1/a+1/b=1/c, what is the average (arithmetic mean) of a and b?

Answers

Answer 1

The arithmetic mean of a and b in the expression  1/a + 1/b = 1/c is 2c.

What is the arithmetic mean or average?

Arithmetic mean or average can be obtained by adding all the given values and then dividing the total sum by the number of values.

Given, An expression of the form 1/a + 1/b = 1/c.

We know average of two numbers is sum of those numbers divided by 2.

So,  {(1/a) + (a/b)}/2 = 1/c.

Now to keep the equality we also have to divide the RHS by 2.

Therefore,   {(1/a) + (a/b)}/2 = (1/c)/2.

{(1/a) + (a/b)}/2 = (1/c)×((1/2).

{(1/a) + (a/b)}/2 = 1/2c.

So, The arithmetic mean of 1/a + 1/b is 1/2c.

Now taking the reciprocal of 1/a and 1/b which is a and b the arithmetic mean is

2c.

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Related Questions

consider the table, which reports the fruit diameter and number of offspring obtained by the researcher in the f2 generation. in the parental lines, l. cheesmanii had a fruit diameter of 8 cm and l. esculentum had a fruit diameter of 16 cm .

Answers

The total number of genes involved in fruit diameter in tomatoes is 4.

[tex]1/4^{n}[/tex] = ratio of F2 individuals expressing either extreme Phenotype

In the above equation, 'n' represents the number of genes involved.

The term 'extreme phenotype' refers to the phenotype of one of the parents from the P1 generation. In this case, it denotes the parents with fruit diameters of 8 cm and 16 cm. In the F2 generation, which consists of a total of 256 offspring, there is only 1 offspring that resembles either P1 parent.

The ratio of individuals expressing either extreme phenotype = Number of springs with either extreme phenotype / Total number of off spring.

ratio of F2 individuals expressing either extreme Phenotype = 1/256

Apply the value of 1/256 to the first equation.

That is, [tex]1/4^{n}[/tex]  = 1/256

1[tex]1/4^{4}[/tex] = 1/256

As shown above, the value of 'n' is 4.

Therefore, the total number of genes involved in fruit diameters is 4.

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Which of the following is the correct boolean expression to test for:
int x is being a value between, including, 500 and 650, or int y not equal to 1000?
O ((x >= 500 && x <= 650)|| (y != 1000))
O ((x > 500 AND x < 650) OR !(y. equal(1000)))
O ((x > 500 && x < 650) || (y != 1000))
O ((x < 500 && x > 650) || !(y == 1000))

Answers

The correct boolean expression to test for int x being a value between, including, 500 and 650, or int y not equal to 1000 is:

((x >= 500 && x <= 650)|| (y != 1000))

This expression uses the "&&" operator to test for x being greater than or equal to 500 and less than or equal to 650, and the "||" operator to test for y not being equal to 1000. The expression is using the correct comparison operators and logical operators to test for the desired conditions.

A boolean expression is a statement that evaluates to either true or false. It is commonly used in programming to control the flow of a program, as the result of a boolean expression can be used to determine whether a certain block of code should be executed or not.

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The path of the airplane the astronauts are flying
in can be modeled using the function h(x) =
10000cos(0.0001x) + 20000 in which h indicates
the height in feet. What is the approximate period
of the wave?

Answers

Answer:

The approximate period of the wave representing the airplane's path is 0.9 hours.

Step-by-step explanation:

The period of a wave is the time it takes for one complete cycle of the wave to occur. In the case of the airplane's path, this would be the time it takes for the airplane to complete one full oscillation, or "up and down" motion.

To find the period of the wave, we need to determine the value of x that corresponds to one complete cycle of the wave. In this case, the wave is defined by the function h(x) = 10000cos(0.0001x) + 20000.

To find the period, we can use the formula T = 2π/ω, where T is the period, π is the mathematical constant pi, and ω is the angular frequency of the wave. The angular frequency is related to the frequency of the wave, which is the number of cycles per second.

In this case, the angular frequency is given by the coefficient of the x term in the function, which is 0.0001. Plugging this value into the formula above, we get T = 2π/0.0001 = 200000π seconds.

