a glass has a radius of 3. a rectangular tray dimensions are 36 by 24. how many glasses can fit on the tray
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If the length of a rectangular garden is twice its width, and the garden is surrounded by a rectangular concrete walk having a uniform width of 4 feet, and the area of the garden and the walk is 330 square feet, then the dimensions of the garden are 10 feet by 20 feet.

The length of a rectangular garden is twice its width, so if we let the width be x, then the length is 2x. The area of the garden is the length times the width, so it is 2x*x = 2x².Now let's add the width of the walk to the dimensions of the garden, so the width of the garden plus the walk is x + 8, and the length plus the walk is 2x + 8. The area of the garden plus the walk is the length plus the walk times the width plus the walk, so it is (x + 8)(2x + 8).

According to the problem, the area of the garden plus the walk is 330 square feet. We can set up an equation to solve for x:(x + 8)(2x + 8) = 330Simplifying and solving for x, we get:x² + 10x - 29 = 0(x + 13)(x - 3) = 0x = -13 or x = 3Since the width of the garden cannot be negative, we must take x = 3. Then the length of the garden is 2x = 6, and the dimensions of the garden are 3 feet by 6 feet.

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The answers are:

1) The area of a triangle is given by the formula A = (1/2)bh, where b is the base and h is the height. For the given triangles:

Triangle 1: A = (1/2)(2ft)(4ft) = 4 sq ft (for one tablecloth), so for two tablecloths, the total area is 8 sq ft.

Triangle 2: A = (1/2)(6ft)(10ft) = 30 sq ft, so for two tablecloths, the total area is 60 sq ft.

Triangle 3: A = (1/2)(12m)(15m) = 90 sq m, so for two tablecloths, the total area is 180 sq m.

2) The area of a parallelogram is given by the formula A = Bh, where B is the base and h is the height. Rearranging this formula, we get h = A/B. For the given parallelogram:

A = 78 mm2 and B = 13 mm, so h = 78/13 = 6 mm.

3) The area of a rectangle is given by the formula A = LW, where L is the length and W is the width. For Charles' den:

The total wall space to be painted is (2 x 9 x 15) + (2 x 8 x 10) = 342 sq ft. One gallon of paint covers 440 sq ft, so Charles needs (342/440) = 0.7778 gallons of paint. Therefore, he does not have enough paint.

4) To calculate the total area of the walls to be painted, we can calculate the area of each wall and add them together.

The area of the two walls that are 9 ft high and 15 ft long is (9 x 15) = 135 sq ft each, for a total of 270 sq ft. The area of the other two walls that are 8 ft high and 10 ft long is (8 x 10) = 80 sq ft each, for a total of 160 sq ft. Adding them together, we get a total of 430 sq ft.

Since one gallon of paint covers 440 sq ft of wall space, Charles has enough paint to cover the den walls.

5) The area of a trapezoid is given by the formula A = (1/2)(b1 + b2)h, where b1 and b2 are the bases and h is the height. Rearranging this formula, we get h = 2A/(b1 + b2). For the given trapezoids:

A = (1/2)(6ft + 7ft)(10ft) = 65 sq ft and h = 2(65)/(6ft + 7ft) = 5 ft.

A = (1/2)(5yds + 8yds)(4yds) = 26 sq yds and h = 2(26)/(5yds + 8yds) = 2 sq yds.

A = (1/2)(9in + 11in)(13in) = 143.5 sq in and h = 2(143.5)/(9in + 11in) = 13.05 in.

For the application in part (d), we are given A = 32 km2 and (b1 + b2) = 16 km.

Rearranging the formula for A, we get h = 2A/(b1 + b2). Substituting the given values, we get h = 4

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This is actually pretty easy and fast let me explain real quick

Converting Decimals to Percentages if one of the most easiest things In algebra heres how to do it! 100% Would = to the whole number 1 or 100% 0.1 would be 10% 0.4 would be 40% do you get it? Well if you don't get it here's a good thing to remember 0.1 = 10% 0.2 = 20% 0.3 = 30% 0.4 = 40% 0.5 = 50% 0.6 = 60% 0.7 = 70% 0.8 = 80% 0.9 = 90% 1 = 100%

Understand yet? If not I hope you do soon!

