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1. y-12 =9

2. 42=7x

3. 5p-7=28

4. 1.5x+1.3x=-8.4

5. 4/3w -12=2/3w

6. 4 (3q-2)=16q

7. -h+4=-h+9

8. t+3t-7=4t-7

9. 1/4(n-6)=1/4-3/2

10. 2d+1/6=6(1/3d+1)

The temperature after a "very long time" in the heat conduction model on a metal circular ring of radius 1, with an initial temperature of 2δ(θ - 4π), approaches a constant value of zero.

The heat equation describes the behavior of temperature distribution over time in a conducting medium. In this case, we have a metal circular ring with a radius of 1, and the initial temperature is given by 2δ(θ - 4π), where δ represents the Dirac delta function and θ is the angular coordinate.

To solve the heat equation for this scenario, we need to consider the boundary conditions, which include the initial temperature distribution and the properties of the ring. The initial temperature distribution indicates a temperature spike at θ = 4π and zero temperature elsewhere.

As time progresses, the heat conduction in the metal ring will cause the temperature to equalize throughout the ring. Since the heat is continuously dissipating to the surroundings, the temperature will tend towards a steady-state condition. In the case of a "very long time," the temperature will approach a constant value of zero.

This result can be understood by considering the heat diffusion process. As time increases, the heat will flow from regions of higher temperature to regions of lower temperature until equilibrium is reached. In this case, since the initial temperature is concentrated at a single point and dissipates continuously, the temperature will eventually reach a state where it is uniformly distributed and approaches zero.

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The angle bisector from a vertex to the opposite side of a triangle is unique. We get AD = BE by subtracting BD from both sides of AB + BD = BE.

Proposition 4.4 states that in every triangle, there exists an angle bisector from a vertex to the opposite side and the angle bisector is unique.

Proof:

Let ΔABC be the given triangle and suppose AD is the angle bisector from A to BC. To prove that AD is unique, suppose BE is another angle bisector from B to AC.

We need to show that AD = BE.

Construct the incenter I of ΔABC. Draw lines AI and BI. AI bisects ∠A and BI bisects ∠B.

So, ∠AIB = 90° + ½ ∠C (proved in proposition 4.3).

Again, ∠AIB = ∠AID + ∠BIE [angle addition property of equality]

Therefore, ∠AID + ∠BIE = 90° + ½ ∠C...(1)

Since AD is the angle bisector from A to BC, we have

∠BAD = ∠CAD

Also, BE is the angle bisector from B to AC, so

∠EB = ∠EC

Adding these two equations, we get

∠BAD + ∠EB = ∠CAD + ∠EC...(2)

Since ∠A + ∠B + ∠C = 180° (angle sum property of a triangle),

∠C/2 + ∠B/2 + ∠A/2 = 180° (angle bisector property)

Therefore, ∠A/2 + ∠B/2 = 90° - ∠C/2

So, 2∠A/2 + 2∠B/2 = 180° - ∠C...(3)

Adding equations (1), (2), and (3), we get

∠AID + ∠BIE + ∠BAD + ∠EB + 2∠A/2 + 2∠B/2 = 360° - ∠C/2 + 180° + ∠C/2 + 180° - ∠C

∠AID + ∠BIE + ∠BAD + ∠EB + ∠A + ∠B = 360°(simplifying)

Therefore,

∠AID + ∠BIE + ∠BAD + ∠EB = 180°...(4)

Now, consider ΔABD and ΔEBD.

∠ABD = ∠EBD (∵ AD and BE are angle bisectors)

∠BAD = ∠BED [from equation (2)]

Therefore, ΔABD ≅ ΔEBD (∵ SAS congruence criterion)

So, BD = BD [by CPCTC]

Thus, we get AD = BE [by subtracting BD from both sides of AB + BD = BE]

Hence, the angle bisector from a vertex to the opposite side of a triangle is unique.

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Therefore ,xa - xb = 3 and σa - σb = √(6/60) + (8/60) respectively are the units that were chosen and standard deviation difference.

How far the data points deviate from the mean is determined by descriptive statistics standard deviation. It quantifies how values are spread out over the sample data and gauges how far out of the mean data points are.

Here,

Given:

For Amanda's chicken, xa = 57 grammes is the average weight.

Chicken from Bernardo weighs, on average, 54 grammes.

The sample mean's difference is -

=> xa - xb

=> 57 - 54

=> 3

The chicken from Amanda's recipe had a standard deviation of 6 grammes.

The Bernardo's chicken standard deviation is b = 8 grammes.

N = 60 total observations were made.

The standard deviation formula is -

σ = √(x - μ)/n

σa - σb = √(6/60) + (8/60)

The figures are as follows: mean = 3; standard deviation = ((6/60) + (8/60).

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Answer:

10 packs

Step-by-step explanation:

150 dollars divided by 15 dollars is 10.