Since one cycle of the wave corresponds to one complete oscillation of the airplane, the period of the wave is approximately 200000π seconds. This is a very large number, so it is usually more useful to express the period in minutes or hours. To convert to minutes, we can divide the period by 60, which gives us a value of about 3334 minutes. To convert to hours, we can divide the period by 3600, which gives us a value of about 0.9 hours.

In summary, the approximate period of the wave representing the airplane's path is 0.9 hours.

Ask me any questions you may have!

The amount of time it takes for a wave to complete one full cycle is known as the wave's period. This would be the amount of time needed for the plane to perform one full oscillation, or “up and down” motion, in the case of the flight path.

What path airplane the astronaut's period of the wave?

Finding the value of x that represents the wave's full cycle is necessary to calculate the wave's period. The equation h(x) = 10000cos(0.0001x) + 20000 in this instance defines the wave.

The formula T = 2/, where T is the period, is the mathematical constant pi, and is the wave's angular frequency, can be used to determine the period. The wave's frequency, or the number of cycles per second, and the angular frequency are connected.

We may convert the period to hours by dividing it by 3600, which gives us a number of approximately 0.9 hours.

Therefore, The wave that represents the course of the airplane has an approximate period of 0.9 hours.

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Please explain your answer to this question! Thank you!

Answers

Answer:

  B.  Incorrectly applied the distributive property

Step-by-step explanation:

You want to find Maria's error in her solution of -2(3x -5) = 40.

Steps

The solution can proceed as follows:

  -2(3x -5) = 40 . . . . . . . . given

  -6x +10 = 40 . . . . . . . . . use the distributive property

  -6x = 30 . . . . . . . . . . subtract 10

  x = -5 . . . . . . . . . . divide by -6

Comparing this solution to Maria's, we find that Maria incorrectly applied the distributive property. (She multiplied (-2)(-5) and got -10 instead of +10.)

How do you classify -15

Answers

-15 is an integer , rational and a real number

What are rational,real numbers and integers?

Real numbers are mainly classified into rational and irrational numbers. Rational numbers include all integers and fractions. All negative integers and whole numbers make up the set of integers. Whole numbers comprise of all natural numbers and zero.

A negative number is not a natural number.

This means that -15 is a real number because real number comprises of rational and irrational number and rational numbers include negative numbers and they are called negative integers.

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does anyone know this ​

Answers

The correct equivalent expression to the square root containing a variable is 2a³/5 and the correct option is E.

How to determine the equivalent expression

We shall simplify the expression of the square root containing a variable by carrying out basic mathematics operations to derive its equivalent as follows:

squre root of (36a⁸/255a²) = square root of (36a⁶ × a²/255 × a²)

a² is common and can be cancel out

square root of (36a⁸/255a²) = square root of (36a⁶/255)

square root of (36a⁸/255a²) = square of 36 multiplied by the square root of a⁶ all divided by the square root of 255 {take square root of each}

square root of (36a⁸/255a²) = 6a³/15

square root of (36a⁸/255a²) = 2a³ × 3/5 × 3

we divide through by the common factor 3

square root of (36a⁸/255a²) = 2a³/5

Therefore, the equivalent expression to square root of (36a⁸/255a²) is derived as 2a³/5 which is option E.

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A tool set is on sale for $424.15. The original price of the tool spt was $499.00. What percent of the original price
is the sale price?

Answers

Answer:

94 percent.

Step-by-step explanation:

Since the tool set used to be worth 499, but is now worth 424.15, we divide the two prices.

             Calculation.

424.15/499 = 0.944654788.

We are figuring out the percent, so we need to round.

0.94465478 is about 0.94

0.94 IS EQUALVENT to 94%, so that is our answer.

11 A fisherman wants to know how many fish there are in a lake. One day, he catches 50, marks them and puts them back. The next day he catches 80 fish. 20 of these fish have marks on them. Estimate the total number of fish in the lake.​

Answers

The total number of fish in the lake would be = 60 fishes

What is total of a data set?

The total of a data set is the addition of the various components that makes up a data set which gives a particular value.

On the first day the number of fish that was marked by the fisher man = 50 fishes.

On the second day the total amount of fishes that was caught = 80 fishes

The number of fishes that where among the 80 fishes that are marked= 20

Therefore the total amount of fishes in the lake = 80 - 20

= 60 fishes.

