Prove that a+b/2≥√ab

Answers

Answer 1
Start by squaring both sides got remove the sqrt
[(a+b)/2]^2 ≥ ab
(a^2 +2ab +b^2 )/4≥ ab
Multiply both sides by 4
a^2 +2ab +b^2 ≥ 4ab
Subtract 2ab from both sides
a^2 + b^2 ≥ 2ab
Subtract 2ab from both sides
a^2 - 2ab + b^2 ≥ 0
Use quadratic equation to solve where a = 1 and b = -2b
2b ± sqrt[(-2b)^2 - (4x1xb^2)]/(2x1)
2b ± sqrt[4b^2 - 4b^2]/2
(2b ± 0)/2
a = b
Substituting for b in the equation a^2 + b^2 ≥ 2ab
2a^2 ≥ 2a^2

Related Questions

Ryan earns $20 for every lawn that he mows.
Which set of ordered pairs represents the relationship between the number
of lawns Ryan mows and the money he earns?
Oa. (20,1),(40,2), (60, 3) Ob.(1, 20), (2, 40), (3, 60)
Oc. (0,20), (1, 40), (2, 60) Od. (1, 20), (2, 30), (3, 40)

Answers

Answer:

A is the correct answer

Answer:

B

Step-by-step explanation:

The first number should represent the lawns, and the second should represent the money he makes on each lawn.

A is incorrect because the numbers are swapped; Ryan does not earn one dollar for mowing 20 lawns.

C is wrong because if Ryan mows zero lawns, how can he make money. Although the multiplication is correct, it does not start at zero.

D is wrong because it is counting the price up by ten instead of adding 20.

B is right because every lawn is 20 more dollars, and that is what is shown.  

Find the value of k that makes the function continuous

Answers

Answer:

13/3

OR

4.33333

Step-by-step explanation:

For this function to be continuous, the second function must have the value of the limit as x approaches 3 of the first function.

To find [tex]\lim_{x \to 3} \frac{2x^2-3-15}{x-3}[/tex] we have to factor the top of the fraction

2x^2 - 3 -15

2x^2 - 18

2* (x^2 - 9)

2 * (x + 3) (x - 3)

this is perfect because this cancels out the x - 3 on the bottom

so the function become f(x) = 2 * (x + 3)

When 3 is plugged in it becomes 2 * (3 + 3) = 2 * 6 = 12

Now if you plug in 3 to the second function and make it equal to 12, you can find the value of k.

k*(3) - 1 = 12

k*3 = 13

k = 13/3

k = 4.33

The sum of three consecutive positive numbers is 147. Find the product of the greatest and the
smallest number.

Answers

Answer:

any how there are three consecutive positive numbers

Which of the following values are in the range of the function graphed below?
Check all that apply.
10
-10
10
- 10 -
I A. -1
B. 0
C. 4
D. -4
E. 1
F. 2

Answers

Answer:

1

Step-by-step explanation:

Consider the parabola given by the equation: f(x) = 2x2 + 14.0 – 4
Find the following for this parabola:
A) The vertex:
B) The vertical intercept is the point
C) Find the coordinates of the two z intercepts of the parabola and write them as a list, separated by
commas:
It is OK to round your value(s) to to two decimal places.

Answers

Answer:

Step-by-step explanation:

f(x)  = 2x² + 14x - 4

= 2(x² + 7x) - 4

= 2(x² +7x + 3.5²) - 2(3.5²) - 4

= 2(x+3.5)² - 28.5

vertex (3.5, -28.5) = (7/2, -57/2)

The vertical intercept is the y-intercept, i.e., f(0) = -4.

The x-intercepts are the values of x for which y=0.

2x² + 14x - 4  = 0

x = [-14±√(14²-4(2)(-4))]/[2(2)] = [-7±√57]/2 ≅ -7.27, 0.27

hey so i need help on my khan so please please please help

Answers

Answer:

Step-by-step explanation:

Create a probability model for the outcome of flipping a coin 3 times. what is the probability of landing on heads at least once
a. 2/3
b. 1/2
c. 7/8
d. 1/8

Answers

Answer:

it is A.2/3

Step-by-step explanation:

g(x) = 2x
Find g(g(-3))

Answers

would it be g^2 - 3g ?

Find the equation of the straight line passing through the point (-4,5) and perpendicular to the line y=2x+7.Suppose the equation is y=cx+d.Find c,d.

