∠GkJ = (4(20°)-10)° = 70°

m∠HJK = (4(20°))° = 80°

What is an angle?

An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. We refer to these as dihedral angles.

Here, we have

Given: Circle B is shown, with GHJK inscribed in the circle. The m∠GHJ = (3x+50)°, and m∠HJK = (4x)° and mLGK] = (4x-10)°.

we have to find the value of HJK and JHG.

We know that

m∠GHJ + m∠GkJ = 180°

(3x+50)° + (4x-10)° = 180°

7x + 40 = 180°

7x = 140°

x = 20°

Hence, the value of

m∠GHJ = (3(20°)+50)° = 110°.

m∠GkJ = (4(20°)-10)° = 70°

m∠HJK = (4(20°))° = 80°

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Answer: Where is the picture?

Step-by-step explanation:

The  surface area of the figure is 456.2 units²,

The area of the square base is:

base area = w² = (10 units)² = 100 units²

The lateral area is 4 times the area of one rectangular face:

lateral area = 4wx = 4(10 units)(5 units) = 200 units²

The area of one triangular face is half the product of its base length (w) and its slant height (h). The latter is found using the Pythagorean theorem:

h² = y² +(w/2)² = (6 units)² +((10 units)/2)² = 61 units²

h = √61 units

So, the area of 4 triangles is ...

area of triangular faces = 4(1/2)wh = 2(10 units)(√61 units) ≈ 156.2 units²

Now we have the areas of the parts, so we can add them together to get the total surface area:

surface area = base area + lateral area + area of triangular faces

= 100 units² + 200 units² + 156.2 units²

therefore,  surface area = 456.2 units²

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Answer:

40%

Step-by-step explanation:

We Know

You have a bag with 4 red marbles, 3 green marbles, 2 blue marbles, and 1 purple marble.

4 + 3 + 2 + 1 = 10 marbles total

What is the probability of drawing a red marble out of the bag?

We Take

(4 ÷ 10) x 100 = 40%

So, 40% of drawing a red marble out of the bag.

Answer:

C

Step-by-step explanation:

+) L = 3W + 6

+) L×W = (3W + 6)×W = 3W² + 6W ≤ 250

Answer:

Likely

Step-by-step explanation:

Answer:

Step-by-step explanation:

a lot (90,000) (i think)

The coordinates of the vertices of the image is A'(0, -3), B'(3, -2), C'(1, -1). The correct option is B.

Triangle ABC is rotated 180 degrees clockwise about the origin and then reflected across the line y=-x.

We are to find the coordinates of the vertices of the image.

We know that

if a point (x, y) is rotated 180 degrees clockwise, then its co-ordinate changes as follows :

(a, b)   ⇒    (-a, -b).

So, after getting rotated 180 degrees clockwise, the coordinates of the vertices of triangle ABC becomes

A(-3, 0)   ⇒  (3, 0)

B(-2, 3)   ⇒   (2, -3)

C(-1, 1)    ⇒   (1, -1).

Therefore, the correct option is B. A'(0, -3), B'(3, -2), C'(1, -1).

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The volume of the rectangular prism is (867/20) cubic inches.

A volume is just the amount of space taken up by any three-dimensional solid. A cube, a cuboid, a cone, a cylinder, or a sphere are examples of solids. Volumes differ depending on the shape.

To find the volume of a rectangular prism, we need to multiply its length, width, and height. In this case, the length is 10 1/5 inches, the width is 4 1/4 inches, and the height is 2 inches. We can convert the mixed numbers to improper fractions and then multiply:

length = 10 1/5 inches = (51/5) inches

width = 4 1/4 inches = (17/4) inches

height = 2 inches

Volume = length x width x height

= (51/5) inches x (17/4) inches x 2 inches

= (867/20) cubic inches

Therefore, the volume of the rectangular prism is (867/20) cubic inches.

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Answer:

yes it is pretty hard but I believe I. you

we can replace the second occurrence of x = -2 with x = 1:

What is function?