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A tree is 108 inches tall. A second tree is 120 inches tall. What is the combined height of the trees?

Answers

Answer:228

Step-by-step explanation:

All you have to do is add 108 to 120.

0+8=8, 2+0=2, 1+1=2

   120

   108

+_____

   228

The answer is 228 this is solved my addition

For 7.45 - 3.029 why do you rewrite 7.45 as 7.450

Answers

For 7.45 - 3.029 the reason why they rewrite 7.45 as 7.450 is so as to have both values in three decimal place so the calculation can be easier.

What is decimal place?

It should be noted that the first digit after the decimal represents the tenths place then the next digit after the decimal  could be reffered to as  hundredths place however the remaining digits continue to fill in the place values until there are no digits left.

It should be noted that Decimal place value  can be described as the place values of all the digits in a given decimal number.

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Find the vertex of each of the following parabolas by averaging the x-intercepts. Then write each equation in graphing form. y=(x-3)(x-11)

Answers

The vertex of the parabola is at the point (7, 0) and since the vertex of this parabola is (7, 0), the equation of the parabola in graphing form is

y = a(x - 7)^2.

The vertex of a parabola is the point on the graph where the parabola reaches its highest or lowest point. To find the vertex of the parabola y = (x - 3)(x - 11), you can average the x-intercepts of the parabola, which are the points where the parabola crosses the x-axis. The x-intercepts of this parabola are at x = 3 and x = 11, so the average of these two points is (3 + 11) / 2 = 7.

To write the equation of the parabola in graphing form, you can use the vertex form of a parabola, which is written as

y = a(x - h)^2 + k

where (h, k) is the vertex of the parabola and a is a coefficient that determines the direction of the parabola (whether it opens upwards or downwards). Plugging in the values for the vertex and the y-coordinate of the vertex (which is 0), we get

y = a(x - 7)^2 + 0.

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Which equation is the inverse of 2(x - 2)² = 8(7+ y)?
O-2(x-2)2 = -8(7+ y)
Oy-x²-x-6
O y=-2± √√28+4x
Oy-2± √√28+4x

Answers

Answer:

[tex]2+2\sqrt{-1(-7-x)}\\2-2\sqrt{-1(-7-x)}[/tex]

Step-by-step explanation:

The inverse of [tex]2(x-2)^2=8(7+y)[/tex] is

[tex]2+2\sqrt{-1(-7-x)}\\2-2\sqrt{-1(-7-x)}[/tex]

. Acme Burgers sells a large pop which is 14 oz and comes in a 8" high container. The small pop comes
in a 6" high container which is the same shape as the small pop container. How much does the small
container hold?

Answers

Answer:

10.5 oz

Step-by-step explanation:

The large pop and container are similar to the small pop and container.

Thus, we can use proportions to find how much the small container can hold, letting x represent the volume of the small container:

[tex]\frac{14}{8}=\frac{x}{6}\\ 8x=84\\ x=21/2=10.5[/tex]

Find The length of the third side. If necessary, round to the nearest tenth. need answer ASAP

Answers

The length of the third side is 16.5 for the given right-angle triangle. By using Pythagoras' theorem, the required length is calculated.

What is the Pythagoras theorem?The theorem is given by (hyp)² = (opp)² + (adj)².This theorem applies to a right-angle triangle only.

Calculation:

The given triangle is a right-angle triangle.

It has two lengths. They are

length of the hypotenuse = 21

length of the adjacent or base = 13

Then, the third side i.e., the opposite side length is calculated by

(hyp)² = (opp)² + (adj)²

⇒ (21)² = (opp)² + (13)²

⇒ 441 = (opp)² + 169

⇒ (opp)² = 441 - 169 = 272

⇒ opposite side length = √272 = 16.49 ≅ 16.5

Therefore, the length of the third side is 16.5.

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What is the value of the expression:

6 - 5x when x = -2?

Answers

Answer: 16

Step-by-step: 6 - (5(-2)=-10 then the - turns into + and your answer is 6 + 10

The positive integers greater than 3 are arranged in rows and columns as illustrated.
In which column is the number 5018?
A) 2
B) 4
C) 6
D) 5
E) 3

Answers

The rows and columns of the positive integers greater than three are as shown. And the number 5018 is found in the third column.

