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Masja [62]
2 years ago
8

1) In the market for apartment housing, the quantity of available apartments is observed to be less than the number of renters w

ho are willing and able to pay the market price of an apartment. In this scenario, the market is said to be _____.(1 point)
A in equilibrium because there is a surplus of apartments on the market


(B) in equilibrium because there is a shortage of apartments on the market


C in disequilibrium because there is a shortage of apartments on the market


D in disequilibrium because there is a surplus of apartments on the market
1) B

2) For a given market, the equilibrium quantity of the good or service will decrease if _____.(1 point)


A demand increases and supply decreases


B demand decreases and supply increases


(C) demand decreases and supply decreases


D demand increases and supply increases

2)C

3) Price Quantity Supplied Quantity Demanded

$10 1,000 2,500

$20 2,000 2,000

$30 3,000 1,500

$40 4,000 1,000


The equilibrium price for this market is _____.


(1 point)


A $10


(B) $20


C $30


D $40

3) B

4) In a given market, the market equilibrium price and quantity are $120 and 5 million units, respectively. At a price of $100, 4.8 million units are supplied, and 5.2 million units are demanded. It can be said that at a price level of $100 there is a _____.(1 point)


A a surplus of 0.4 million units


(B) a shortage of 0.4 million units


C a shortage of 0.2 million units


D a surplus of 0.2 million units

4) B

5)The supply and demand curves for a market are graphed below with price in dollars and quantity in thousands.


Two intersecting lines are graphed. The horizontal axis labeled Quantity goes from 0 to 70 in increments of 10. The vertical axis labeled Price goes from 0 to 50 in increments of 10. A line with a negative slope is labeled D and a line with a positive slope is labeled S. The lines intersect at approximately left parenthesis 33.7 comma 30 right parenthesis. A horizontal dashed line extends from left parenthesis 0 comma 30 right parenthesis to the point of intersection.


Which of the following would result from an increase in the supply curve?


(1 point)

(A) a market equilibrium price less than $30


B a market equilibrium quantity less than $30


C a market equilibrium quantity greater than $30


D a market equilibrium price greater than $30

5) A
5/5 Good job
Mathematics
1 answer:
jeka942 years ago
4 0

Answer:

Hey

Step-by-step explanation:

Hey did you find the answers to this? i really need it. im desperate!

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As the Remainder Theorem points out, if you divide a polynomial p(x) by a factor x – a of that polynomial, then you will get a zero remainder. Let's look again at that Division Algorithm expression of the polynomial:

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p(x) = (x – a)q(x) + r(x)

If x – a is indeed a factor of p(x), then the remainder after division by x – a will be zero. That is:

p(x) = (x – a)q(x)

In terms of the Remainder Theorem, this means that, if x – a is a factor of p(x), then the remainder, when we do synthetic division by

x = a, will be zero.

The point of the Factor Theorem is the reverse of the Remainder Theorem: If you synthetic-divide a polynomial by x = a and get a zero remainder, then, not only is x = a a zero of the polynomial (courtesy of the Remainder Theorem), but x – a is also a factor of the polynomial (courtesy of the Factor Theorem).

Just as with the Remainder Theorem, the point here is not to do the long division of a given polynomial by a given factor. This Theorem isn't repeating what you already know, but is instead trying to make your life simpler. When faced with a Factor Theorem exercise, you will apply synthetic division and then check for a zero remainder.

Use the Factor Theorem to determine whether x – 1 is a factor of

    f (x) = 2x4 + 3x2 – 5x + 7.

For x – 1 to be a factor of  f (x) = 2x4 + 3x2 – 5x + 7, the Factor Theorem says that x = 1 must be a zero of  f (x). To test whether x – 1 is a factor, I will first set x – 1 equal to zero and solve to find the proposed zero, x = 1. Then I will use synthetic division to divide f (x) by x = 1. Since there is no cubed term, I will be careful to remember to insert a "0" into the first line of the synthetic division to represent the omitted power of x in 2x4 + 3x2 – 5x + 7:

completed division: 2  2  5  0  7

Since the remainder is not zero, then the Factor Theorem says that:

x – 1 is not a factor of f (x).

Using the Factor Theorem, verify that x + 4 is a factor of

     f (x) = 5x4 + 16x3 – 15x2 + 8x + 16.

If x + 4 is a factor, then (setting this factor equal to zero and solving) x = –4 is a root. To do the required verification, I need to check that, when I use synthetic division on  f (x), with x = –4, I get a zero remainder:

completed division: 5  –4  1  4  0

The remainder is zero, so the Factor Theorem says that:

x + 4 is a factor of 5x4 + 16x3 – 15x2 + 8x + 16.

In practice, the Factor Theorem is used when factoring polynomials "completely". Rather than trying various factors by using long division, you will use synthetic division and the Factor Theorem. Any time you divide by a number (being a potential root of the polynomial) and get a zero remainder in the synthetic division, this means that the number is indeed a root, and thus "x minus the number" is a factor. Then you will continue the division with the resulting smaller polynomial, continuing until you arrive at a linear factor (so you've found all the factors) or a quadratic (to which you can apply the Quadratic Formula).

Using the fact that –2 and 1/3 are zeroes of  f (x) = 3x4 + 5x3 + x2 + 5x – 2, factor the polynomial completely.   Copyright © Elizabeth Stapel 2002-2011 All Rights Reserved

If x = –2 is a zero, then x + 2 = 0, so x + 2 is a factor. Similarly, if x = 1/3 is a zero, then x – 1/3 = 0, so x – 1/3 is a factor. By giving me two of the zeroes, they have also given me two factors: x + 2 and x – 1/3.

Since I started with a fourth-degree polynomial, then I'll be left with a quadratic once I divide out these two given factors. I can solve that quadratic by using the Quadratic Formula or some other method.

The Factor Theorem says that I don't have to do the long division with the known factors of x + 2 and x – 1/3. Instead, I can use synthetic division with the associated zeroes –2 and 1/3. Here is what I get when I do the first division with x = –2:

completed divison: bottom row:  3  –1  3  –1  0

The remainder is zero, which is expected because they'd told me at the start that –2 was a known zero of the polynomial. Rather than starting over again with the original polynomial, I'll now work on the remaining polynomial factor of 3x3 – x2 + 3x – 1 (from the bottom line of the synthetic division). I will divide this by the other given zero, x = 1/3:

completed division:  bottom row:  3  0  3  0

 

3x2 + 3 = 0

3(x2 + 1) = 0

x2 + 1 = 0

x2 = –1

x = ± i

If the zeroes are x = –i and x = i, then the factors are x – (–i) and x – (i), or x + i and x – i. I need to   divided off a "3" when I solved the quadratic; it is still part of the polynomial, and needs to be included as a factor. Then the fully-factored form is:

3x4 + 5x3 + x2 + 5x – 2 = 3(x + 2)(x – 1/3)(x + i)(x – i)

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Subtract. Write the difference in simplest form. (6p + 3) - (2p + 1)
Sonja [21]

Answer:

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Step-by-step explanation:

(6p + 3) - (2p + 1)

Distribute the minus sign

6p +3 -2p -1

4p +2

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