For small changes in temperature, the formula for the expansion of a metal rod under a change in temperature is: g-L=aL(t-T), where g is the length of the object at temperature t,and L is the length at temperature T,and a is a constant which depends on the type of metal a) express g as the linear function of t.Find the slope and vertical intercept in terms of L,T,a

Answer:

3x+2y=-3

Slope = -3.000/2.000 = -1.500

 x-intercept = -3/3 = -1

 y-intercept = -3/2 = -1.50000

2x-3y=-15

Slope = 1.333/2.000 = 0.667

 x-intercept = -15/2 = -7.50000

 y-intercept = 15/3 = 5

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OTHER PROBLEM

y=2x-2

Slope = 4.000/2.000 = 2.000

 x-intercept = 2/2 = 1

 y-intercept = -2/1 = -2.00000

y=3x-7

Slope = 6.000/2.000 = 3.000

 x-intercept = 7/3 = 2.33333

 y-intercept = -7/1 = -7.00000

Answer:

1/2

Step-by-step explanation:

16^-1/4

We know that a^ -b = 1/a^b

1/( 16^1/4)

Rewriting 16 as 2^4

1/( 2^4^1/4)

We know that a^b^c = a^ (b*c)

1/( 2^(4*4))

1/2^1

1/2

Answer: 1/2 is 16^-1/4

Step-by-step explanation:

When you have a fraction as the exponent, it is the root. ^1/2 would be the square root. ^1/4 is the 4th root. That is 2.

A negative exponent means that it is the reciprocal.

The reciprocal of 2 is 1/2

That's the answer.

I hope this explanation helps you!

Answer:

Step-by-step explanation:

The distance between two points can be found by using the formula

[tex]d = \sqrt{ ({x1 - x2})^{2} + ({y1 - y2})^{2} } \\[/tex]

where

(x1 , y1) and (x2 , y2) are the points

From the question the points are

(-4, 4) & (-1, 0)

The distance between them is

[tex]d = \sqrt{ ({ - 4 + 1})^{2} + ({4 - 0})^{2} } \\ = \sqrt{ ({ - 3})^{2} + {4}^{2} } \\ = \sqrt{9 + 16} \\ = \sqrt{25} \: \: \: \: \: \: \: \: \\ = 5 \: \: \: \: \: \: \: \: \: \: \: \: \: \: [/tex]

We have the final answer as

Hope this helps you

Answer:

Step-by-step explanation:

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Answer:

The Answer is 4. it is two times larger.

Step-by-step explanation:

The limit of the expression x² + 5x + 2e² as x approaches 0 is 2e². Option C.

To find the limit of the expression x² + 5x + 2e² as x approaches 0, we substitute the value of x into the expression and evaluate it.

Plugging in x = 0 into the expression, we get:

0² + 5(0) + 2e² = 0 + 0 + 2e² = 2e²

Therefore, the limit of the expression as x approaches 0 is 2e².

This result is obtained by evaluating the expression at the specific value x = 0. The limit gives us the behavior of the expression as x gets arbitrarily close to 0, but not necessarily equal to 0. In this case, no matter how close x gets to 0, the value of the expression remains 2e².

It's important to note that the value of e² is approximately 7.3891. Thus, the final answer can be expressed as 2 * 7.3891 = 14.7782.

Therefore, the limit of the expression x² + 5x + 2e² as x approaches 0 is approximately 14.7782. So Option C is correct.

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This equation shows that the amount Steven charges (y) is directly proportional to the number of hours he babysits (x) with a constant of proportionality of $5.25 per hour.

To write the equation to represent the relationship between the number of hours Steven babysits and the amount he charges, we need to first find the rate of charging per hour.

Then we can use this rate to write the equation.Let x represent the number of hours Steven babysits and y represent the amount he charges.We can find the rate of charging per hour by dividing the amount he charges by the number of hours he babysits.

Rate of charging per hour when Steven babysits for 4 hours = $21 ÷ 4 = $5.25/hourRate of charging per hour when Steven babysits for 6 hours = $31.50 ÷ 6 = $5.25/hour

We see that Steven charges a flat rate of $5.25 per hour for babysitting.Using this information, we can now write the equation to represent the relationship between x and y:y = 5.25x

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Answer:

He's wrong.