When performing a permutation test, you repeatedly rearrange one of the variables without affecting the other variable (s). From the given table, we can start with column 4. Here, each row has about 6 numbers. That is singular row has numbers from columns 1 to 6 and an even row from columns 7 to 2.

Then subtract 5018 by 3. We get 5018-3=5015.

Divide this by 6,

5015/6 = 836.

So 5018 is located in an even row from 7 to 2.

Therefore, 5018 is located in the 836th row and 3rd column.

So the required answer is E) 3.

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Determine the whole number of standard deviations that includes all data values. The mean price of the nonfiction books on a best-sellers list is $24.18; the standard deviation is $ 3.98.

$19.95, $24.00, $21.00, $28.95, $19.00, $27.95, $19.00, $25.95, $26.00, $29.95

All of the values fall within __ standard deviation (s) of the mean.

Answers

All of the values fall within 1.45 standard deviation of the mean.

How to illustrate the standard deviation?

From the information given, the mean price of the nonfiction books on a best-sellers list is $24.18 and the standard deviation is $3.98.

It should be noted that from the problem, the variable that is the farthest from the mean is $29.25.

Therefore, the z score will be illustrated as:

Z = (29.95 - Mean) / Standard deviation

Z = (29.95 - 24.18)) / 3.98

= 1.45

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Solve for y:
2π=2y+6x

Answers

Answer: y=pi-3

Step-by-step explanation:

2pi=2y+6

2pi-6=2y

(2pi-6)/2=y

pi-3=y

y=pi-3

hope this helped

What reason would you use to prove ΔFGH ≅ ΔJHK ?
Select one:
ASA
HL
SAS
cannot prove congruency
SAA

Answers

The reason that is used to prove ΔFGH ≅ ΔJHK is SAS property

If the three angles and the three sides of a triangle are equal to the corresponding angles and the corresponding sides of another triangle, then both the triangles are said to be congruent.

The two triangles need to be of the same size and shape to be congruent. Both the triangles under consideration should superimpose on each other.

According to the question,

Given : (1) ∠FGH and ∠JHK are right angles

(2) H is midpoint of GK

(3) GH ≅ JK

In ΔFGH and ΔJHK

∠FGH = ∠JHK ( right angles )GH ≅ JK (given) GH = KH ( H is midpoint of GK )

Therefore ,  ΔFGH  ≅ ΔJHK using  SAS property

Hence , The reason use to prove ΔFGH ≅ ΔJHK is SAS

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a response variable y has correlation coefficient 0.3 with each of the predictors x1 and x2. however, these predictors are heavily correlated r x1x2

Answers

If the response variable y has a correlation coefficient of 0.3 with each of the predictors x1 and x2, it means that there is a weak linear relationship between y and both x1 and x2.

This means that as x1 and x2 increase or decrease, y is likely to change by a small amount. If x1 and x2 are heavily correlated, it means that there is a strong linear relationship between the two variables. This means that as x1 increases or decreases, x2 is likely to change by a large amount in the same direction. When two predictors are highly correlated, it can be difficult to determine the individual contribution of each predictor to the response variable y.

In this situation, it may be useful to use techniques such as multi-collinearity analysis or principal component analysis to understand the relationship between the predictors and the response variable better.

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i need help asap!!!!!

Answers

Answer:

The slope is same for both points.

Step-by-step explanation:

1st set of points: (1, 4) and (7, 2)

m = 2-4/7-1

m = -2/6

m = -1/3

2nd set of points: (7, 2) and (10, 1)

m = 1-2/10-7

m = -1/3

The slope is same for both points.

An entry-level civil engineer earns an average bi-weekly net pay of $2,175.25. The engineer has created a monthly budget using the following percentages for expenses:


Percent
Housing 35%
Food/Household 10%
Savings 10%
Transportation 15%
Debt 5%
Entertainment 6%
Medical/Personal Care 5%
Giving 5%
Clothing 4%
Miscellaneous 5%


Which balance sheet correctly represents the engineer's income, expenses, and balance?

