twice the difference of a number and 4 is less than the sum of the number and five. Solve please

Answer:

1) The values of 'a' and 'b' are [tex]$ \frac{3}{4} $[/tex] and [tex]$ \frac{3}{4} $[/tex] respectively.

2) The values of 'a' and 'b' are '3' and '-3' respectively.

Step-by-step explanation:

1) Given: [tex]$ \frac{3x}{(x - 2)(3x + 2)} = \frac{a}{x - 2} + \frac{b}{3x + 2} $[/tex]

We solve this by partial fraction method.

Taking LCM in the RHS we get,

[tex]$ \frac{3x}{(x - 2)(3x + 2)} = \frac{a(3x + 2) + b(x - 2)}{(x - 2)(3x + 2)} $[/tex]

[tex]$ \implies 3x = a(3x + 2) + b(x - 2) $[/tex]

To find the value of 'a', substitute x = 2. This would make 'b' vanish leaving an equation with 'a'.

[tex]$ \therefore 3(2) = a(3.2 + 2) + b (2 - 2) \implies 6 = a(8) $[/tex]

[tex]$ \implies a = \frac{-2}{3} $[/tex]

Now, Substitute [tex]$ x = \frac{-2}{3} $[/tex] to solve for 'b'.

[tex]$ \implies 3(\frac{-2}{3}) = a (3.\frac{-2}{3} + 2) + b(\frac{-2}{3} -2) $[/tex]

[tex]$ \implies -2 = b \frac{-8}{3} $[/tex]

[tex]$ \implies b = \frac{3}{4} $[/tex]

Therefore, a = [tex]$ \frac{3}{4} $[/tex] and b = [tex]$ \frac{3}{4} $[/tex]

2) Given [tex]$ \frac{3}{x^2 - 5x + 6} = \frac{a}{x - 2} + \frac{b}{x - 3} $[/tex]

We follow the same procedure as (1).

Taking LCM we get

[tex]$ \frac{3}{x^2 - 5x + 6} = \frac{a (x - 3) + b(x - 2)}{(x^2 - 5x + 6)} $[/tex]

[tex]$ \implies 3 = a(x - 3) + b(x - 2) $[/tex]

Substituting x = 2, we get:

3 = a(-1) [tex]$ \implies a = -3 $[/tex]

Also, Substituting x = 3, we get:

3 = b(1)

[tex]$ \implies b = 1 $[/tex]

Therefore, the values of a and b are -1 and 1 respectively.

Answer:488

Step-by-step explanation:

1464 divided by 3=488

Answer:

The maximum revenue that can be generated is $128.13

Step-by-step explanation:

we have

[tex]R(p)=-5.2p^{2}+65p-75[/tex]

where

R(p) represent the amount of revenue in dollars

p the product price

This is a vertical parabola open downward

The vertex represent a maximum

so

The y-coordinate of the vertex represent the maximum revenue that can be generated

Solve by graphing

using a graphing tool

Graph the quadratic equation

The vertex is the point (6.25,128.125)

see the attached figure

the y-coordinate of the vertex is 128.125

therefore

The maximum revenue that can be generated is $128.13

Answer:

[tex]\left\{\begin{array}{l}x\ge 0\\ \\y\ge 0\\ \\x+y\ge 20\\ \\3.5x+5y\le 80\end{array}\right.[/tex]

Step-by-step explanation:

Let x be the number of small candles and y be the number of large candles.

Santhi needs to buy at least 20 candles, so

[tex]x+y\ge 20[/tex]

Small candles:

Cost of 1 small candle = $3.50

Cost of x small candles = $3.50x

Large candles:

Cost of 1 large candle = $5.00

Cost of y large candles = $5.00y

Total cost of all candles:

$3.50x + $5.00y

Thus,

[tex]3.5x+5y\le 80[/tex]

Using Desmos, plot the system of two inequalities:

[tex]\left\{\begin{array}{l}x+y\ge 20\\ \\3.5x+5y\le 80\end{array}\right.[/tex]

Answer: 1. 210 meters per second .

2.  756  kilometers per hour.