Answers

Answer:

The equation of the line is:

[tex]y = -\frac{1}{2}x + 3[/tex]

Step-by-step explanation:

Equation of a line:

The equation of a line has the following format:

[tex]y = mx + b[/tex]

In which m is the slope and b is the y-intercept.

Perpendicular lines:

If two lines are perpendicular, this means that the multiplication of their slopes is -1.

Perpendicular to y=2x+7

This means that:

[tex]2m = -1[/tex]

[tex]m = -\frac{1}{2}[/tex]

So

[tex]y = -\frac{1}{2}x + b[/tex]

Passing through the point (-4,5)

This means that when [tex]x = -4, y = 5[/tex]. We use this to find b.

[tex]y = -\frac{1}{2}x + b[/tex]

[tex]5 = -\frac{1}{2}(-4) + b[/tex]

[tex]2 + b = 5[/tex]

[tex]b = 3[/tex]

The equation of the line is:

[tex]y = -\frac{1}{2}x + 3[/tex]

What percent of 84 is 42

Answers

Sorry if I’m wrong but i believe it’s 50.

Rewrite the number in Standard form
6 x 10^8

Answers

Answer:

10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 = 100,000,000 x 6 = 600,000,000.

Answer:

600000000

Step-by-step explanation:

10^8=100000000

6×100000000=600000000

hope this helps

Can you help me please?!

Answers

30.) d=26

Take the equation

2 x (7 + d)

Now plugin 6 for d

2 x (7 + 6)

2 x (13)

26

31.) c

Take the equation

16b+8/2

Now plugin 4 for b

16(4)+8/2

64+8/2

64+4

68

3^16 as a power of 1/9

Answers

Answer:

x = -9

Step-by-step explanation:

3^16 = (1/9)^x

9^18 = 9^-x

On comparing co-efficients :

-x = 9

x = -9

PLS HELP I WILL GIVE BRAINLYEST

Answers

Answer:

hey

Step-by-step explanation:

pls help me then i help u

Help me answer the question ​

Answers

Answer:

cubic

Step-by-step explanation:

you can eliminate all of the other ones

Answer:

cubic

Step-by-step explanation:

quadratic = makes a parabola - U shaped

linear = makes a straight line

cubic = makes a shape just like the one in the picture

square root = makes a curved shape and its also a shape that looks like half of a parabola lying on its side

A rectangle with an area of 61 units” is dilated by a scale factor of ;. Find the area of
the rectangle after dilation. Round your answer to the nearest lenth, if necessary.

Answers

Answer:

34 units

Step-by-step explanation:

I decided that one side is 61 units and the other is 1 unit, since that would make the area 61 units.

Then I multiplied 61 by 3/4, which equals a new length of 45.75 units, and I also multiplied 1 by 3/4, which equals a new length of 0.75 units.

Finally, I solve for the area of the rectangle:

45.75 x 0.75 ≈ 34 units (rounded to the nearest whole number)

12+x=46
what is the answer to x?

Answers

Answer:

x=34

Step-by-step explanation:

Which of the following lines is perpendicular to the line 8x + 6y = 12 and passes through the point (-12,-2)?​

Answers

Answer:

y = 3/4x + 7

Step-by-step explanation:

8x + 6y = 12

6y = -8x + 12

y = -4/3x + 2

Perpendicular slope: 3/4

y - y1 = m(x - x1)

y + 2 = 3/4(x + 12)

y + 2 = 3/4x + 9

y = 3/4x + 7

If Matrix A is 3 x 4, and Matrix B is 4 x 2, what is the size of matrix BA? If BA is undefined, please state so.

Answers

Answer:

Joe Mok

Step-by-step explanation:

Joe MAMA

5 members or 20% of the math league did not come to the meet. how many total members are there

Answers

5 = (20%) x (total)

5 = (0.20) x (total)

Divide each side by (0.20):

Total = (5 / 0.20)

Total = 25

Pls hurry I need an instant answer ASAP! Thank you

Answers

Answer:

A= -2

Step-by-step explanation:

Hope I helped!! Negitive 2

8ty grade math, please help.
-Find the volume-

Answers

Answer:

47.12389 Rounded is 47.12

Step-by-step explanation:

V=πr2h=π·12·15≈47.12389

5 1/3 + (2 2/3 + 1 1/3)

Answers

answer: 9 and 1/3!! brainliest are appreciated

what is the value of x when h(x) x-3

Answers

Answer:

-1

Step-by-step explanation:

I did it in my review

Answer:
x= -3/h

hope this helps :)

URGENT PLZ HELP

Solve for x. Assume that lines which appear to be diameters are actual diameters.