Income
Amount
Bi-weekly income $2,175.25
Total Monthly Income $2,175.25
Expenses
Percent Amount
Housing 35% $761.34
Food/Household 10% $217.53
Savings 10% $217.53
Transportation 15% $326.29
Debt 5% $108.76
Entertainment 6% $130.52
Medical/Personal Care 5% $108.76
Giving 5% $108.76
Clothing 4% $87.01
Miscellaneous 5% $108.76
$2,175.25
Balance
Income $2,175.25
Expenses $2,175.25
Balance $0

Income
Amount
Bi-weekly income $2,175.25
Total Monthly Income $3,262.88
Expenses
Percent Amount
Housing 35% $1,142.01
Food/Household 10% $326.29
Savings 10% $326.29
Transportation 15% $489.43
Debt 5% $163.14
Entertainment 6% $195.77
Medical/Personal Care 5% $163.14
Giving 5% $163.14
Clothing 4% $130.52
Miscellaneous 5% $163.14
$3,262.88
Balance
Income $3,262.88
Expenses $3,262.88
Balance $0

Income
Amount
Bi-weekly income $2,175.25
Total Monthly Income $4,713.04
Expenses
Percent Amount
Housing 35% $1,649.56
Food/Household 10% $471.30
Savings 10% $471.30
Transportation 15% $706.96
Debt 5% $235.65
Entertainment 6% $282.78
Medical/Personal Care 5% $235.65
Giving 5% $235.65
Clothing 4% $188.52
Miscellaneous 5% $235.65
$4,713.04
Balance
Income $4,713.04
Expenses $4,713.04
Balance $0

Income
Amount
Bi-weekly income $2,175.25
Total Monthly Income $4,350.50
Expenses
Percent Amount
Housing 35% $1,522.68
Food/Household 10% $435.05
Savings 10% $435.05
Transportation 15% $652.58
Debt 5% $217.53
Entertainment 6% $261.03
Medical/Personal Care 5% $217.53
Giving 5% $217.53
Clothing 4% $174.02
Miscellaneous 5% $217.53
$4,350.50
Balance
Income $4,350.50
Expenses $4,350.50
Balance $-

PLEASE HELP

Answers

The balance sheet that correctly represents the engineer's income, expenses and balance is balance number 4.

How tp determine percentages of income?

We should know that balance sheet is a summary of assets and liabilities and income and expenses of a  legal person.

We are told that the the balance sheet shows a bi-weekly net pay

This implies that a month has two bi-weeks.  therefore every income and expenses is multiplied by 2 to get the following figures.

Income                                             Amount

Bi-weekly income                          $2,175.25

Total Monthly Income                   $4,350.50

Expenses                 Percent                              Amount

Housing                      35%                                $1,522.68

Food/Household          10%                               $435.05

Savings                         10%                                $435.05

Transportation              15%                                $652.58

Debt                              5%                                   $217.53

Entertainment              6%                                   $261.03

Medical/Personal Care 5%                                  $217.53

Giving                             5%                                 $217.53

Clothing                        4%                                  $174.02

Miscellaneous              5%                                 $217.53

                                                                           $4,350.50

Balance

Income $4,350.50

Expenses $4,350.50

Balance $0

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Secondary Mortgage Purchasing Company (SMPC) wants to buy your mortgage from the local savings and loan. The original balance of your mortgage was $153,000 and was obtained five years ago with monthly payments at 10 percent interest. The loan was to be fully amortized over 30 years.



Required:

a. What should SMPC pay if it wants an 11 percent return?

b. What is the balance of the original loan after five additional years (10 years from origination)?

Answers

SMPC should pay 136,992.36$ if it wants an 11 percent return. and the balance of the original loan after additional years 142,229.05$.

What is the monthly rate of the loan?

A monthly rate is a fee for services calculated over a thirty-day period.

Given, Your mortgage will be purchased by the Secondary Mortgage Purchasing Company (SMPC) from the nearby savings and loan. Your mortgage had an initial amount of $153,000 and was obtained five years ago with regular payments at a 10% interest rate. The loan was to be completely repaid over a 30-year period.

Payment Formula  =   PMT (monthly rate, month, -mortgage)

Present value formula   =  PV( monthly rate, month left, - payment, - repayment)

Loan value formula  = PV (monthly rate, month left, -payment)

a. formula   = PMT( 10%/12, 30*12, -153000)

Payment  =  $1342.68

Formula    =  PV(11%/ 12, (30-5)* 12, -1342.68)

Smpc pays  =  $136,992.36

b. Loan balance    =    139134.70$

Formlua   = PV(11%12,5*12, - 1342.68, -139134.7)

Smpc pays  = 142,229.05$

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A roller coaster ride holds a total of 48 passengers. The ratio of males to females on the ride is 5 : 7. Let x represent the number of males on the ride. Let y represent the number of females on the ride. Which two linear equations form a system that you can use to find the number of males and the number of females on the ride?

Answers

Answer:

5x + 7y = 48 (total number of passengers on the ride)

x + y = 48 (total number of males and females on the ride)

Step-by-step explanation:

To find the number of males and the number of females on the roller coaster ride, you can use the following two linear equations to form a system:

5x + 7y = 48 (total number of passengers on the ride)

x + y = 48 (total number of males and females on the ride)

The first equation states that the total number of passengers on the ride is equal to the sum of the number of males (5x) and the number of females (7y). The second equation states that the total number of males and females on the ride is equal to the sum of the number of males (x) and the number of females (y).

To solve this system, you can use algebraic techniques to eliminate one of the variables and solve for the other. For example, you could multiply the first equation by 5 and the second equation by 7, then subtract the two equations to eliminate the y variable:

5 * 5x + 7 * 7y = 5 * 48

7 * x + 7 * y = 7 * 48

25x + 49y = 240

49x + 49y = 336

24x = 336 - 240

24x = 96

x = 4

Substituting this value for x in the first equation, we can solve for y:

5 * 4 + 7 * y = 48

20 + 7 * y = 48

7 * y = 28

y = 4

Therefore, there are 4 males and 4 females on the roller coaster ride.

What is the slope in the given line?

Answers

-2/3 because it’s rise over run

Answer:

[tex]-\frac{2}{3}[/tex]

Step-by-step explanation:

The slope/gradient of a line is defined by this formula:

[tex]\frac{y_{1}-y_{0} }{x_{1}-x_{0} }[/tex]

Where you pick two coordinates, find the change in the [tex]y[/tex] values, and divide it by the change in the [tex]x[/tex] values.

Two coordinates that this line passes through are (3, -2) and (-3, 2).

You can take the second [tex]y[/tex]-value (2) from the first [tex]y[/tex]-value (-2) or vice versa, so long as you do it in the same order the [tex]x[/tex] values.

For this example, I will take the first [tex]y[/tex]-value (-2) from the second [tex]y[/tex]-value (2), and take the first [tex]x[/tex]-value (3) from the second [tex]x[/tex]-value (-3).

The gradient/slope is defined by [tex]m[/tex] in the following:

[tex]m=\frac{2--2}{-3-3}=\frac{4}{-6}=-\frac{4}{6}=-\frac{2}{3}[/tex]

Calculate the slope over the interval 1≤ x<3.

Answers

The slope over the interval 1 ≤  x < 3 is m = 3 / 2 .

Given :

the slope over the interval 1 ≤  x < 3

From the graph :

take two points which lies on the interval

( 1 , 0 ) and ( 3 , 3 )

slope :

Slope is the ratio of the rise, the vertical change, to the run, the horizontal change of a line .

slope m = y2 - y1 / x2 - x1

= 3 - 0 / 3 - 1

= 3 / 3 - 1

= 3 / 2

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The perimeter of a triangle is 3x² + 6x - 9. If one side length is x² + 2x - 1 and the
other is x² + x - 5, what is the length of the 3rd side?

Answers

Answer:

x^2+3x-3

Step-by-step explanation:

(x^2+2x-1)+(x^2+x-5)

2x^2+3x-6

(3x^2+6x-9)-(2x^2+3x-6)

x^2+3x-3

hopes this helps

Answer:

[tex]x^2 + 3x - 3[/tex]

Step-by-step explanation:

The perimeter of a triangle, can be calculated as, the sum of the sides.

So let's first assume the third side is a polynomial, and more specifically, a quadratic in the form: [tex]ax^2+bx+c[/tex]. This assumption is denoted from the fact that the perimeter only has terms up to the degree of 2, also known as x squared. The answer is also a quadratic, so it isn't an unreasonable assumption that if we add two quadratics (the ones given), and add one more quadratic, we should still have quadratic.

So, the sum of the three sides can be expressed as: [tex](x^2 + 2x - 1) + (x^2 + x - 5) + (ax^2 + bx + c)[/tex]

We can combine like terms to get:

[tex](x^2+x^2+ax^2)+(2x+x+bx)+(-1-5+c)[/tex]

Now from here, we can combine like terms (add coefficients):

[tex](2+a)x^2 + (3+b)x + (-6+c)[/tex]

From here, we simply set this equal to the given perimeter of: [tex]3x^2 + 6x-9[/tex], which gives us the equation:

[tex](2+a)x^2 + (3+b)x+(-6+c) = 3x^2 + 6x - 9[/tex]

Now from here, the coefficients need to correspond for both quadratics to be equal to each other, so that means that the following must be true:
[tex](2+a)=3\implies a = 1\\(3 + b) = 6\implies b = 3\\(-6 +c) = -9 \implies c = -3[/tex]

We now plug this into the quadratic standard form to get:

[tex]x^2 + 3x - 3[/tex]

Which is our third side!

the sugar sweet company delivers sugar to its customers. let be the total cost to transport the sugar (in dollars). let be the amount of sugar transported (in tons). the company can transport up to tons of sugar. suppose that gives as a function of . identify the correct description of the values in both the domain and range of the function. then, for each, choose the most appropriate set of values.

Answers

The domain and the range of a function are the possible input and output values of the function.

The function is given as:

C = 130S + 3500

The domain

This is the possible S values of the function.

S cannot be less than 0, because it represents a physical quantity (i.e. tons of sugar)

The value of S can be any value greater than 0

Hence, the domain of the function is [0, ∞)

The range

This is the possible C values of the function.

The function is given as:

C = 130S + 3500

When S = 0

C = 130(0) + 3500

C = 3500

The above means that:

C cannot be less than 3500

The value of C can be any value greater than 3500

Hence, the range of the function is [3500, ∞)

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3. The graph of function g(x) is shown below.

Answers

Answer:

Step-by-step explanation:

g(x) = 2*[tex]\sqrt{x}[/tex] + 4

Domain is the input  so what limits are there to the input?

for the square root, you are told that you can't not put in negative numbers until you learn about imaginary number in the for m  a+bi,  but for now, just say  the input is  0 to ∞,  for now   The domain is  0 to ∞

Range is the output

so that is from 4 to ∞

Answer:

  a. translation 2 right and up 4

  b. g(x) = √(x -2) +4

  c. domain: x ≥ 2; range: y ≥ 4

Step-by-step explanation:

You have the graph of a square root function with its vertex at (2, 4). You want to know what transformation that represents, the equation of the graph, and the domain and range of the function.

a. Transformation

The vertex of the square root function f(x) = √x is located at (0, 0). In the given graph, it has moved to (2, 4). The vertical and horizontal scale factors remain unchanged. This transformation is ...

  translation right 2 units and up 4 units

b. Equation

Translation of function f(x) by h units right and k units up gives you ...

  g(x) = f(x -h) +k

Here, we have (h, k) = (2, 4), and f(x) = √x, so the transformed function is ...

  g(x) = √(x -2) +4

c. Domain and Range

The domain is the horizontal extent of the graph. For a square root function it is the x-value of the vertex, and all points to the right of that.

  domain of g(x): x ≥ 2

The range is the vertical extent of the graph. For a square root function it is the y-value of the vertex, and all points above that.

  range of g(x): y ≥ 4

Convert 13/50 to percent

Answers

Answer:

26%

Step-by-step explanation:

To convert a fraction to a percentage, you need to first convert the fraction to a decimal.To convert 13/50 to a decimal, you can divide 13 by 50, which gives you 0.26.To convert a decimal to a percentage, you need to move the decimal point two places to the right, which gives you 26%.So, 13/50 is equivalent to 26%.

The value of number 13/50 into percentage is,

⇒ 26%

What is mean by Percentage?

A number or ratio that can be expressed as a fraction of 100 or a relative value indicating hundredth part of any quantity is called percentage.

To Calculate the percent of a number , divide the number by whole number and multiply by 100.

Given that;

The number is,

⇒ 13/50

Now, We get;

The value of number 13/50 into percentage is,

⇒ 13/50 x 100%

⇒ 13 x 2%

⇒ 26%

Thus, The value of number 13/50 into percentage is,

⇒ 26%

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