MATHEMATICS HIGH SCHOOL

The arithmetic mean (A) of two numbers (a and b) is given by the formula A=a b2, and their geometric mean (G) is given by G=ab−−√. Their harmonic mean (H) is given by the formula G=AH−−−√. Which formula correctly gives H in terms of a and b?

Answers

Answer 1

Answer:

Answer:

$H = (2ab)/(a+b)$

Step-by-step explanation:

As per the given statement:

The arithmetic mean (A) of two numbers (a and b) is given by the formula:

$A = (a+b)/(2)$ .....[1]

and

their geometric mean (G) is given by :

$G = √(ab)$ .....[2]

Their harmonic mean (H) is given by the formula:

$G = √(AH)$

Squaring both sides we get;

$G^2 = AH$

Substitute the given values we have;

$(√(ab))^2 =(a+b)/(2) \cdot H$

⇒ $ab = (a+b)/(2) \cdot H$

Multiply by 2 both sides we have;

$2ab = a+b \cdot H$

Divide both sides by a+b we have;

$(2ab)/(a+b) =H$

$H = (2ab)/(a+b)$

Therefore, the formula correctly gives H in terms of a and b is, $H = (2ab)/(a+b)$

Answer 2

Answer: $G=√(AH) \n G^2=(√(AH))^2 \nG^2=AH \nH=(G^2)/(A) \n \n A=(a+b)/(2) \hbox{ and } G=√(ab) \n \Downarrow \nH=(G^2)/(A)=((√(ab))^2)/((a+b)/(2))=(ab)/((a+b)/(2))=ab * (2)/(a+b)=(2ab)/(a+b) \n \n\boxed{H=(2ab)/(a+b)}$

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Determine the value of A1 withreason/s

Answers

Answer:A1 = a If A1 represents a variable in an equation, we need the equation and any additional information to solve for its value. Once we have the equation and any given values, we can substitute those values into the equation and solve for A1. Without more context or information, it is not possible to determine the value of A1. If you can provide the equation or any additional details, I will be able to help you further in determining the value of A1.

Step-by-step explanation:

A map has a scale of 1 cm to 2.3 km. The real-life distance between two towns is 69 km. What is the distance between the two towns on the map?

Answers

Answer:

Step-by-step explanation:

Cm : km

1 : 2.3

x : 69 Cross multily

2.3x = 69

x = $(69)/(2.3)$

x = 30cm

the distance between the two towns on the map is 30cm

Answer:

30 cm

Step-by-step explanation:

69/2.3 = 30

Help answer all questions please and tell me how you got the answers

Answers

8. You start with 240 gallons if in march you use 40% (.4(240)=96) you used 96 gallons in march, leaving you with 144 gallons. If you then used 25% in April (.25(144)=36) you would have used 36 gallons leaving you with 108 gallons at the end of April.

9. If 2277 is 110% the number of 2013 to find what 2013 was you would divide by 110%(1.1)
2277/1,1=2070 at the end of 2013
If 2070 is 90% then we will want to divide by 90% (.9) to get the year before that
2070/.9=2300 so 2300 people were signed up in the year 2012

10. 57.5=p(250)
to solve this divide both sides by 250 to get p=.23
As for the different elements to the equation, there are various answers such as what percentage of people donated $250 if the average amount of money donate from each one is 57.5 although that may no be what you instructor is looking for. pretty much just make up something that sounds okay and you should be fine

If the sales tax is 7% and the purchase price is $161, what is the amount of tax?

Answers

$7 \% \ from \ 161 \ = \ (7)/(100) * 161 = ( 1127)/(100) = 11,27\ is \ amount \ of \ tax \$

Rachel works for a clothing store. She is paid $150 every week plus a 10% commission on any clothes that she sells.

Answers

Answer:

$165

Step-by-step explanation:

Rachel works for a clothing store. She is paid $150 every week plus a 10% commission on any clothes that she sells.

Let's find the total amount she is being paid per week

Amount paid originally = $150

Percentage Commission = 10%

Commission = 10% of 150

Commission = 0.1×150

Commission = $15

Total amount paid = originally amount + Commission

Total amount paid = $150+$15

Total amount paid =$165

Hence the amount paid to Rachel okus Commission is $165

What is the area of a triangle with vertices at (0, −2) ,(8, −2) , and (9, 1) ?
Enter your answer in the box

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Answers

The area of a triangle with vertices at (0, −2) ,(8, −2) and (9, 1) is 12 square units

Solution:

Given, vertices of the triangle are A(0, -2), B(8, -2) and C(9, 1).

We have to find the area of the given triangle.

The area of triangle when vertices are given is:

$\text { Area of triangle }=(1)/(2)\left|x_(1)\left(y_(2)-y_(3)\right)+x_(2)\left(y_(3)-y_(1)\right)+x_(3)\left(y_(1)-y_(2)\right)\right|$

$\text { Where, }\left(x_(1), y_(1)\right),\left(x_(2), y_(2)\right),\left(x_(3), y_(3)\right) \text { are vertices of the triangle. }$

Here in our problem,

$\left(\mathrm{x}_(1), \mathrm{y}_(1)\right)=(0,-2),\left(\mathrm{x}_(2), \mathrm{y}_(2)\right)=(8,-2) \text { and }\left(\mathrm{x}_(3), \mathrm{y}_(3)\right)=(9,1)$

Now, substitute the above values in the formula:

$\text { Area of triangle }=(1)/(2)\left|x_(1)\left(y_(2)-y_(3)\right)+x_(2)\left(y_(3)-y_(1)\right)+x_(3)\left(y_(1)-y_(2)\right)\right|$

$\begin{array}{l}{=(1)/(2)|0(-2-1)+8(1-(-2))+9(-2-(-2))|} \n\n {=(1)/(2)|0+8(1+2)+9(2-2)|} \n\n {=(1)/(2)|0+24+0|} \n\n {=(24)/(2)} \n\n {=12 \text { square units }}\end{array}$

Hence, the area of the triangle is 12 square units.

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