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Answer:

awesome thats so cool to know

Answer:

7-12 months.

Step-by-step explanation:

Typically from7-12 months. Hair normally grows at ½in. per month. But hair could also grow as fast as 1in. per month. Certain hair growth genes come from your parents. So depending on how fast your parents hair grow can have an effect on your hair growth/loss.

1. The solution of equation dy/dx + y = e^(-x) is y(x) = -1/2 * e^(-x) + 1/2 * e^(2x)

2. The series  \(\sum n=1[infinity](-1)^n-1/(n(n+1))\) is conditionally convergent

4. The power series expansion of f(x) = e^(2x) * (e^x + 1) is ∑(2^n * x^(2n) / (n!)^2) from n = 0 to infinity

5. The general solution of the differential equation y'' = y' + x is \(y = e^x (x - 1) + C1\)

6. Therefore, \(dx^2/d^2y = (1+t^2)^2 / [-4t^2 + 2]\)

1. First, we will consider the homogeneous equation. Let us assume that the solution is of the form

y = e^mx

Now, differentiating this, we get:

y' = me^mx

Now, the given equation is

dy/dx + y = e^(-x)

So, substituting the value of y = e^mx, we get

me^mx + e^mx = e^(-x)

on simplification, we get me^(2x) + e^x = 1 So

y(x) = e^(mx) - 1/m

which is the solution of the homogeneous equation. Now, we will consider the non-homogeneous part of the equation. We have y(x) = 1 for x = 0. Using the method of variation of parameters, we assume that y = u(x) * v(x). So,

u(x) = exp[(-∫(p(x) dx)]dx   Let p(x) = 1 Therefore,

u(x) = exp[-x]dx = -exp[-x]

Substituting this, we get:

Y = [-exp[-x] * ∫(e^(-x) * e^x dx)] - [∫(e^(-x) * -exp[-x] * e^(-x) dx)]

on simplification, we get

y(x) = -1/2 * e^(-x) + 1/2 * e^(2x)

2. \(\sum n=1[infinity](-1)^n-1/(n(n+1))\)

The series is convergent by Alternating Series Test. The absolute value of each term in the series is

|(-1)^(n-1)/(n(n+1))| = 1/(n(n+1))

Therefore, we can say that the series is conditionally convergent.

4. To expand the function f(x) = e^(2x) * (e^x + 1) into a power series, we can start by expanding e^(2x) and e^x using their respective power series:

e^(2x) = ∑(2^n * x^n / n!) from n = 0 to infinity

e^x = ∑(x^n / n!) from n = 0 to infinity

Multiplying the two power series:

f(x) = e^(2x) * e^x = ∑((2^n * x^n / n!) * (x^n / n!)) from n = 0 to infinity

Simplifying the expression:

f(x) = ∑(2^n * x^n * x^n / (n!)^2) from n = 0 to infinity

f(x) = ∑(2^n * x^(2n) / (n!)^2) from n = 0 to infinity

Therefore, the power series expansion of f(x) = e^(2x) * (e^x + 1) is ∑(2^n * x^(2n) / (n!)^2) from n = 0 to infinity.

5. Given: y'' = y' + x On rearranging, we get: y'' - y' = x This is a first-order linear differential equation. We can solve this using the method of integrating factors, where the integrating factor is given by:

e^-dx/dx - e^-x * y = xe^-x

On multiplying both sides by the integrating factor, we get:

d/dx(ye^-x) = xe^\(e^-dx/dx - e^-x * y = xe^(-x)\)-x

Therefore, \(ye^-x = ∫(x e^(-x) dx) + C_1.\)Therefore, the general solution of the differential equation is:

\(y = e^x (x - 1) + C1\)

6. We have: y = ln(1+t^2)x = t - arctan(t) Differentiating y with respect to x, we get:

dy/dx = [1/(1+t^2)] * [2t/(1+t^2)] - [1/(1+t^2)]

Therefore,

\(d^2y/dx^2 = -2[2t/(1+t^2)]^2 - 2[1/(1+t^2)]^2 + 4t/(1+t^2)^2 = [-4t^2 + 2]/(1+t^2)^2\)

Therefore, \(dx^2/d^2y = (1+t^2)^2 / [-4t^2 + 2]\)

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Answer:

Rhombus.