Step-by-step explanation:

Given : The formula [tex]S(d)=\sqrt{9.8d}[/tex] to calculate the estimated speed, in meters per second of a tsunami.

1. If the disturbance occurred at an ocean depth of 4,500 meters.

Then put d= 4500 in the above formula , we get

[tex]S(d)=\sqrt{9.8\times4500}[/tex]

[tex]S(d)=\sqrt{44100}=\sqrt{21\times21\times10\times10}\\\\=\sqrt{210^2}=210[/tex]

Hence, if the disturbance occurred at an ocean depth of 4,500 meters , the estimated speed would be 210 meters per second .

Also, A meter per second is equal to 3.6 kilometers per hour.

i.e. 1 meter per second = 3.6 kilometers per hour

Then by unitary method ,

210 meters per second  =[tex]3.6\times210[/tex] kilometers per hour

=756  kilometers per hour.

Answer:

x=1y=3

Step-by-step explanation:

i just got it right

x=1 and y=3 are solutions of the system of equations

The given system of equations are

21x+7y=42 .....(1) and

-5x+5y=10....(2)

Multiply equation (1) with 5 and equation 2 with 7 to eliminate y

105x+35y=210..(3)

-35x+35y=70...(4)

Subtract equation 4 from 3

105x+35y+35x-35y=210-70

140x=140

Divide both sides by 140

x=1

Now plug in x value in equation 1

21+7y=42

7y=42-21

7y=21

Divide both sides by 7

y=3

Hence, the solutions of the system of equations are x=1 and y=3

To learn more on Equation:

https://brainly.com/question/10413253

#SPJ2

Answer:

C = (5/9)(F-32)

Step-by-step explanation:

F = (9/5)C + 32    (subtract 32 from both sides)

F - 32 = (9/5)C     (multiply both sides by 5/9 and rearrange))

C = (5/9)(F-32)

F = 9/5·C + 32

5F = 9C + 32·5

9C = 5F - 5·32

9C = 5(F - 32)

C = 5(F - 32)/9

Answer:

1.5 miles per hour

Step-by-step explanation:

9 (1/6) = 1.5

Answer:

1.5 miles per hour

Step-by-step explanation:

In the attached file

Answer:

3x + 4y = 50

x + y = 15

Five 4-point questions

Step-by-step explanation:

Change x + y = 15 to determine what y equal

y = (-x) + 15

Plug it in the original equation using the substitution method

3x + 4(-x + 15) = 50

3x - 4x + 60 = 50

Combine like terms:

-x = -10, two negative signs equals a positive. x = 10

Plug 10 in for x in the equation x + y = 15

10 + y = 15

Subtract 10 from both sides

y = 5

Answer:

14/70 or 1/5

Step-by-step explanation:

Final answer:

Carlo has read 14 out of 70 books about George Washington.

Explanation:

To find the fraction of the books about George Washington that Carlo has read, we need to divide the number of books Carlo has read by the total number of books about George Washington in the library.

Carlo has read 14 books and there are 70 books about George Washington, so the fraction of books Carlo has read is 14/70.

Answer:

2/6, 3/9, 4/12 ...

Step-by-step explanation:

We can find equivalent fractions to 1/3 by multiplying the numerator, or top number, and the denominator, or bottom number, by the same factor.

The correct choices B, C, and D all represent the equation that Conner scored 25% more points than Max, using algebraic terms to demonstrate this proportional increase. Choices B and C show the total score as a multiple of Max's score, while D adds an extra 25% to Max's score.

The problem presented is an algebraic representation of a proportional relationship. Given that Conner scored 25% more points than Max, we can express this relationship in different but equivalent equations. Choices B, C, and D effectively communicate that Conner's score, c, is increased by 25% more than Max's score, m.

Choice B is written as c = (1 + 0.25)m, which represents a 100% (which is 1 in decimal form) of Max's score plus an additional 25%. Choice C simplifies this to c = 1.25m, which is another way to represent a 25% increase on Max's score. Choice D is expressed as c = m + 0.25m which sums Max's score with another 25% of it. Each of these equations correctly translates the scenario into a mathematical expression.

Answer:

see explanation

Step-by-step explanation:

Since l and m are parallel lines, then

11x - 47 = 6x - 2 ( corresponding angles )

Solve this equation for x

Subtract 6x from both sides

5x - 47 = - 2 ( add 47 to both sides )

5x = 45 ( divide both sides by 5 )

x = 9

Answer:

A

[tex]F(x)=-\frac{1}{1500}(x+20)(x+5)(x-15)[/tex]

B

[tex]=> F(x)=-\frac{x^3}{1500}-\frac{x^2}{150}+\frac{11x}{60}+1[/tex]

Step-by-step explanation:

Function and its graphs

Part A

The graph shown in the image corresponds to a cubic function because of its classical infinite branches, three real roots and two extrema values

Part B

Knowing the value of the three roots x=-20, x=-5, and x=15 we can express the cubic function in factored form:

[tex]F(x)=C(x+20)(x+5)(x-15)[/tex]

The value of C will be determined by using any particular point from the graph. Let's use (0,1)

[tex]1=C(0+20)(0+5)(0-15)[/tex]

[tex]C=-\frac{1}{1500}[/tex]

Replacing, we find the factored form of the function

[tex]F(x)=-\frac{1}{1500}(x+20)(x+5)(x-15)[/tex]

The standard form demands to expand all the products and simplify

[tex]F(x)=-\frac{1}{1500}(x^3+10x^2-275x-1500)[/tex]

[tex]=> F(x)=-\frac{x^3}{1500}-\frac{x^2}{150}+\frac{11x}{60}+1[/tex]

Answer:b

Step-by-step explanation: because if you subtract 44,640 minus 43,200 which equal 1440

44,640-43,200=1,440

Answer: B) 1440

Step-by-step explanation:

March: 44,640 Minutes

April: 43,200 Minutes

Subtract 44,640-43,200=1440

Answer:

3+2i

Step-by-step explanation:

(3+2i)(1)

3+2i

Answer: The answer is D

Answer:

Step-by-step explanation:

Hope this Helps ;)

Answer:

[tex]1.2 \times 10^{10}[/tex] spents on housing for each year for the state.

Step-by-step explanation:

Given:

Population of State = 2000000

Average Citizen spends on housing = 6000

We need to find total spent on housing for the state.

For finding total spent on housing for state we need to multiply Population of state with average citizen spends on housing.

Total spent on housing for state = Population of State [tex]\times[/tex] Average Citizen spends on housing = [tex]2000000 \times 6000 = 12000000000[/tex]

Now expressing the above in scientific notation we get;

Total spent on housing for state = [tex]1.2 \times 10 ^{10}[/tex]

Final answer:

The total amount spent on housing for a state with a population of 2,000,000, where each spends $6,000 annually, is $12,000,000,000, which is expressed in scientific notation as[tex]$1.2 x 10^{10}.[/tex]

Explanation:

The question asks us to calculate the total amount spent on housing for a state with a population of 2,000,000, where the average citizen spends $6,000 on housing each year. To find the total, we multiply the average spending per citizen by the total number of citizens, which is 2,000,000 citizens times $6,000 per citizen. The calculation is:

2,000,000 x $6,000 = $12,000,000,000

To express this astronomical sum of money in scientific notation, we convert the standard form into a product of a number between 1 and 10 multiplied by a power of 10. So:

$12,000,000,000 = [tex]$1.2 x10^{10}[/tex]

Answer:

43:12

Step-by-step explanation:

Answer:

3 7/12 or 43/12

Step-by-step explanation:

It's just 86/24

Question is Incomplete, Complete question is given below.

When mack babysits, he charges $12 an hour plus bus fare. The amount mack is paid depends on the number of hours he babysits.

1. If mack babysits for 1 hour and the bus fare is $2.50, how much will mack be paid?

2. If mack babysits for 4 hours and the bus fare is $2.50, how much will mack be paid?

Answer:

1. Total Amount mack will be paid for 1 hour is $14.50.

2. Total Amount mack will be paid for 4 hours is $50.50.

Step-by-step explanation:

Given:

Charges of mack for 1 hour = $12

bus fare = $2.50

We will fist find for part 1.

1) Given:

Number of Hours= 1

Charges of mack for 1 hour = $12

bus fare = $2.50

we need to find the amount he get paid for it can be calculated by Multiplying Charges of mack for 1 hour with number of hours and then adding bus fare

Total amount he will get paid = Charges of mack for 1 hour × Number of Hours + Bus fare = [tex]\$12\times 1 +\$2.50= \$14.50[/tex]

Hence, Total Amount mack will be paid for 1 hour is $14.50.

Now we will find for part 2.

2) Given:

Number of Hours= 4

Charges of mack for 1 hour = $12

bus fare = $2.50

we need to find the amount he get paid for it can be calculated by Multiplying Charges of mack for 4 hour with number of hours and then adding bus fare

Total amount he will get paid = Charges of mack for 1 hour × Number of Hours + Bus fare = [tex]\$12\times 4 +\$2.50= \$50.50[/tex]

Hence, Total Amount mack will be paid for 4 hour is $14.50.

Answer:

63

Step-by-step explanation:

[(5.5+3)*7]+[(12/3)*2]-4.5

[8.5*7]+[4*2]-4.5

59.5+8-4.5

67.5-4.5

63

Multiplication: (-2)(3) = -6

Division: (-2)/(3) = [tex]-\frac{2}{3}[/tex] or -0.67

Final answer:

The solution to the inequality -2x ≤ -10 is found by dividing both sides by -2 and reversing the inequality sign, resulting in C) x ≥ 5.

Explanation:

The expression that represents the solution to -2x ≤ -10 is found by dividing both sides of the inequality by -2. When dividing by a negative number, we must reverse the inequality symbol. Thus, dividing both sides by -2 would give us x ≤ 5. However, since the inequality symbol was reversed, the correct solution is x ≥ 5.

Here are the steps broken down:

Starting with -2x ≤ -10.

Dividing both sides by -2 gives x ≥ 5.

Therefore, the correct answer is C) x ≥ 5.

Answer:

51.5 therms of natural gas

Step-by-step explanation:

19.57/0.38= 51.5

Answer: 51.5 therms

Step-by-step explanation:

$0.38 per therm

amount of money paid/rate=therms used

19.57/0.38=51.5

Answer: 11

Step-by-step explanation: The factors of 88 are 1,2,4,8,11,22,44,88; The factors of 121 are 1,11,121.

Final answer:

To find the greatest common factor (GCF) of 88 and 121, determine the common factors through their prime factorizations, which results in 11 as the GCF.

Explanation:

The greatest common factor (GCF) of 88 and 121 can be found by determining the largest number that can evenly divide both numbers. To find the GCF:

Answer:

18 pieces are needed

Step-by-step explanation:

Edgings are put all around the rectangular flower garden. So we need to know the perimeter (sum of all sides) of the rectangle. The formula is:

Perimeter of Rectangle = 2(Length + Width)

Given,

Length = 15

Width = 12

So,

Perimeter = 2(Length + Width)

Perimeter = 2(15 + 12)

Perimeter = 2(27)

Perimeter = 54

So, we need to cover 54 feet. Each edging is 3 feet in length, so 54 feet will be covered by:

54/3 = 18 edgings

Answer:

27

Step-by-step explanation:

Substitute x = 3 into the expression

2(3)² + 3(3) = 2(9) + 9 = 18 + 9 = 27

Answer:

13

Step-by-step explanation:

2×2=4+3(3)=4+9=13

Answer:

x=39, y = 5 and z = -4.

Step-by-step explanation:

x + y - 5z = 24

y + z = 1

z = -4

Plug z = -4 into the second equation:

y + -4 = 1

y = 5.

Now plug x = -4 and y = 5 into the first equation:

x + 5 - 5*4 = 24

x = 24 - 5 + 20

x = 39.

Answer:

19 and 20

Step-by-step explanation:

19^3 = 6859

20^3 = 8000

7201 is between the two numbers.