At a price of $180 there is demand for 2520 items and a supply of 1440 items. At a price of $330 there is demand for 1470 items and a supply of 2640 items. Assuming supply and demand are linear, find the equilibrium price and quantity.

This is given by the limit

[tex]\displaystyle \lim_{x\to1} \frac{f(x) - f(1)}{x - 1} = \lim_{x\to1} \frac{(2x^2 - 5x+1) - (-2)}{x - 1} = \lim_{x\to1} \frac{2x^2 - 5x + 3}{x - 1}[/tex]

Observe that [tex]2x^2-5x+3=0[/tex] when [tex]x=1[/tex], and factorizing gives

[tex]2x^2 - 5x + 3 = (x - 1) (2x - 3)[/tex]

so that

[tex]\displaystyle \lim_{x\to1} \frac{f(x) - f(1)}{x - 1} = \lim_{x\to1} (2x-3) = 2\cdot1 - 3 = \boxed{-1}[/tex]

(A)

Answer:

Step-by-step explanation:

The absolute value of -3 is 3.

Answer: 3

Step-by-step explanation:

Answer:

x=0

Step-by-step explanation:

Answer:

No.1 is 89 No.2 is 11 No.3 is 60 and the last one is 29

Answer:

y = - 8

Step-by-step explanation:

substitute x = 8 into the equation

y = 8 - 2(8) = 8 - 16 = - 8

Answer: g=14

Step-by-step explanation:

5(g + 8) - 7 = 117 - g

5g+40-7=117-g

5g+33=117-g

6g+33=117

6g=84

g=14

[tex]5(g + 8) - 7 = 117 - g[/tex]

[tex]5g + 5 \cdot 8 -7 = 117 -g\\[/tex]

[tex]5g + 40 -7 = 117 -g[/tex]

[tex]6g = 117 - 40 + 7[/tex]

[tex]6g = 84[/tex]

[tex]g = 94 : 6[/tex]

[tex]g = 14[/tex]

Answer:

5.8

Step-by-step explanation:

Area = (h x b)/2

A = (2.5 x 4.6)/2 = 5.75 = 5.8

The 21% of taxes and annual percentage decrease of 0.32, using arithmetic progression gives;

The percentage of tax that comes from corporate income tax = 21%

Amount by which the percentage decreased each year = 0.32

Period during which the tax reduced = Between 1960 and 2010

Required;

The year corporations pay zero taxes.

Solution;

The amount of tax paid each year can be given by the arithmetic progression formula,

[tex] a_{n} = a + (n - 1) \cdot d[/tex]

Where;

a = The first term = 21

[tex] a_{n} = value \: on \: the \: nth \: year[/tex]

d = The common difference = -0.32

When [tex] a_{n} = 0 [/tex], we have;

[tex] 0 = 21 + (n - 1) \times (-0.32) [/tex]

0.32•(n - 1) = 21

n - 1 = 21/0.32 = 65.625

n = 65.625 - 1 = 64.625 ≈ 65

The year the corporations will pay no taxes is 1960 + 65 = 2025

Corporations will pay no taxes in the year 2025

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The value of 4²×3³×(-1)¹²² is 432.

When a number is repeatedly multiplied by itself, the result is a power of that number.

A power of the original number would be produced if you multiplied a number by itself any number of times.

When a single number is added up several times, it is said to be multiplied.

given that 4²×3³×(-1)¹²²

now find the value of 4²×3³×(-1)¹²².

4² = 4 × 4

3³ = 3 × 3 × 3

(-1)¹²² = 1

then, multiply these numbers.16 X 27 X 1 = 432

Hence, the value of 4²×3³×(-1)¹²² is 432.

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Answer:

1885.714

Step-by-step explanation:

I = ptr

5280 = 7×0.4×p

p = 5280/2.8

p = 1885.7

The quadratic equation that passes through points (1, - 9) and (0, - 8) is y = x² - 2 · x - 8.

Graphically speaking, quadratic equations are parabolas. The quadratic equation in vertex form is described by this formula:

y - k = C · (x - h)²

Where:

If we know that (x, y) = (0, - 8) and (h, k) = (1, - 9), then the vertex constant is:

- 8 + 9 = C · (0 - 1)²

1 = C · (- 1)²

1 = C

C = 1

Then, the quadratic equation in vertex form is:

y + 9 = (x - 1)²

Whose standard form is:

y + 9 = x² - 2 · x + 1

y = x² - 2 · x - 8

The quadratic equation that passes through points (1, - 9) and (0, - 8) is y = x² - 2 · x - 8.

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Answer:

12

Step-by-step explanation:

There are 4 entrances and 3 exits, and thus 4(3)=12.

A person will take 5.88672 × [tex]10^{8}[/tex] breaths in 70 years.

Here, we are given that on average a person at rest takes approximately 16 breaths per minute.

1 hour = 60 minutes

Thus, in 1 hour a person will take-

60 × 16

= 960 breaths

Now, 1 day = 24 hours

Thus, in 1 day, a person will take-

24 × 960

= 23,040 breaths

Further, 1 year = 365 days

Thus, in 1 year, a person will take-

23,040 × 365

= 8,409,600 breaths

In 70 years, a person will take-

8,409,600 × 70

= 588,672,000 breaths

We can express this in exponential notation as-

5.88672 × [tex]10^{8}[/tex]

Thus, a person will take 5.88672 × [tex]10^{8}[/tex] breaths in 70 years.

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Answer:wow we have the same homework

Step-by-step explanation:

Answer:.......................

Answer:

0.06

Step-by-step explanation:

0x x it expand almost done ✅✅✅

The exports to each country are:

So,

let the exports to Mexico be 'x'.