Step-by-step explanation:

0.9 = 9/10

0.009 = 9/1000

Answer:

[tex]Volume = 210L[/tex]

Step-by-step explanation:

Given

Base:

[tex]Front = 100cm[/tex]

[tex]Back = 50cm[/tex]

[tex]Width = 40cm[/tex]

[tex]Height = 70cm[/tex]

Required

Determine the volume (in litres)

First, we need to calculate the area;

Base on the parameters given, we have:

[tex]Area = \frac{1}{2}(Front + Back) * Width[/tex]

[tex]Area = \frac{1}{2}(100cm + 50cm) * 40cm[/tex]

[tex]Area = \frac{1}{2}(150cm) * 40cm[/tex]

[tex]Area = 75cm * 40cm[/tex]

[tex]Area = 3000cm^2[/tex]

[tex]Volume = Area * Height[/tex]

[tex]Volume = 3000cm^2 * 70cm[/tex]

[tex]Volume = 210000cm^3[/tex]

[tex]1cm^3 = 0.001L[/tex]

So:

[tex]Volume = 210000 * 0.001L[/tex]

[tex]Volume = 210L[/tex]

Answer:

74.94

Step-by-step explanation:

As, we will see how many 4 feet panels will cover 24 feet wall

So, 24/4 = 6

So we need 6 panels

So, 6x 12.46 = 74.94

So no. of panels = 6

Total cost: $74.94

The number of planes either on the runway or waiting to take off is 17.

The question states that safety regulations require that the time between airplane takeoffs (on the same runway) will be at least 2 minutes.

When taking off, the run time of an airplane on the runway is 48 seconds.

Planes are on average waiting time 5 minutes and 30 seconds for take-off.

On average, there are 16 planes taking off per hour.

We need to determine the number of planes either on the runway or waiting to take off.

The number of seconds an airplane takes on the runway is 48 seconds and the minimum time between airplane takeoffs is

2 minutes = 2 × 60 seconds

= 120 seconds.

So the time taken by a plane from the beginning of the runway to the end is

48 seconds + 120 seconds = 168 seconds.

There are 16 planes taking off per hour.

Therefore there are

60 minutes/hour × 16 planes/hour ÷ 60 minutes = 16 planes.

So in a minute, there are

16 planes/60 = 0.2666... planes.

Now, let’s find out the number of planes that are waiting to take off in 1 minute:

0.2666 planes/min × 5.5 minutes = 1.466 planes.

So, on average, there are 1.466 planes waiting to take off and there are 16 planes taking off per hour.

So the number of planes either on the runway or waiting to take off is:

1.466 planes + 16 planes = 17.466 planes

≈ 17 planes.

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a. The graph of the budget line would have hamburgers on the x-axis and bags of figs on the y-axis. b. the budget line equation represents Rachel's affordability based on her income and the prices of hamburgers and figs. Changes in prices, income, or additional resources can affect the slope, position, or rotation of the budget line on a graph.

a) Rachel's budget line equation can be written as follows:

Budget = (Price of Hamburger * Quantity of Hamburgers) + (Price of Figs * Quantity of Figs)

Since the price per hamburger is $3 and the price per bag of figs is $2, the equation becomes:

Budget = 3x + 2y

Where x represents the quantity of hamburgers and y represents the quantity of bags of figs. The graph of the budget line would have hamburgers on the x-axis and bags of figs on the y-axis.

b) If the price of figs increases to $3, the new budget line equation becomes:

Budget = 3x + 3y

The graph of the new budget line would show a steeper slope compared to the original budget line. This indicates that the relative price of figs has increased, making them relatively more expensive compared to hamburgers.

c) In this scenario, Rachel has an income of $50, the price per hamburger is $3, the price per bag of figs is $3, and she receives an additional $10 in cash from a friend. The new budget line equation can be written as:

Budget = (3x + 3y) + 10

The graph of the new budget line would shift upward parallel to the original budget line. The additional cash from Rachel's friend increases her purchasing power, allowing her to afford more hamburgers and/or bags of figs.

d) Now, Rachel's friend gives her a gift basket containing 3 free bags of figs. In this case, the budget line equation remains the same as in part c:

Budget = (3x + 3y) + 10

However, since Rachel receives 3 free bags of figs, she can allocate more of her budget towards purchasing hamburgers. This would cause the budget line to rotate outward from the y-intercept, resulting in a flatter slope. The new budget line would reflect Rachel's ability to purchase more hamburgers with the same income and price of figs.

In summary, the budget line equation represents Rachel's affordability based on her income and the prices of hamburgers and figs. Changes in prices, income, or additional resources can affect the slope, position, or rotation of the budget line on a graph.

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Answer:

A: the same line

Step-by-step explanation:

Answer:  $110230 in 2015

Answer:

g(x)=6x^(3)-5x^(2)-17x+6

Step-by-step explanation:

Answer: Our required two terms will be 18 and 22.

Explanation:

Since we have given that  The sequence : 2,6,10,14........

Here, a = 4  common difference = d is given by

We also have a formula to find the nth term, i.e.

We need to find the next two terms , that is 5th and 6th term

So it will be

Hence , our required two terms will be 18 and 22.