Step-by-step explanation:

A rhombus is a  quadrilateral, meaning that it has four lateral sides. A Rhombus is a 2-dimensional shape, and has two lines of symmetry.  A Rhombus has a rotational symmetry of order two, and the opposite sides are parallel. Also, the opposite angles in Rhombus are equal. Th diagonals of a Rhombus bisect each other at a right angle.

Other quadrilateral shapes includes the Rectangle, Parallelogram, and the Kite.

The value of function, f(t) for L⁻¹ ( e−s /(s²+ 1)) is equals to sin( t - π ) u(t-π) .

The Laplace transform is the essential term of the given derivative function. Moreover, it comes with a real variable (t) for converting into complex function with variable (s). For ‘t’ ≥ 0, let ‘f(t)’ be given, the Laplace transform of ‘f(t)’, denoted by 'L{f(t)}' or ‘F(s)’ is definable with the equation:

\( L(f(t)) = F(s) = ₀∫^{ \infty } e⁻ˢᵗ f(t)dt\)

we have L⁻¹ ( e−s /(s²+ 1))

Now, L⁻¹ (1 /(s²+ 1)) = sin(t)

so, L⁻¹ ( e−s /(s²+ 1)) = sin( t - π ) u(t-π)

where u(t-π) is unit of step function.

so, required function f(t) is sin( t - π ) u(t-π).

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Complete question:

Find f(t) ℒ−1 (e−s /(s²+ 1))

f(t)=? + (?) (t - ?)

The solution to the expression 4+(−634) is -630

From the question, we have the following parameters that can be used in our computation:

4+(−634)

Rewrite the expression properly

So, we have the following representation

4 + (−634)

Remove the bracket in the above expression

This gives

4 + (−634) = 4 - 634

Evaluate the difference

4 + (−634) = -630

Hence, the solution is -630

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Diane will have the same bank balance amount as Teresa after 171.2 months.

Diane owes amount $39231.00 and Teresa has $4328.00. We can set up two equations using the given information, with Diane's equation representing the decrease in her balance and Teresa's representing the decrease in her balance. Diane's equation is 39231 - 174x = 4328 and Teresa's equation is 4328 - 256x = 4328. We can solve for x in both equations and set them equal to each other to find out how many months it will take for Diane and Teresa to have the same balance. When we solve for x, we get 171.2 months. Therefore, Diane will have the same bank balance as Teresa after 171.2 months, rounded to the nearest tenth.

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Kelli spends 75 minutes studying math over a 5-day period.

Kelli studies for 45 minutes per night, with 1/3 of her time devoted to math.

To find how many minutes she spends on math, multiply 45 minutes by 1/3:

45 * (1/3) = 15 minutes per night.

To determine the total time spent on math in 5 days, multiply 15 minutes by 5:

15 * 5 = 75 minutes.

Based on the calculation, Kelli studies for 5 nights, so she spends 15 minutes x 5 nights = 75 minutes studying math in 5 days.

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Answer:

Step-by-step explanation:

Here is your ratio:

Here is the equivalent ratio:

To make the ratios equivalent, you need to find an equivalent fraction.

Option D is the right choice.

The Gallup poll randomly selected 1000 individuals from Rhode Island (population just over 1,000,000) and 1000 individuals from California (population over 35,000,000). Because both samples have the same sample sizes, it can be assumed that they will be roughly equally accurate.

Taking a poll in the US. The department of Gallup that routinely conducts public opinion polls is called The Gallup Poll. In the form of data-driven news, Gallup Poll findings, analysis, and videos are released every day.

A simple random sample is a subset of people chosen at random from a larger group, all of whom were chosen with the same probability. It is a method of choosing a sample at random. Random sampling makes sure that the findings you get from your sample should be close to what you would have gotten if you measured the complete population.