Answer:

2n=12

Step-by-step explanation:

The next step would be to subtract four from each side getting 2n=12 or B

Answer:

In the first law, an object will not change its motion unless a force acts on it.

In the second law, the force on an object is equal to its mass times its acceleration.

In the third law, when two objects interact, they apply forces to each other of equal magnitude and opposite direction.

Step-by-step explanation:

Hope this helped!

also if you want can you answer my two most recent questions :))

Answer:

In the first law, an object will not change its motion unless a force acts on it.

In the second law, the force on an object is equal to its mass times its acceleration.

In the third law, when two objects interact, they apply forces to each other of equal magnitude and opposite direction

Your Welcome :)

Answer:

(\(\frac{2}{3} , \frac{1}{5}\))

Step-by-step explanation:

The fastest way to do this is to convert both equations into slope-intercept form and graph it to find the solution point. If you wanted to do this algebraically, you might want to start out by getting rid of the fractions and using either substitution or elimination to find x and y.

Basically, in a function, you draw a vertical line. If that vertical line crosses the function more than once, then it is an invalid function.

Let me know if you need an example and I'll edit a picture in for you.

Answer:

A vertical line test is used to find out whether if a curve is a graph of a function or not.  If you are able to draw a vertical line, and it intersects more than one point on the curve, then it is not a function.

Step-by-step explanation:

Most common is 7

So

Use distributive law to verify

Verified

GCF is 7

No, the ordered pair (-8,1) is not a solution to the equation y=(1/2)x-3.

In the question ,

an equation y=(1/2)x-3 is given ,

if the ordered pair (-8,1) is a solution of the equation , then it should satisfy the equation .

Substituting x=-8 and y=1 in the equation y=(1/2)x-3 , we get

y=(1/2)x-3

1 = (1/2)(-8) -3

1 = -8/2 -3

1 = -4-3

1 ≠ -7

Since 1≠7 , the ordered pair (-8,1) is not a solution to the equation y=(1/2)x-3 .

Therefore , No , the ordered pair (-8,1) is not a solution to the equation y=(1/2)x-3.

The given question is incomplete , the complete question is

Is the ordered pair (-8,1) a solution to the equation y=1/2x-3  ?

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Since the 1980s, the percentage of Americans who are members of a workplace union has declined significantly.

According to data from the Bureau of Labor Statistics, the union membership rate in the United States has experienced a substantial decrease over the past few decades. In the 1980s, the union membership rate was around 20% of the total workforce. However, as of the most recent available data, which is from 2020, the union membership rate stands at approximately 10.8%.

This indicates a decline of about 9.2 percentage points since the 1980s. The reasons for this decline include various factors such as changes in labor laws, economic shifts, and shifts in industries and employment patterns.

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From a 100-foot roll of paper, you can get 18 sections that are 5.5 feet long. To determine the number of 5.5-foot sections you can obtain from a 100-foot roll of paper. Divide the total length of the roll by the length of each section.

Dividing 100 by 5.5 gives us approximately 18.18 sections. Since we cannot have a fraction of a section, we round down to the nearest whole number. Therefore, you can obtain 18 sections that are 5.5 feet long from the 100-foot roll of paper.

In conclusion, you can get 18 sections, each measuring 5.5 feet, from the 100-foot roll of paper.

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Answer:

2x=-4

x=-2

Step-by-step explanation:

Answer:

x= -2

Step-by-step explanation:

isolate x

2x+8=4 subtract 8 on both sides

2x=-4 divide 2 on both sides

x= -2

We can write the inequality system as -

16c + 12t ≤ M

c + t ≤ N

and the region common to both the inequalities will be the solution set of the given system of inequalities.

An inequality in mathematics is used to compare two or more numbers or expressions.

Given is that a camp manager needs to hire counselors {c}, and counselors-in-training, or trainees {t}, to staff summer camps. She will pay each counselor $16 per hour and each trainee $12 per hour.

Since the complete information is not given, assume that her total budget is ${M} and she can hire a total of {N} members. Then, we can write the inequality as -

16c + 12t ≤ M

c + t ≤ N

Plotting the inequalities, the region common to both the inequalities will be the solution set of the given system of inequalities.

Therefore, we can write the inequality system as -

16c + 12t ≤ M

c + t ≤ N

and the region common to both the inequalities will be the solution set of the given system of inequalities.

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\(250 ft\: \: the \: nearest \: tenth.\)

Step-by-step explanation:

\(d \: = \sqrt{(270 - 90) {}^{2} + (270 - 90) {}^{2} } = \\ 254.55844123 = 250 \: to \: the \: \\ nearest \: tenth.\)

\(where \: the \: first \: base \: hieght \: is \: 90ft, \\ and \: third \: base \: hieght \: is \: 270(i.e \: 3 \times 90),\\

so \: by \: using \: the \: above \: pythagorean \\ \: equation, \: the \: shortest \: distance, d \: is \: 250ft\)

Answer:

24

Step-by-step explanation:

8*3=24

Answer:

24

Step-by-step explanation:

To find the area you have to multiply 3 and 8 together to get 24

3x8=24

Answer:

36, 60, 84

Step-by-step explanation:

3+5+7=15

180/15=12

12*3=36

12*5=60

12*7=84

Alpha one is equal to two is the null hypothesis and the alternate hypothesis says at least one pair is different.