In mathematics, a function is a relationship between two sets of elements, called the domain and the range, such that each element in the domain is associated with a unique element in the range.

For the table to be a function, each x-value must correspond to a unique y-value. To determine the missing x-value, we need to find if there are any repeated x-values with different y-values.

The x-value 3 is paired with y-values -3 and -1, which means that the table is not a function. Therefore, we need to replace one of the x-values that appears twice with a different value.

Since x = 0 is already paired with y = 5, we cannot use 0 as the replacement. The only other x-value that appears more than once is x = -2. Therefore, we can replace one of the occurrences of x = -2 with a different value.

For example, we can replace the second occurrence of x = -2 with x = 1:

x    y

3   -3

1    4

-2  -1

-2  -2

0    5

Now each x-value corresponds to a unique y-value, so the table represents a function.

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the correct answers are 1.159, 4.038, and 5.819 radians. Which is found according to the given question

How to solve the question?

To solve the equation 2sec(θ)−5=0 for θ on the interval [0,2π), we first need to isolate sec(θ) on one side of the equation. We can do this by adding 5 to both sides, which gives us:

2sec(θ) = 5

Next, we divide both sides by 2:

sec(θ) = 5/2

Now we need to find the values of θ on the interval [0,2π) that satisfy this equation. Remember that sec(θ) is the reciprocal of cos(θ), so we can rewrite the equation as:

1/cos(θ) = 5/2

Multiplying both sides by cos(θ), we get:

1 = (5/2)cos(θ)

Dividing both sides by (5/2), we get:

2/5 = cos(θ)

Taking the inverse cosine of both sides, we get:

θ = cos⁻¹(2/5)

Using a calculator, we find that. cos⁻¹(2/5) approximately 1.159 radians. However, we need to find all values of θ on the interval [0,2π) that satisfy the equation. Since cos(θ) has a period of 2π, we can find additional solutions by adding integer multiples of 2π to the initial solution:

θ = 1.159 + 2πn, where n is an integer.

Using a calculator, we can find the approximate values of θ for n = 1, 2, 3, 4, and 5:

θ = 4.038, 5.819, 7.500, 9.282, and 11.063 radians.

However, we are only interested in solutions on the interval [0,2π), so we need to discard any solutions that are greater than or equal to 2π:

θ = 1.159, 4.038, and 5.819 radians.

Therefore, the correct answers are 1.159, 4.038, and 5.819 radians.

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This is false, which means that the region below the line does not satisfy the inequality. So,we should shade the region above the line.

A linear inequality is a mathematical statement that compares two expressions using one of the inequality symbols: < (less than), > (greater than), ≤ (less than or equal to), or ≥ (greater than or equal to).

One can write a linear inequality in one variable as ax + b  c, ax + b > c, ax + b  c, or ax + b  c.

The linear inequality given is:

m = 1/4, b = -2

To graph this inequality, we first need to plot the line with equation y = mx + b, where m = 1/4 and b = -2.

y = 1/4 x - 2

We can plot this line by finding two points on it. One way to do this is to set x to two different values and solve for y. For example, when x = 0, y = -2, and when x = 4, y = -1.

Next, we need to shade the region above or below the line to show all possible solutions.

We can determine which region to shade by choosing a test point that is not on the line and substituting its coordinates into the inequality

For example, the point (0,0) is not on the line, so we can substitute its coordinates into the inequality:

y < 1/4 x - 2

0 < 1/4 (0) - 2

0 < -2

Emma's mistake could be that she shaded the region below the line instead of above it. To do the problem correctly, we should shade the region above the line, as explained above.

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The solution of the quadratic equation is option C {-3, 2}.

Numerous techniques, such as factoring, completing the square, and the quadratic formula, can be used to solve quadratic equations. The values of x that make a quadratic equation true are represented by the solutions to the equation, which are known as its roots or zeros.