Exports to Canada will be x + 39.4.

Given:

So, the equation becomes:

So, exports to Mexico are 243 billion.

Exports to Canada are 243 + 39.4 = 282.4

Therefore, the exports to each country are:

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Answer:

B.

Step-by-step explanation:

Vegans by definition do not eat any products containing the meat of an animal. Therefore if Mindy truly follows a vegan diet, she would not eat steak.

Answer:People who follow a vegan diet do not eat steak. Mindy follows a vegan diet. Therefore, Mindy does not eat steak.

Step-by-step explanation:

Because deductive reasoning is when you make an inference about something. In option 2 they are making an inference that if Mindy does not eat steak she is a vegetarian. They have come to that conclusion by inferring she is a vegetarian because she does not eat steak.

Answer:

The answer is D

The time it would take to drive to the beach if you leave from the friend's house is 1 hour 12 minutes

From the question,  we are to calculate how long it would take to drive to the beach if you leave from your friend's house

From the given information,

The beach is 80 miles from your house and the drive takes about 1 hour 30 minutes

Distance, d, varies directly with time, t.

d ∝ t

d = vt

Where v is the proportionality constant.

Now, we will find v

d = 80 miles

t = 1.5 hours = 3/2 hours

Thus,

80 = (3/2)v

v = (2 × 80)/3

v = 160/3 miles/hour

Now, we will determine t when d is 64 miles

d = vt

64 = 160/3 × t

t = (64 × 3)/160

t = 192/160 hours

t = 6/5 hours

t = 1 hour 12 minutes

Hence, the time it would take to drive to the beach if you leave from the friend's house is 1 hour 12 minutes

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It will take 6.14 weeks for the plant to grow the required length

The growth rate of the plant each week = 1 1/6 inches

Converting the mixed fraction into an improper fraction we multiply the whole number by the denominator and add the numerator to get the improper fraction, therefore

The growth rate of a plant in improper form = 7/6 inches

Required growth rate = 6 1/6 inches

The required growth rate in improper fraction = 43/6 inches

Number of weeks it will take the plant to grow the required length = Required length/Growth rate each week = (43/6)/(7/6)

= 43/7 weeks or 6.14 weeks

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Answer:

You only show one answer A. Lucky for you it's the correct one.

Step-by-step explanation:

From the graph of the function y = x - 1, it is found that f(1) = 0.

This problem is incomplete, but researching it on a search engine, it gives us the graph of the function y = x - 1.

To find the numeric value of a function at x = a, we have to check the value of the horizontal axis when the vertical axis is of a.

For this problem, we want the numeric value at x = 1, hence, when the horizontal axis is of 1, the vertical axis is of 0, hence f(1) = 0.

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[tex]\displaystyle\\Answer:\ \frac{z}{4} +1[/tex]

Answer:

Elizabeth has 403 toys.

Step-by-step explanation:

The main goal is to figure out how many toys Elizabeth has. So she has 4 boxes and each box has 100 toys. If she has 4 boxes of 100 it mean she have 400 toys but that's not the final answer. she also has 3 toys not in the boxes so we have to add that as well. So if we add 3 toys to the 400 toys we'd get a total of 403. Therefore Elizabeth has 403 toys and that would be our final answer.

I hope this helps, have a blessed day! :D

Answer:

The last answer is correct

y = [tex]\frac{-3}{5 }[/tex] x - 1

Step-by-step explanation:

You can see that the graph crosses the y axis at (0,-1).  So, the graph crosses the y axis at -1.  Count how much you go down and the to right from the point on the left to the point on the right.  You go down 3 and left 5.  This is a negative slope of [tex]\frac{-3}{5}[/tex].

y = mx + b  Put in the slope for m  and the y-intercept by b

y = [tex]\frac{-3}{5}[/tex]x = 1

In the given case, we can conclude Mr. Arcos needs to buy 10 sets of plates for his restaurant.

To find out how many sets of plates Mr. Arcos needs to buy, we first need to determine the total number of people his restaurant can accommodate.

There are 8 tables with places for 4 people each, so these tables can seat a total of 8 x 4 = 32 people.
Additionally, there are 4 tables with places for 6 people each, which can seat a total of 4 x 6 = 24 people.

Therefore, the restaurant can accommodate a total of 32 + 24 = 56 people.

Since the plates come in sets of 6, we divide the total number of people (56) by the number of people served by each set (6) to find out how many sets of plates Mr. Arcos needs to buy: 56 / 6 = 9.33 sets. Since plates cannot be bought in fractions, he will need to round up to the nearest whole number. Therefore, he will need to buy at least 10 sets of plates for his restaurant.

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Hence , using synthetic division the quotient and remainder of given equation are x²- 9x + 23  and -36 respectively.

We have given an equation , x³ - 7x² + 5x + 10 which is divided by -2

Steps for using synthetic division are

Step 1 -  Write the coefficients of x within the dividend within associate inverted division image.

                   |  1    -7      5     10

                   |                                            

Step 2 - As provides put = -2  place at the left.

             -  2 |  1    -7      5     10

                   |                                            

Step 3 - Drop the primary constant of the dividend below the division image.

           -    2 |  1    -7      5     10

                   |                                            

                       1

Step 4 - Multiply the result by the constant, and place the merchandise within the next column.

           -   2 |  1    -7      5     10  

                   |        -2                                    

                      1    

Step 5 - Add down the column.

             -  2 |  1    -7      5     10  

                   |        -2                                    

                      1     -9

Step 6 - Repeat Steps Four and 5 till you'll go no further.

            -   2 |  1    -7      5     10  

                   |        -2    18   - 46                        

                      1     -9    23     -36

Hence the quotient is x²- 9x + 23 and remainder is -36

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