Classification modes X is alpha + ц T and X is ц T + alpha

Therefore , P  value is 01.0197

Therefore, This value is smaller than 0.0 , this is the decision rule.

The null hypothesis will be rejected at that point since there is enough data to say that the therapy had a meaningful impact.

The null hypothesis means that there will be no observed effect in our experiment. In a mathematical formulation of the null hypothesis, there will typically be an equal sign. This hypothesis is denoted by H0.

The alternate hypothesis means that there will be an observed effect for our experiment. In a mathematical formulation of the alternative hypothesis, there will typically be an inequality, or not equal to symbol. This hypothesis is denoted by either Ha or by H1.

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Yes, they can use the walkie-talkies to talk to each other.

The distance between them is given as 28.2 meters.

The horizontal and vertical distances should be considered when calculating the distance between their apartments using the three-dimensional form of the Pythagorean theorem.

This comes out as \(\sqrt((18^2 + 19^2 + 7^2))\), which equals \(\sqrt(798)\) square root meters, or, to the nearest tenth, 28.2 meters.

Since this distance is less than the 35-meter range of the walkie-talkies, communication should be possible between the two apartments.

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Answer: The real part is -7, the imaginary part is 8i

Step-by-step explanation:

Answer: The Real Part: -7

               The imaginary Part: 8i

Step-by-step explanation:

Scale shows weight = 193

Weight of assistant = 135

Weight of dog = x

x = 193 - 135

x = 58

The dog weighs 58 pounds.

The 45th term of the sequence is 267.

The 45th term of a sequence can be calculated using the formula:

Tn = a + (n – 1)d

Where,

Tn = the nth term

a = the first term

n = the term position

d = the common difference

In this sequence, the first term is 3, the common difference is 6, and the term position is 45.

Therefore, the 45th term of the sequence is:

T45 = 3 + (45 – 1)6

T45 = 3 + (44)6

T45 = 3 + 264

T45 = 267

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Answer:

x + y = -1

x + 4y = 0

8x – 3y = 20

Step-by-step explanation:

answer on edge

Answer:

x + y = -1

x + 4y = 0

8x – 3y = 20

Step-by-step explanation:

Answer: 4 i think

Step-by-step explanation:

Answer:

n = 14

Step-by-step explanation:

(n + 6)4 = 5

1. multiply by 4

n + 6 = 20

2. substract 6

n = 14

The required value of n is 14 in the given sum.

Algebra is the analysis of mathematical representations, while logic is the manipulation of those symbols.

We have been given that the sum of a number, n, and 6 is divided by 4 the result is equal to 5.

According to the given question, we can write the algebraic form would be as:

⇒ (n + 6)/4 = 5

Apply the cross-multiplication operation,

⇒ (n + 6) = 5 × 4

Apply the multiplication operation,

⇒ (n + 6) = 20

⇒ n = 20 - 6

Apply the subtraction operation,

⇒ n = 14

Therefore, the required value of n is 14.

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Answer:

the answer is 5:7

Step-by-step explanation:

as a fraction, the ratio looks like this:

1500/2100

where 1500 is the number of rolls with double prints and 2100 is the amount of rolls developed.

if you simplify the fraction, you get 5/7.

5/7 is 5:7 written as a ratio in this problem.

hope this helped!!

Answer: The area of the larger square is 9 times the area of the smaller square.

Step-by-step explanation:

Answer:

(0,3)

Step-by-step explanation:

Answer: 15.2

Step-by-step explanation:

(14)^2 + (6)^2 = c^2

196 + 36 = c^2

232 = c^2

Square root both sides

15.231546 = c

15.2 ≈ c

The distance of the straight line from the starting  point by the is  is 15.2 miles.

The distance between a point and a line is the shortest distance between them.

It states that if a triangle is right-angled (90 degrees), then the square of hypotenuse is equals to the  sum of the squares of the other two sides.

If ΔOAB is a right angled triangle, right angle at A

then the Pythagoras equation will be

\(OB^{2} =AB^{2} +OA^{2}\)      

(where OB, OA and AB are the length of the sides of triangle OAB)

According to the question

We have to find ,the distance of straight line from the starting point.

From, the provided figure we can conclude that OB is the straight line whose distance to be find

In ΔOAB, we have

\(OB^{2} =OA^{2} +AB^{2}\)                              (By Pythagoras theorem)

\(OB^{2} =14^{2} +6^{2}\)

\(OB^{2} =196+36\)

\(OB=\sqrt{232} \\OB= 15.23 miles\)

\(OB=15.2 miles\)

Hence, the distance of straight line from the starting point is 15.2 miles.

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