The Gallup survey randomly selected 1000 individuals from Rhode Island (population just over 1,000,000) and 1000 individuals from California (population over 35,000,000). Because both samples have the same sample sizes, it may be assumed that they will be roughly equally accurate.

Therefore, Option D is correct.

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COMPLETE QUESTION:

A random sample of 1000 people from California (population over 35,000,000) and 1000 people from Rhode Island (population just over 1,000,000) was taken by the Gallup Poll. Which is correct?

a) The sample from California will be more biased because the sampling fraction is smaller

b) The sample from Rhode Island will be substantially more accurate than that from California because a higher sampling fraction was chosen.

c) The sample from California will have a larger sampling error than from Rhode Island because less of the population is sampled.  

d) Both samples will be approximately equally accurate because the sample sizes are the same

Answer:

C = 100 + 25t

Step-by-step explanation:

7 x 3 = 21 so it is 21 ft cm your welcome

Answer:

The answer is C = 63π

Step-by-step explanation:

V = πr2 h

V = π (3)2 x 7

V = π (9) (7)

V = 63 π

Answer:

y=4,x= -1

Step-by-step explanation:

2y-3 =y+1

2y-y=1+3

y=4

∆CBD

2x+7=2y-3

2x+7=5

2x= 5-7

2x= -2

x= -1

"Static-Reports" differ from "dynamic-reports" in that static-reports are fixed.

The "Static-Reports" differ from dynamic reports in that static reports are fixed and do not change once generated, while dynamic reports are capable of updating and adapting in real-time or based on user interactions.

Static reports are pre-generated and provide a snapshot of information at the time of creation. They are static in nature and do not reflect any changes which may occur after their generation. Static reports are commonly in formats like PDF or printed documents.

The dynamic reports are designed to be interactive and responsive. They can be connected to live databases, which allows for real-time updates and dynamic visualizations.

Dynamic reports can be customized, filtered, and adjusted by users to explore data from different angles.

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The main difference between static and dynamic reports is that static reports are fixed documents that do not change or update automatically, while dynamic reports can update and change in real-time.

In the field of business, reports play a crucial role in presenting and analyzing data. Two types of reports commonly used are static reports and dynamic reports. The main difference between static and dynamic reports lies in their nature and functionality.

Static reports are fixed documents that present information at a specific point in time. They do not change or update automatically. These reports are typically created using tools like Microsoft Word or Excel. Static reports are often used for presenting historical data or summarizing information. For example, a static report may be used to present sales figures for a specific quarter or to summarize the financial performance of a company for a particular year.

Dynamic reports, on the other hand, are capable of updating and changing in real-time. They are usually generated using specialized software or programming languages. Dynamic reports can pull data from various sources and provide up-to-date information. These reports are commonly used for monitoring and analyzing real-time data. For instance, a dynamic report may be used to track website traffic in real-time or to monitor stock prices as they fluctuate throughout the day.

In summary, static reports are fixed documents that do not change or update automatically, while dynamic reports can update and change in real-time.

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The exact area of the region is 12 square units.

The Riemann sum for the area of the triangle is \(A = B\times \sum (1-\frac{h}{H} ) \Delta h\)

The integral that gives the area is \(A = B[\int\limits^H_0 {} \, dh - \frac{1}{H} \int\limits^H_0 {h} \ dh\) where a = 0 and b = h,

The exact area of the region is 12 square units.

The Riemann sum of the triangle is described by the following formula:

\(A = \sum b(h)\Delta h\).............(i)

Where:

b(h) - Base of the rectangle.

Δh - Height of the rectangle.

A - Area of the rectangle.

Now we derive an expression for the base of the rectangle in terms of the base and height of the triangle:

\(b(h) / B = H-h / H\).............(ii)

Where:

B - Base of the triangle.

H - Height of the triangle.

h - Position of the rectangle within the triangle.

Using the equations 1 and 2, we obtain a Riemann sum for the area of the triangle:

\(A = B\times \sum (1-\frac{h}{H} ) \Delta h\)...............(3)

The integral that gives the area of the triangle is based on (3):

\(A = B[\int\limits^H_0 {} \, dh - \frac{1}{H} \int\limits^H_0 {h} ]\ dh\)

Now we obtain the exact expression by integration:

\(A = B. [(H-0) - \frac{1}{2H} (H^2-0^2)]\\\\\\A = B\times H\)

If we know that, B = 3, and H = 8, then the exact area of the region is:

A = 1/2 × 3 × 8

Hence the exact area of the region is 12 square units.

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After answering the provided question, we can conclude that As a result, probability the correct answer is C) A• The expected point value is 0.13, so guessing is advantageous.

Probability of how likely an event is to occur. It is represented by a number is for both 0 and 1, with 0 representing an unlikely event and 1 representing an unavoidable event. Shifting a fair coin and coin flips has a probability of 0.5 or 50% because there are two equally likely outcomes. (Heads or tails). Probability theory is a mathematical discipline that investigates random events instead than their properties. It is applied in many fields, including facts and figures, finance, scientific knowledge, and engineering.

After eliminating one of the six possible answers, the remaining five options are equally likely to be correct, so the probability of correctly guessing is now 1/5 and the probability of incorrectly guessing is 4/5.

Point value expected = (probability of gaining points x point value) - (probability of losing points x point value)

(1/5 x 1) is the expected point value. - (4/5 x 1/6)

1/5 - 1/30 = expected point value

5/30 - 1/30 = expected point value

4/30 is the expected point value.

The expected point value is 0.13. (rounded to two decimal places)

It is advantageous to guess because the expected point value is positive.

As a result, the correct answer is C) A• The expected point value is 0.13, so guessing is advantageous.

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Let's represent the area of the lawn with "x" (in square meters).

Maria charged $135 plus $9.55 per square meter, so her total earnings can be expressed as:

Total earnings = $135 + $9.55 x

We know that Maria was paid $1854, so we can set up an equation and solve for x:

$1854 = $135 + $9.55 x

Subtracting $135 from both sides:

$1719 = $9.55 x

Dividing both sides by $9.55:

x = 180

Therefore, the area of the lawn is 180 square meters.

The probability of both events happening is 0.6 × 0.5 = 0.3, or 30%, and the probability that at least one university will make an offer is 1 - 0.2 = 0.8, or 80%.

The probability that both universities will make an offer can be found by multiplying the probabilities of each event happening. The probability of receiving an offer from university A is 0.6, and the probability of receiving an offer from university B is 0.5. Therefore, the probability of both events happening is 0.6 × 0.5 = 0.3, or 30%.

The probability that at least one university will make an offer can be found by subtracting the probability that neither university will make an offer from 1. The probability that neither university will make an offer is the product of the probabilities that each university will not make an offer, which is 0.4 × 0.5 = 0.2, or 20%. Therefore, the probability that at least one university will make an offer is 1 - 0.2 = 0.8, or 80%.

Overall, the probability that the graduate will receive an offer from both universities is 30%, and the probability that she will receive an offer from at least one university is 80%.

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The new coordinates of points M and O is determined as;

M = (0.5, - 1)

O = (2.5, -2).

The new coordinate of points M and O after applying the scale factor is calculated as follows;

The given scale factor = 1/2

The current coordinates of point M and O is;

M = (1, - 2)

O = (5, - 4)

A scale factor can be used to either enlarge a figure or decrease a figure.

When the scale factor is less than 1, it means the new figure will be smaller than the original figure.

However, if the scale factor is greater than 1, the new figure will be greater than the original figure.

The new coordinates of points M and O is determined as follows;

M = (1 x 1/2,  -2 x 1/2) = (0.5, - 1)

O = (5 x 1/2, -4 x 1/2) = (2.5, -2)

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Answer: (a) P = 6W + 2

(b) L = 2W + 1

(c) Width = 13cm

Length = 27cm

Step-by-step explanation:

The formula for perimeter of a rectangle is 2(length + width). Since the length is 1 cm more than twice its width, then the length will be:

L = (2 × W) + 1

(b) L = 2W + 1

Therefore, P = 2(L + W)

P = 2( 2W + 1) + 2W

P = 4W + 2 + 2W

(a) P = 6W + 2

Since perimeter is given as 80cm. Therefore,

P = 6W + 2

6W + 2 = 80

6W = 80 - 2

6W = 78

W = 78/6

W = 13

Width is 13cm

Length = 2W + 1

Length = 2(13) + 1

Length = 27cm

The width of the rectangle is 13cm and the length is 27cm.

A rectangle is a quadrilateral. Opposite sides are equal. The four angles in a rectangle is equal to 90 degrees.

The formula for determining the perimeter of a rectangle = 2x (length + width)

P = 2(L + W)

80 = 2(1 + 2w + w)

80 = 2(1 + 3w)

40 = 1 + 3w

40 - 1 = 3w

39 = 3w

w = 13cm

Length = 1 + 2(13) = 27cm

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The implicit equation for the plane passing through the points (1, -3, -2), (-3, -7, -6), and (1, 0, 1) can be written as 2x + y - 3z + 4 = 0.

To find the implicit equation of a plane, we need to determine the coefficients of the equation that satisfy all three given points. Using the point-normal form of a plane equation, where (x, y, z) is a point on the plane and (a, b, c) is the normal vector, we can set up a system of equations.

By substituting the coordinates of the three points, we can solve for the coefficients. The resulting equation is 2x + y - 3z + 4 = 0, which represents the plane passing through the given points.

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Answer: 3x2 + 3x - 7

Step-by-step explanation: The first term is,  3x2  its coefficient is 3

The middle term is, +3x  its coefficient is 3

The last term, the constant, is  -7

1.Multiply the coefficient of the first term by the constant   3 times -7 = -21

2. Find two factors of  -21  whose sum equals the coefficient of the middle term, which is 3

Answer:

3x^2 + 3x - 7

Step-by-step explanation:

1. Distribute the - sign to 3x^2 - 7x + 2

(6x^2 - 4x - 5) - 3x^2 + 7x - 2

2. Combine like terms 6x^2 and 3x^2

^ - 4x - 5 + 7x - 2

3. Combine like terms -4x and 7x

3x^2 + - 5 - 2

4. Finally combine like terms -5 and -2

3x^2 + 3x -

So your final answer is 3x^2 + 3x - 7!

I hope this helped :)

a. all solutions contain (0,0), we note that when x = 0, y = 0 + C(0) = 0 for any value of C. b. the particular solution is y = x + x = 2x. c. There are no horizontal asymptotes because y approaches infinity as x approaches infinity and negative infinity as x approaches negative infinity.

(a) To verify that y = x + Cx, x = -C and C = 0 is a general solution, we substitute y = x + Cx into the differential equation:

dxdy = x*(x + Cx) - (x + Cx)^2 = x^2 - C^2x^2

The right-hand side simplifies to (1 - C^2)x^2, which is a function of x only. Therefore, y = x + Cx is a solution for any value of C, including C = 0.

To show that all solutions contain (0,0), we note that when x = 0, y = 0 + C(0) = 0 for any value of C.

(b) To find the particular solution that passes through (1,2), we plug in x = 1 and y = 2 into the general solution:

y = x + Cx

2 = 1 + C*1

C = 1

So the particular solution is y = x + x = 2x.

To find dxdy at (0,0), we take the derivative of y with respect to x:

dxdy = 2

(c) To find the vertical asymptotes, we look for values of x such that the denominator of y' (which is y^2 - x^2) becomes zero. This occurs when y = x or y = -x. Thus, the lines y = x and y = -x are vertical asymptotes.

There are no horizontal asymptotes because y approaches infinity as x approaches infinity and negative infinity as x approaches negative infinity.

(d) The particular solution that passes through (1,2) is a straight line with slope 2, passing through the point (0,0). To sketch both branches of this curve, we extend the line through the origin in both directions.

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Answer:

The measure of 4 is 79 degrees.

Step-by-step explanation:

Since 3 and 4 are on the same straight line, their angles together form 180 degrees. To solve this, you would subtract 101 from 180 to get 79.

Hope this helps!