Answer:

the answer is D

Step-by-step explanation:

i explain it here

Answer:

the answer is d

Step-by-step explanation:

Answer:

it's 82

Step-by-step explanation:

26+72=98

180-98=82

Lily signed a personal loan of $7,500 with her aunt, Joanne, to pay for her MBA tuition fees for the first year of her studies.

In this agreement, Lily made a promise to repay Joanne the principal amount and 3.8% interest on this loan to compensate her aunt against the expected inflation on overall groceries and other costs Joanne has to cover per year based on the average rate of inflation observed in Canada since 1960 to 2021. Lily will start making the first payment after graduating her MBA.Calculate the amount of annual interest for this loan:To calculate the amount of annual interest for this loan, we need to multiply the principal amount with the annual interest rate. Since the principal amount is $7,500 and the annual interest rate is 3.8%, we can calculate the annual interest as follows:Annual Interest = Principal Amount * Annual Interest RateAnnual Interest = $7,500 * 3.8%Annual Interest = $7,500 * 0.038Annual Interest = $285Therefore, the amount of annual interest for this loan is $285. In the scenario given above, Lily has signed a personal loan with her aunt Joanne for $7,500 to pay for her MBA tuition fees during her first year of study. The agreement states that Lily will repay Joanne the principal amount plus 3.8% annual interest on the loan to compensate Joanne against the expected inflation on overall groceries and other costs she has to cover per year. This rate is based on the average rate of inflation observed in Canada from 1960 to 2021.The annual interest for this loan is calculated by multiplying the principal amount with the annual interest rate. In this case, since the principal amount is $7,500 and the annual interest rate is 3.8%, the annual interest is $285.Lily will start to make her first payment after graduation. However, if she decides to repay the loan six months upon graduation, she will save on interest. To calculate the amount of interest Lily saves, we need to find out the total amount of interest that would be due if she repays the loan after six months of graduating from her MBA program.To calculate the interest Lily saves, we need to find the amount of interest that would have accrued in six months. To do this, we need to calculate the interest on the loan for six months using the formula:Interest for six months = Principal amount * (Annual interest rate / 2)Interest for six months = $7,500 * (3.8% / 2)Interest for six months = $7,500 * 0.019Interest for six months = $142.50Therefore, if Lily pays back the loan six months upon graduating her MBA, she saves $142.50 in interest.

Thus, the annual interest for this loan is $285, and if Lily pays back the loan six months upon graduation, she saves $142.50 in interest.

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Answer:

A. $2.00

Step-by-step explanation:

if they sold 20 t-shirts and made $40.

$40 ÷ 20 = $2

Answer:

3/5

Step-by-step explanation:

always the numerator is the X and the denominator is the Y.

so 3 goes up

and 5 go rise

Answer:

hb≈1.89in

Step-by-step explanation:

The given information provides the estimated index model for stocks A and B, but it lacks the values for the coefficients and error terms. Thus, it is incomplete and cannot be used to draw any specific conclusions.

The provided information presents the index model for stocks A and B, which relates their excess returns to the excess return of the market (RM). However, the values for the coefficients and error terms (eA and eB) are missing from the given equation.

To draw meaningful conclusions and analyze the relationship between stocks A and B with the market, we would need the specific values of the coefficients (intercepts and slopes) and error terms.

The information also mentions R-square values, which indicate the proportion of the total variation in the stocks' excess returns that can be explained by the market's excess return. However, since the R-square values are given as 0.29 and 0, respectively, it suggests that the model does not have a significant explanatory power for either stock A or stock B.

In summary, without the complete values for the coefficients and error terms, it is not possible to make any conclusive statements about the relationship between stocks A and B and the market.

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A= 180°

B= 110°

C= 30°

D= 180°

E= 150°

Answer:

[tex]4[/tex]

Step-by-step explanation:

Step 1: Define

[tex]\frac{15m}{n+1}-m^2[/tex]

m = 1

n = 2

Step 2: Substitute and Evaluate

[tex]\frac{15(1)}{2+1} -1^2[/tex]

[tex]\frac{15}{3} -1[/tex]

[tex]5 -1[/tex]

[tex]4[/tex]

Answer: 2

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

If two is subtracted from a number: let's give the number a name and call it  X . And this difference is tripled: so we get  3(X−2) . The result is 4 more than the number, so

3(X−2)=4+X .

We want to know  X  so we need to get it to one side of the equation. That's done by repeatedly doing the same operation on both sides of the equation. First get rid of the parentheses:

3X−6=4+X.  

Now subtract  X  and add  6 :

2X=10  

Divide by 2:

X=5

Answer:

x = 1

Step-by-step explanation:

The mathematical equation is 1-3x=2-4x

plz mark brainliest

Answer:

45

Step-by-step explanation: