Find the value of b if a+b+c/4=2 where a = 1, №18010427, 14.05.2022 21:21

Mathematics

Find the value of b if a+b+c/4=2 where a = 1 and c=2

Step-by-step answer

P Answered by Specialist

b = 5

Step-by-step explanation:

Solving

Step 1: Plug in the values of a and c.

$\frac{1+b+2}{4} =2$

Step 2: Combine like terms on both sides.

$\frac{(2+1)+b}{4}=2$ $\frac{3+b}{4}=2$

Step 3: Multiply both sides by 4.

$\frac{3+b}{4} *4 = 2*4$ 3+b=8

Step 4: Subtract 3 from both sides.

Step 5: Check if solution is correct.

$\frac{1+5+2}{4} = 2$ $\frac{8}{4} =2$ 2=2

Have a lovely rest of your day/night, and good luck with your assignments! ♡

Business

An organization expresses its reason for being, what it aspires to be, and the values it wants to emphasize in its mission, vision, and values statements, respectively. This activity is important because these three statements are the necessary foundation for a successful organizational planning process. The goal of this exercise is to challenge your knowledge of important components of organizational mission, vision, and values statements. Read the descriptions and select whether the description pertains to a mission, vision, or value statement.

Step-by-step answer

P Answered by Specialist

8

Solution :

Vision statement : A vision statement is defined as an inspirational statement of the economic future of any organization. It is what the organization is going to be in the future.

Mission statement : A mission statement supports the vision statement and says the ways to achieve and meet the vision.

Value statement : A value statement describes and defines in what any organization believes and how its employees should behave in the organization.

The following statements describes :

1. Describes the image the organization wants to project

it is a Mission Statement

2. Inspires enthusiasm and encourages commitment

it is a Vision Statement

3. Illuminates the organization’s attitude toward its employees

it is a Mission Statement

4. Is intended to guide all of the actions in the organization

it is a Value Statement

5. Is easily understood and well-articulated

it is a Vision Statement

6. Outlines the organization’s customer base

it is a Mission Statement

7. Expresses the company’s worldview

it is a Value Statement

8. Is appropriate for the times and for the organization

it is a Vision Statement

9. Limits itself to a small number that employees can recall when making decisions

it is a Value Statement

10. Articulates the geographical locations where the company competes

it is a Mission Statement

11. Unchanging; As applicable in 100 years as it is today

it is a Value Statement

12. Reflects high ideals

it is a Vision Statement

Business

An organization expresses its reason for being, what it aspires to be, and the values it wants to emphasize in its mission, vision, and values statements, respectively. This activity is important because these three statements are the necessary foundation for a successful organizational planning process. The goal of this exercise is to challenge your knowledge of important components of organizational mission, vision, and values statements. Read the descriptions and select whether the description pertains to a mission, vision, or value statement.

Step-by-step answer

P Answered by Specialist

8

Solution :

Vision statement : A vision statement is defined as an inspirational statement of the economic future of any organization. It is what the organization is going to be in the future.

Mission statement : A mission statement supports the vision statement and says the ways to achieve and meet the vision.

Value statement : A value statement describes and defines in what any organization believes and how its employees should behave in the organization.

The following statements describes :

1. Describes the image the organization wants to project

it is a Mission Statement

2. Inspires enthusiasm and encourages commitment

it is a Vision Statement

3. Illuminates the organization’s attitude toward its employees

it is a Mission Statement

4. Is intended to guide all of the actions in the organization

it is a Value Statement

5. Is easily understood and well-articulated

it is a Vision Statement

6. Outlines the organization’s customer base

it is a Mission Statement

7. Expresses the company’s worldview

it is a Value Statement

8. Is appropriate for the times and for the organization

it is a Vision Statement

9. Limits itself to a small number that employees can recall when making decisions

it is a Value Statement

10. Articulates the geographical locations where the company competes

it is a Mission Statement

11. Unchanging; As applicable in 100 years as it is today

it is a Value Statement

12. Reflects high ideals

it is a Vision Statement

StudenGPT

X 单选题第12分 IF-20231030-Q15 截止时间:2023-11-01 08:30 1. Which one of the following equalities expresses the condition of equilibrium in the money market? (where L = the demand for cash balances in real terms, which is a function of R = interest rate, and Y = national income). a. P = Ms x L(R, Y) b. P = Ms / L(R, Y) C. Ms P/L(R, Y) d. Ms x P = L(R, Y) 单选题第2题 2分 B 2. (Continuation) From the previous equality professor Krugman concludes that "if, for interest rate does not change. A example, the money supply doubles (to 2Ms) (...), the price level

Step-by-step answer

P Answered by Studen AI

1

The task you provided appears to be a multiple-choice question test related to macroeconomics and monetary policy. I will provide explanations for each question and the correct answer.

1. Which one of the following equalities expresses the condition of equilibrium in the money market? (where L = the demand for cash balances in real terms, which is a function of R = interest rate, and Y = national income).

Answer: b. P = Ms / L(R, Y)

Explanation: In the money market equilibrium, the demand for cash balances (L) must be equal to the money supply (Ms) divided by the function of interest rate (R) and national income (Y). This equation represents the equilibrium condition between the demand and supply of money.

2. (Continuation) From the previous equality, Professor Krugman concludes that "if, for example, the money supply doubles (to 2Ms) (...), the price level must also double (to 2P) to maintain the equilibrium in the market." What are the assumptions for this statement to be true?

Answer: a. That output does not change, but the interest rate changes.

Explanation: The statement assumes that there is no change in output (national income) but only a change in the interest rate. This assumption allows the conclusion that if the money supply doubles, the price level will also double to maintain equilibrium.

3. Country A has gone through a currency reform consisting of reducing the nominal value of each banknote and coin to 1/10 of its previous value (e.g., a 1,000-note becomes a 10-note). What are the effects of this reform in terms of money supply and prices?

Answer: c. A contraction of money supply and a price fall.

Explanation: The nominal value reduction of currency notes and coins implies a contraction of the money supply. The reform does not change the real value of money but reduces the quantity of money available in the economy. This contraction, coupled with a decrease in the quantity of money circulating, will lead to a decrease in prices.

4. Which one of the following is an assumption in the long-run analysis of the relationship between the money market and the foreign exchange market?

Answer: b. Prices are sticky in the long run.

Explanation: The assumption of sticky prices in the long-run analysis of the money market and the foreign exchange market implies that prices do not adjust immediately to changes in the money supply or other factors. This assumption allows for the examination of long-run effects and relationships between these markets.

5. Which one of the following is the conclusion in the long-run analysis about the relationship between the money market and the foreign exchange market?

Answer: a. A permanent increase in a country's money supply causes a proportional long-run depreciation of its currency against foreign currencies.

Explanation: In the long run, according to the analysis, a permanent increase in a country's money supply leads to depreciation of its currency exchange rate against foreign currencies. This depreciation occurs proportionally due to the increased money supply affecting the relative value of the domestic currency.

Please note that these explanations are simplified for a schoolchild's understanding.

Mathematics

16. photon lighting company determines that the supply and demand functions for its most popular lamp are as follows: s(p) = 400 - 4p + 0.2p4 and d(p) = 2,800 - 0.0012p3, where p is the price. determine the price for which the supply equals the demand. a) $93.24 b) $100.24 c) $96.24 d) $99.24 17. write a polynomial function of minimum degree with real coefficients whose zeros include those listed. write the polynomial in standard form. 2, -4, and 1 + 3i (1 point) a) f(x) = x4 - 2x2 + 36x - 80 b) f(x) = x4 - 3x3 + 6x2 - 18x + 80 c) f(x) = x4 - 9x2

Step-by-step answer

P Answered by PhD

80

QUESTION 16

If the demand and supply are equal, then we equate the two functions in p and solve for p.

That is

S(p)=D(p)

$400 - 4p + + 0.00002 {p}^{4} = 2800 - 0.0012 {p}^{3}$

We can rearrange to obtain,

$0.00002 {x}^{4} + 0.0012 {x}^{3} - 4x - 2400 = 0$

$2 {p}^{2} + 1200 {p}^{3} - 400000p - 240000000 = 0$

The real roots of this polynomial equation are:

$p = - 118.26 \: p = 96.24$

Since price can not be negative, we discard the negative value ,

p = 96.24

The correct answer for question 16 is C.

QUESTION 17

We were given the solution to this polynomial as

x=2,x=-4, x=1+3i

We need to recognize the presence of the complex root and treat it nicely.

There is one property about complex roots of polynomial equations called the complex conjugate property. According to this property, if

a + bi

is a solution to

p(x)

then the complex conjugate

a - bi

is also a root.

Since

x = 1 + 3i

is a solution then,

x = 1 - 3i

is also a solution.

Therefore we have

f(x) = (x - 2)(x + 4)(x - (1+3i))(x - (1 - 3i)

$f(x) = ( {x}^{2} + 4x - 2x - 8)( {x}^{2} - (1 - 3i)x - (1 + 3i)x + (1 + 3i)(1 - 3i))$

We expand to obtain,

$( {x}^{2} + 4x - 2x - 8)( {x}^{2} - x + 3xi - x - 3xi + 1 + 9)$

Note that:

${i}^{2} = - 1$

$f(x) = ( {x}^{2} + 2x - 8)( {x}^{2} - 2x + 10)$

We now expand to obtain,

$f(x) = {x}^{4} - 2 {x}^{3} + 10 {x}^{2} + 2 {x}^{3} - 4 {x }^{2} + 20x - 8 {x}^{2} + 16x - 80$

We simplify further to obtain,

$f(x) = {x}^{4} + 2 {x}^{2} + 36x - 80$

The correct answer for question 17 is A.

QUESTION 18

If

-2i

is a zero of the polynomial,

f(x)=x^4-45x^2-196

then the complex conjugate

is also a zero,

This means that ,

(x+2i), (x-2i)

are factors of the polynomial.

The product of these two factors,

(x+2i), (x-2i) =x^2-(2i)^2=x^2+4

is also a factor , so we use it to divide and get the remaining factors.

see diagram for long division.

The above polynomial can therefore factored completely as,

f(x)=(x^2+4)(x^2-49)

Applying our knowledge from difference of two squares, we obtain,

f(x)=(x+2i)(x-2i))(x-7)(x+7)

Hence all the zeroes of these polynomial can be found by setting

(x+2i)(x-2i))(x-7)(x+7)=0

This implies,

x=-2i,x=2i,x=7,x=-7

The correct answer for question 18 is B

QUESTION 19

We were asked to find the horizontal and vertical asymptote of

$f(x)=\frac{2x^2+1}{x^2-1}$

To find the horizontal asymptote, divide the term with the highest degree in the numerator by the term with the highest degree in the denominators. That is the horizontal asymptote is given by,

$y=\frac{2x^2}{x^2}=2$

For vertical asymptote, equate the denominator to zero and solve for x.

x^2-1=

$\Rightarrow x=-1, x=1$

None of the options is correct, so the correct answer for question 19 is A.

QUESTION 20

We are converting,

$\frac{5\pi}{6}$

to degrees .

To convert from radians to degrees, multiply by,

$\frac{180\degree}{\pi}$

That is,

$\frac{5\pi}{6}=\frac{5\pi}{6} \times \frac{180\degree}{\pi}$

We simplify to obtain,

$\frac{5\pi}{6}=\frac{5}{1} \times \frac{180\degree}{1}=5\times30\degree =150\degree$

The correct answer is B.

QUESTION 21

Recall the mnemonics, SOH CAH TOA

The sine ratio is given by,

$\sin(B)=\frac{21}{75}=\frac{7}{25}$

From the diagram,

$\tan(B)=\frac{21}{72}=\frac{7}{24}$

The correct answer is C.

QUESTION 22

From the above diagram, We can determine the value of x using the sine or cosine ratio, depending on where the 17 is placed.

Using the cosine ratio, we obtain,

$\cos(58\degree)=\frac{17}{x}$

We can simply switch positions to make x the subject.

$x=\frac{17}{\cos(58\degree)}$

$x=\frac{17}{0.5299}$

x=32.08

Hence the correct answer is A.

QUESTION 23

Coterminal angles have the same terminal sides.

To find coterminal angles, we keep adding or subtracting 360 degrees.

See diagram.

$x=202\degree$

is coterminal with

$202\degree +360\degree =562\degree$

or

$202\degree -360\degree =-158\degree$

The correct answer is D.

See the attached file for continuation.

16. photon lighting company determines that the supply and demand functions for its most popular lam

Mathematics

16. photon lighting company determines that the supply and demand functions for its most popular lamp are as follows: s(p) = 400 - 4p + 0.2p4 and d(p) = 2,800 - 0.0012p3, where p is the price. determine the price for which the supply equals the demand. a) $93.24 b) $100.24 c) $96.24 d) $99.24 17. write a polynomial function of minimum degree with real coefficients whose zeros include those listed. write the polynomial in standard form. 2, -4, and 1 + 3i (1 point) a) f(x) = x4 - 2x2 + 36x - 80 b) f(x) = x4 - 3x3 + 6x2 - 18x + 80 c) f(x) = x4 - 9x2

Step-by-step answer

P Answered by PhD

80

QUESTION 16

If the demand and supply are equal, then we equate the two functions in p and solve for p.

That is

S(p)=D(p)

$400 - 4p + + 0.00002 {p}^{4} = 2800 - 0.0012 {p}^{3}$

We can rearrange to obtain,

$0.00002 {x}^{4} + 0.0012 {x}^{3} - 4x - 2400 = 0$

$2 {p}^{2} + 1200 {p}^{3} - 400000p - 240000000 = 0$

The real roots of this polynomial equation are:

$p = - 118.26 \: p = 96.24$

Since price can not be negative, we discard the negative value ,

p = 96.24

The correct answer for question 16 is C.

QUESTION 17

We were given the solution to this polynomial as

x=2,x=-4, x=1+3i

We need to recognize the presence of the complex root and treat it nicely.

There is one property about complex roots of polynomial equations called the complex conjugate property. According to this property, if

a + bi

is a solution to

p(x)

then the complex conjugate

a - bi

is also a root.

Since

x = 1 + 3i

is a solution then,

x = 1 - 3i

is also a solution.

Therefore we have

f(x) = (x - 2)(x + 4)(x - (1+3i))(x - (1 - 3i)

$f(x) = ( {x}^{2} + 4x - 2x - 8)( {x}^{2} - (1 - 3i)x - (1 + 3i)x + (1 + 3i)(1 - 3i))$

We expand to obtain,

$( {x}^{2} + 4x - 2x - 8)( {x}^{2} - x + 3xi - x - 3xi + 1 + 9)$

Note that:

${i}^{2} = - 1$

$f(x) = ( {x}^{2} + 2x - 8)( {x}^{2} - 2x + 10)$

We now expand to obtain,

$f(x) = {x}^{4} - 2 {x}^{3} + 10 {x}^{2} + 2 {x}^{3} - 4 {x }^{2} + 20x - 8 {x}^{2} + 16x - 80$

We simplify further to obtain,

$f(x) = {x}^{4} + 2 {x}^{2} + 36x - 80$

The correct answer for question 17 is A.

QUESTION 18

If

-2i

is a zero of the polynomial,

f(x)=x^4-45x^2-196

then the complex conjugate

is also a zero,

This means that ,

(x+2i), (x-2i)

are factors of the polynomial.

The product of these two factors,

(x+2i), (x-2i) =x^2-(2i)^2=x^2+4

is also a factor , so we use it to divide and get the remaining factors.

see diagram for long division.

The above polynomial can therefore factored completely as,

f(x)=(x^2+4)(x^2-49)

Applying our knowledge from difference of two squares, we obtain,

f(x)=(x+2i)(x-2i))(x-7)(x+7)

Hence all the zeroes of these polynomial can be found by setting

(x+2i)(x-2i))(x-7)(x+7)=0

This implies,

x=-2i,x=2i,x=7,x=-7

The correct answer for question 18 is B

QUESTION 19

We were asked to find the horizontal and vertical asymptote of

$f(x)=\frac{2x^2+1}{x^2-1}$

To find the horizontal asymptote, divide the term with the highest degree in the numerator by the term with the highest degree in the denominators. That is the horizontal asymptote is given by,

$y=\frac{2x^2}{x^2}=2$

For vertical asymptote, equate the denominator to zero and solve for x.

x^2-1=

$\Rightarrow x=-1, x=1$

None of the options is correct, so the correct answer for question 19 is A.

QUESTION 20

We are converting,

$\frac{5\pi}{6}$

to degrees .

To convert from radians to degrees, multiply by,

$\frac{180\degree}{\pi}$

That is,

$\frac{5\pi}{6}=\frac{5\pi}{6} \times \frac{180\degree}{\pi}$

We simplify to obtain,

$\frac{5\pi}{6}=\frac{5}{1} \times \frac{180\degree}{1}=5\times30\degree =150\degree$

The correct answer is B.

QUESTION 21

Recall the mnemonics, SOH CAH TOA

The sine ratio is given by,

$\sin(B)=\frac{21}{75}=\frac{7}{25}$

From the diagram,

$\tan(B)=\frac{21}{72}=\frac{7}{24}$

The correct answer is C.

QUESTION 22

From the above diagram, We can determine the value of x using the sine or cosine ratio, depending on where the 17 is placed.

Using the cosine ratio, we obtain,

$\cos(58\degree)=\frac{17}{x}$

We can simply switch positions to make x the subject.

$x=\frac{17}{\cos(58\degree)}$

$x=\frac{17}{0.5299}$

x=32.08

Hence the correct answer is A.

QUESTION 23

Coterminal angles have the same terminal sides.

To find coterminal angles, we keep adding or subtracting 360 degrees.

See diagram.

$x=202\degree$

is coterminal with

$202\degree +360\degree =562\degree$

or

$202\degree -360\degree =-158\degree$

The correct answer is D.

See the attached file for continuation.

Mathematics

1. the width w of a rectangular swimming pool is x+4. the area a of the pool is 2x^3-29+12. what is an expression for the length of the pool? a. 2x^2+8x+3 b. 2x^2-8x-3 c. 2x^2-8x+3 d. 2x^2+8-3 2. simplify x/6x-x^2 a. 1/6-x; where x = 0,6 b. 1/6-x; where x=6 c. 1/6; where x=0 d. 1/6 3. simplify -12x4/x4+8x^5 a. -12/1+8x; where x= -1/8 b. -12/1+8x; where x= -1/8,0 4. simplify x+5/ x^2+6x+5 a. 1/x+1; where x= -1 b. 1/x+1; where x=-1, -5 5. simplify x^2-3x-18/x+3 a. x-3 b. x-6; where x= -3 c. x-6; where x= 6 d. 1/x+3; where x= -3 6. simplify 2/3a .

Step-by-step answer

P Answered by PhD

20

Question 1

To find the width of the rectangle, we divide the area by the length
$2x^{3}-29x+12$ ÷ x+4

We use the method of long division to get the answer. The method is shown in the first diagram below

$2x^{2}-8x+3$

Question 2:
$\frac{x}{6x-x^{2} } = \frac{x}{x(6-x)} = \frac{1}{6-x}$

Question 3:
$\frac{-12 x^{4} }{x^{4}+8 x^{5} }= \frac{-12 x^{4} }{ x^{4}(1+8x)}= \frac{-12}{1+8x}$

Question 4:
$\frac{x+5}{x^{2}+6x+5}= \frac{x+5}{(x+1)(x+5)}= \frac{1}{x+1}$

Question 5:
$\frac{x^{2}-3x-18} {x+3}= \frac{(x-6)(x+3)}{x+3}= \frac{x-6}{1}=x-6$

Question 6:
$\frac{2}{3a}$ × $\frac{2}{a^{2}}$ = $\frac{4}{3a^{3} }$ where $a \neq 0$

Question 7: (Question is not written well)
$\frac{x-5}{4x+8}$ × $(12x^{2}+32x+8)$
$\frac{12 x^{3}-28 x^{2} -152x-40 }{4x+8}$
By performing long division we get an answer $3 x^{2} -x-36$ with remainder of 248

Question 8:
$( \frac{x^{2}-16} {x-1})$ ÷ (x+4)

$( \frac{ x^{2}-16 }{x-1})$ × $\frac{1}{x+4}$
$\frac{(x+4)(x-1)}{x-1}$ × $\frac{1}{x+4}$
Cancelling out x+4

we obtain $\frac{x+1}{x-1}$

Question 9:
$\frac{x^{2}+2x+1} {x-2}$ ÷ $\frac{x^{2-1} }{x^{2}-4 }$
$\frac{ x^{2}+2x+1 }{x-2}$ × $\frac{x^{2}-4 }{x^{2}-1}$
Factorise all the quadratic expression gives
$\frac{(x+1)(x+1)}{x-2}$ × $\frac{(x-2)(x+2)}{(x+1)(x-1)}$
Cancelling out (x+1)

and

gives a simplest form
$\frac{(x+1)(x+2)}{x-1}$

Question 10:

$\frac{24 w^{10}+8w^{12} }{4 x^{4} }= \frac{24w^{10} }{4 x^{4} } + \frac{8 w^{12} }{4 x^{4} }$
Cancelling out the constants of each fraction
$\frac{6w^{10} }{x^{4} }+ \frac{2w^{12} }{x^{4}}= \frac{6w^{10}+2w^{12} }{ x^{4}}$

Question 11:

$\frac{-6m^{9}-6m^{8}-16m^{6} }{2m^{3} } = \frac{-2m^{6}(3m^{3}-3m^{2}-8)}{2m^{3} }$
Cancelling $2m^{3}$ gives us the simplified form
$-m^{3}(3m^{3}-3m^{2}-8) = -3m^{6}+3m^{5}+8m^{3}$

Question 12:

$\frac{-4x}{x+7} - \frac{8}{x-7} = \frac{-4x(x-7)-8(x+7)}{(x+7)(x-7)}$
$\frac{-4 x^{2} +28x-8x-56}{(x+7)(X-7)}= \frac{-4 x^{2} +20x-56}{(x+7)(x-7)}$
Factorising the numerator expression
$\frac{(-4x+28)(x-2)}{(x+7)(x-7)} = \frac{-4(x-7)(x-2)}{(x+7)(x-7)}$
Cancelling out x-7

gives the simplified form
$\frac{-4x+8}{x-7}$

Question 13:

$\frac{3}{x-3} - \frac{5}{x-2}= \frac{x3(x-2)-5(x-2)}{y(x-3)(x-2)}$
$\frac{3x-6-5x+15}{(x-3)(x-2)}= \frac{-2x+9}{(x-3)(x-2)}$

Question 14:

$\frac{9}{x-1}- \frac{5}{x+4}= \frac{9(x+4)-5(x-1)}{(x-1)(x+4)}$ $\frac{9x+36-5x+5}{(x-1)(x+4)}= \frac{4x+41}{(x-1)(x+4)}$

Question 15:

$\frac{-3}{x+2}- \frac{(-5)}{x+3}= \frac{-3(x+3)-(-5)(x+2)}{(x+2)(x+3)}$
$\frac{-3x-9+5x+10}{(x+2)(x+3)}= \frac{2x+1}{(x+2)(x+3)}$

Question 16:

$\frac{4}{x}+ \frac{5}{x}=-3$
$\frac{9}{x}=-3$
x=-3

Question 17:

$\frac{1}{3x-6}- \frac{5}{x-2}=12$
$\frac{(x-2)-5(3x-6)}{(3x-6)(x-2)} = \frac{x-2-15x+30}{(3x-6)(x-2)}= \frac{-14x+28}{(3x-6)(x-2)}$

Question 18

1. the width w of a rectangular swimming pool is x+4. the area a of the pool is 2x^3-29+12. what is

1. the width w of a rectangular swimming pool is x+4. the area a of the pool is 2x^3-29+12. what is

SAT

Ineed i am studying for my sat and i have the answer to the problems can someone just explain and show me how to get them i don t want you have me figure them out my self because i am on a tight schedule and won t be able to respond. ! 1.) if 8x + 6=6m, what is the value of 4x + 3 in terms of m?3m 2.)3x +4y=18 y= 3/2x which of the following ordered pairs (x,y) is a solution of the system of equations above?(2,3) 3.) which of the following is equivalent to 3x +4/12?x/4 + 1/3 4.) if x-3 is a factor of the expression x^2 +kx + 12, what is the value

Step-by-step answer

P Answered by Specialist

29

Ans1) 8x+6=6m then u will take the common factor of 8x+6 which is 2(4x+3) so it will be 2(4x+3)=6m then u should find 4x+3 so u will divide both by 2 and it will be 4x+3=3m so the answer is 3m

Mathematics

1. the width w of a rectangular swimming pool is x+4. the area a of the pool is 2x^3-29+12. what is an expression for the length of the pool? a. 2x^2+8x+3 b. 2x^2-8x-3 c. 2x^2-8x+3 d. 2x^2+8-3 2. simplify x/6x-x^2 a. 1/6-x; where x = 0,6 b. 1/6-x; where x=6 c. 1/6; where x=0 d. 1/6 3. simplify -12x4/x4+8x^5 a. -12/1+8x; where x= -1/8 b. -12/1+8x; where x= -1/8,0 4. simplify x+5/ x^2+6x+5 a. 1/x+1; where x= -1 b. 1/x+1; where x=-1, -5 5. simplify x^2-3x-18/x+3 a. x-3 b. x-6; where x= -3 c. x-6; where x= 6 d. 1/x+3; where x= -3 6. simplify 2/3a .

Step-by-step answer

P Answered by PhD

20

Question 1

To find the width of the rectangle, we divide the area by the length
$2x^{3}-29x+12$ ÷ x+4

We use the method of long division to get the answer. The method is shown in the first diagram below

$2x^{2}-8x+3$

Question 2:
$\frac{x}{6x-x^{2} } = \frac{x}{x(6-x)} = \frac{1}{6-x}$

Question 3:
$\frac{-12 x^{4} }{x^{4}+8 x^{5} }= \frac{-12 x^{4} }{ x^{4}(1+8x)}= \frac{-12}{1+8x}$

Question 4:
$\frac{x+5}{x^{2}+6x+5}= \frac{x+5}{(x+1)(x+5)}= \frac{1}{x+1}$

Question 5:
$\frac{x^{2}-3x-18} {x+3}= \frac{(x-6)(x+3)}{x+3}= \frac{x-6}{1}=x-6$

Question 6:
$\frac{2}{3a}$ × $\frac{2}{a^{2}}$ = $\frac{4}{3a^{3} }$ where $a \neq 0$

Question 7: (Question is not written well)
$\frac{x-5}{4x+8}$ × $(12x^{2}+32x+8)$
$\frac{12 x^{3}-28 x^{2} -152x-40 }{4x+8}$
By performing long division we get an answer $3 x^{2} -x-36$ with remainder of 248

Question 8:
$( \frac{x^{2}-16} {x-1})$ ÷ (x+4)

$( \frac{ x^{2}-16 }{x-1})$ × $\frac{1}{x+4}$
$\frac{(x+4)(x-1)}{x-1}$ × $\frac{1}{x+4}$
Cancelling out x+4

we obtain $\frac{x+1}{x-1}$

Question 9:
$\frac{x^{2}+2x+1} {x-2}$ ÷ $\frac{x^{2-1} }{x^{2}-4 }$
$\frac{ x^{2}+2x+1 }{x-2}$ × $\frac{x^{2}-4 }{x^{2}-1}$
Factorise all the quadratic expression gives
$\frac{(x+1)(x+1)}{x-2}$ × $\frac{(x-2)(x+2)}{(x+1)(x-1)}$
Cancelling out (x+1)

and

gives a simplest form
$\frac{(x+1)(x+2)}{x-1}$

Question 10:

$\frac{24 w^{10}+8w^{12} }{4 x^{4} }= \frac{24w^{10} }{4 x^{4} } + \frac{8 w^{12} }{4 x^{4} }$
Cancelling out the constants of each fraction
$\frac{6w^{10} }{x^{4} }+ \frac{2w^{12} }{x^{4}}= \frac{6w^{10}+2w^{12} }{ x^{4}}$

Question 11:

$\frac{-6m^{9}-6m^{8}-16m^{6} }{2m^{3} } = \frac{-2m^{6}(3m^{3}-3m^{2}-8)}{2m^{3} }$
Cancelling $2m^{3}$ gives us the simplified form
$-m^{3}(3m^{3}-3m^{2}-8) = -3m^{6}+3m^{5}+8m^{3}$

Question 12:

$\frac{-4x}{x+7} - \frac{8}{x-7} = \frac{-4x(x-7)-8(x+7)}{(x+7)(x-7)}$
$\frac{-4 x^{2} +28x-8x-56}{(x+7)(X-7)}= \frac{-4 x^{2} +20x-56}{(x+7)(x-7)}$
Factorising the numerator expression
$\frac{(-4x+28)(x-2)}{(x+7)(x-7)} = \frac{-4(x-7)(x-2)}{(x+7)(x-7)}$
Cancelling out x-7

gives the simplified form
$\frac{-4x+8}{x-7}$

Question 13:

$\frac{3}{x-3} - \frac{5}{x-2}= \frac{x3(x-2)-5(x-2)}{y(x-3)(x-2)}$
$\frac{3x-6-5x+15}{(x-3)(x-2)}= \frac{-2x+9}{(x-3)(x-2)}$

Question 14:

$\frac{9}{x-1}- \frac{5}{x+4}= \frac{9(x+4)-5(x-1)}{(x-1)(x+4)}$ $\frac{9x+36-5x+5}{(x-1)(x+4)}= \frac{4x+41}{(x-1)(x+4)}$

Question 15:

$\frac{-3}{x+2}- \frac{(-5)}{x+3}= \frac{-3(x+3)-(-5)(x+2)}{(x+2)(x+3)}$
$\frac{-3x-9+5x+10}{(x+2)(x+3)}= \frac{2x+1}{(x+2)(x+3)}$

Question 16:

$\frac{4}{x}+ \frac{5}{x}=-3$
$\frac{9}{x}=-3$
x=-3

Question 17:

$\frac{1}{3x-6}- \frac{5}{x-2}=12$
$\frac{(x-2)-5(3x-6)}{(3x-6)(x-2)} = \frac{x-2-15x+30}{(3x-6)(x-2)}= \frac{-14x+28}{(3x-6)(x-2)}$

Question 18

1. the width w of a rectangular swimming pool is x+4. the area a of the pool is 2x^3-29+12. what is

Mathematics

1. an unknown number y is 15 more than an unknown number x. the number y is also x less than 8. the equations to find x and y are shown below. y = x + 15 y = –x + 8 which of the following statements is a correct step to find x and y? (4 points) multiply the equations to eliminate y. add the equations to eliminate x. write the points where the graphs of the equations intersect the x-axis. write the points where the graphs of the equations intersect the y-axis. 2. variable a is 4 more than variable b. variable a is also 1 less than b. which of the

Step-by-step answer

P Answered by PhD

8

1. add the 2 equations, since you have x and -x the x would be removed giving you y

2. a is 4 more than b = a = b+4

a is 1 less than b = a=b-1

so the first pair is correct.

3. Solve w + 11 = 3w – 15 to find the value of w, then you can use the value of w to find b

4. 3rd

28 children and 7 adults
Equation 1: a + c = 35 ( 28+7 = 35)
Equation 2: 6a + c = 70 (6*7=42, 42+28 = 70)

5. 25x+60 = 30x+10

50 = 5x

x = 50/5 = 10 weeks

25(10) = 250+60 = 310 dollars

2nd answer 10 weeks, $310

Find the value of b if a+b+c/4=2 where a = 1 and c=2

Step-by-step answer

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