In several disciplines, including physics, engineering, economics, and finance, quadratic equations are frequently employed to simulate real-world occurrences. They can be used to depict a variety of phenomena, including a projectile's motion, an electrical circuit's behaviour, a satellite's trajectory, the cost of production, and many more.

The solutions of the quadratic equation are the x-intercepts of the graph. That is the point at which the graph, crosses the x-axis.

For the given graph the x-intercepts are {-3, 2}.

Hence, the solution of the quadratic equation is option C {-3, 2}.

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Answer:

A) $2510

B) $209.17

C) $128,273.36

Step-by-step explanation:

Let's break this problem down into three parts:

a) To find out how much will be saved each year, we first need to calculate the annual salary and then determine 10% of it. Since the newscaster earns $25,100, we can calculate the annual savings as follows:

Annual savings = Annual salary * 10%

Annual savings = $25,100 * 0.1

Annual savings = $2,510

So, the newscaster will save $2,510 each year.

b) To find the monthly deposit, we need to divide the annual savings by the number of months in a year:

Monthly deposit = Annual savings / 12

Monthly deposit = $2,510 / 12

Monthly deposit ≈ $209.17

The newscaster will deposit approximately $209.17 per month into the retirement account.

c) To find the amount in the account after 29 years, we will use the formula for the future value of an ordinary annuity, since the investment has a monthly deposit and a monthly compounding interest rate:

FV = P * [(1 + r)^nt - 1] / r

Where FV is the future value, P is the monthly deposit, r is the monthly interest rate (annual interest rate divided by 12), n is the number of times interest is compounded per year (monthly, so 12), and t is the number of years.

In this case, P = $209.17, r = 4.1%/12, n = 12, and t = 29 years.

First, convert the annual interest rate to a decimal and then find the monthly interest rate:

Monthly interest rate = (4.1%/12) / 100

Monthly interest rate = (0.041/12)

Now, plug the values into the formula:

FV = $209.17 * [(1 + 0.041/12)^(12*29) - 1] / (0.041/12)

Calculate the future value:

FV ≈ $209.17 * [(1.003417)^(348) - 1] / (0.003417)

FV ≈ $209.17 * (3.42307) / (0.003417)

FV ≈ $128,273.36

After 29 years, the newscaster will have approximately $128,273.36 in the retirement account.

Jackson's total cost after the discount and before tax would be $24.67.

When a store offers a discount, it reduces the price of the item by a certain percentage. In this case, Jackson has a loyalty card that gives him a 10% discount on his purchase.

To calculate the price after the discount, we multiply the original price by 1 minus the discount percentage (in decimal form).

Here we have

Jackson has a 10% discount at his local hardware store.

Let 'x' be the cost before tax

After a 10% discount,

The amount that Jackson could pay 90% of the cost

Given that he wants to buy $ 27.40  

The cost of items after discount = 90% of 27.40

= [ 90/100 ] × 27.40

= [ 0.9 ] × 27.40

= 24.66

Therefore,

Jackson's total cost after the discount and before tax would be $24.67.

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Answer:

y=9 (3x/9-2) + 18=3x

Step-by-step explanation:

a) The lateral area of a rectangular prism is 360 square units. b) The total area of a rectangular prism is 6 square units. c) The volume of is 1200 cubic units.

A prism is a three-dimensional solid consisting of two bases that are parallel and congruent and are joined by a series of parallelograms. A prism's lateral faces are all parallelograms or rectangles. On the other hand, a pyramid is a three-dimensional solid with a polygonal base and an apex. A pyramid's lateral faces are triangles that converge at the top. The perpendicular distance between the bases of a prism determines its height, whereas the distance between the apex and base of a pyramid determines its height.

a) The lateral area of a rectangular prism is given by 2h(l+w):

Substituting the values we have:

2(6)(20+10) = 360 square units

b) The total area of a rectangular prism is given by 2lw + 2lh + 2wh:

Substituting the values we have:

2(20)(10) + 2(20)(6) + 2(10)(6) = 520 square units.

c) Volume is given as V = lwh substituting the values we have:

(20)(10)(6) = 1200 cubic units.

For Cube:

a) The lateral area is give as 4s(s)

Substituting the values:

LA = 4(1)(1) = 4

b) The total area is given as 6(s)(s):

Substituting the values:

TSA = 6(1)(1) = 6 square units.

c) The volume is given as s^3:

(1)^3 = 1 cubic unit.

For the triangular prism:

a) The lateral area is given as perimeter of base multiplied by height.

The perimeter of the base is (8 + 6 + 10) = 24, and h = 8.

LA = (24)(8) = 192 square units.

b) The total area is given by area of base + the lateral area:

Area of the base triangle is:

A = 1/2(6)(8) = 24

For two triangles at the base we have: 2(24) 48

Thus, total area of the prism is 176 + 48 = 224 square cm.

c) The volume of the triangular prism is given as:

1/2(base x height) x length = 1/2(6)(8)(8) = 192 cubic cm.

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Answer:

Tyshawn would have to sell 6 computers on a given day to get paid $225

Step-by-step explanation:

We can use the information in the table to find the equation of the linear relationship between a (the number of computer sales) and p (Tyshawn's total pay):p = 75 + 25aThis equation tells us that Tyshawn's total pay is $75 plus $25 for each computer he sells.To find out how many computers Tyshawn would have to sell in order to get paid $225 on a given day, we can substitute p = 225 into the equation and solve for a:225 = 75 + 25a150 = 25aa = 6

Answer:

Step-by-step explanation:

You want the initial mass, and the mass after 7 weeks, of a sample of Palladium-100 with a half-life of 4 days and a mass of 2 mg after 16 days.

The amount of Palladium-100 remaining after t days can be modeled by ...

  a(t) = (initial amount)·(1/2)^(t/(half-life period))

  a(t) = a0·(1/2)^(t/4) . . . . . . where t is in days, and a0 is the initial amount

Using this model to find a0, we have ...

  a(16) = 2 mg = a0·(1/2)^(16/4) = a0/16

  a0 = 32 mg . . . . . . multiply by 16

The initial mass of the sample is 32 mg.

The mass after 7 weeks (49 days) will be ...

  a(49) = (32 mg)·(1/2)^(49/4) ≈ 0.0065698 mg

The mass after 7 weeks is about 6.57 µg or 0.00657 mg.

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The percentage of females with brown eyes as follows is 25%.

Percentage is a way of expressing a number as a fraction of 100. It is represented by the symbol "%". The word "percent" means "per hundred".

Let's assume that the total population of Math town is 100 people for the sake of simplicity. Then, we can use the following information to create a table:

Population Males Females

Total         60         40

Brown eyes 18         ?

From the table, we can see that 60% of the population are males, so there are 60 x 0.3 = 18 males with brown eyes.

We also know that the total population with brown eyes is 28%, so there are 100 x 0.28 = 28 people with brown eyes. Therefore, there must be 28 - 18 = 10 females with brown eyes.

Finally, we can calculate the percentage of females with brown eyes as follows:

% of females with brown eyes = (10 / 40) x 100% = 25%

Therefore, the answer is (C) 25%.

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x = -3 is the vertical asymptote of the function.

A vertical asymptote of a function is a vertical line on the graph where the function approaches positive or negative infinity as the input (x-value) approaches a certain value.

To identify the vertical asymptote(s) of the rational function f(x) = (x + 4)/(2x + 6), we need to look for the values of x that make the denominator equal to zero.

So, we solve the equation 2x + 6 = 0 for x:

2x = -6

x = -3

Therefore, x = -3 is the vertical asymptote of the function.

The other answer choices (B) x = -4 and (C) y = 1/2 are not correct as they do not make the denominator of the function equal to zero. And (D) is also not correct as this function has a vertical asymptote at x = -3.

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