Answers

Answer:

Step-by-step explanation:

This is a central angel so the degree of the angle is equal to the degree of the arc which is 111.

X+114=111

add negative -114 to each side to get X alone.

-114+X+114= 111+-114

X=-3 .   Answer negative 3

30. President Ronald Reagan earned a yearly salary of 2 x 10^5 dollars as
president. He served 8 years as president. What was the total amount of
money Ronald Reagan earned as president?
A 1.6 x 106 dollars
B. 2.0 x 106 dollars
c. 1.6 x 107 dollars
D. 2.0 x 107 dollars

Answers

Answer:

a) 1.6 x 10 ^6 dollars.

Step-by-step explanation:

since President Ronald Reagan served for 8 years. So the total amount of money that he earned is 2 x 10^5 x 8 = 16 x 10 ^ 5 = 1.6 x 10^6 dollars.

A customer service representative must spend different amounts of time with each customer to resolve various concerns. The amount of time spent with each customer can be modeled by the following distribution : X~Exp (0.2)
Find the quartile 3. Round to the nearest tenth.

Answers

Answer:

The quartile 3 is 0.3

Step-by-step explanation:

Exponential distribution:

The exponential probability distribution, with mean m, is described by the following equation:

[tex]f(x) = \mu e^{-\mu x}[/tex]

In which [tex]\mu = \frac{1}{m}[/tex] is the decay parameter.

The probability that x is lower or equal to a is given by:

[tex]P(X \leq x) = \int\limits^a_0 {f(x)} \, dx[/tex]

Which has the following solution:

[tex]P(X \leq x) = 1 - e^{-\mu x}[/tex]

The probability of finding a value higher than x is:

[tex]P(X > x) = 1 - P(X \leq x) = 1 - (1 - e^{-\mu x}) = e^{-\mu x}[/tex]

X~Exp (0.2)

This means that [tex]m= 0.2, \mu = \frac{1}{0.2} = 5[/tex]

Find the quartile 3.

The 3rd quartile is the 75th percentile, for which [tex]P(X \leq x) = 0.75[/tex], or [tex]P(X > x) = 1 - 0.75 = 0.25[/tex]

Since

[tex]P(X > x) = e^{-\mu x}[/tex]

[tex]e^{-5x} = 0.25[/tex]

[tex]\ln{e^{-5x}} = \ln{0.25}[/tex]

[tex]-5x = \ln{0.25}[/tex]

[tex]x = -\frac{\ln{0.25}}{5}[/tex]

[tex]x = 0.277[/tex]

Rounding to the nearest tenth, the quartile 3 is 0.3.

If you know how to do this please help me.

Answers

Answer:

Undefined or no values (assuming no negative zero)

Step-by-step explanation:

The absolute value of a number (a) keeps/turns it positive. A positive number can never be equal to a negative number.

Write 5x – 4y = 10 in slope-intercept form

Answers

y=5/4x + 5/2 hope this helped

PLS HELP ASAP IM RUNNING OUT OF POINTS PLSS

Answers

Answer:

x = 35°

Step-by-step explanation:

180 - (40+40) = 2x+30

180 -80 = 2x+30

100 = 2x+30

2x = 100-30

x = 70/2

x = 35°

Other Questions
A firm' s sales procedure involves preparing sales invoices based on shipping documents; posting the sales amounts to accounts receivable records; and posting quantities billed to the inventory records. Due to control weaknesses in the procedure, certain goods that are shipped may not be reflected in the sales invoices. The exposure from this risk can result in: Which of the populations shown in Figure 6 do you think is most likely to get bigger in size? Explain your reasoning. Which values for A and B will create infinitely many solutions for this system of equations? A x minus y = 8. 2 x + y = B. A rectangle with an area of 61 units is dilated by a scale factor of ;. Find the area ofthe rectangle after dilation. Round your answer to the nearest lenth, if necessary. The partnership agreement of Owens, Gehrig, and Nagurski provides for the following income ratio: (a) Owens, the managing partner, receives a salary allowance of $18,000, (b) each partner receives 15% interest on average capital investment, and (c) remaining net income or loss is divided equally. The average capital investments for the year were: Owens $100,000, Gehrig $200,000, and Nagurski $300,000. If partnership net income is $90,000, the amount distributed to Owens should be 12+x=46what is the answer to x? leroy is calculating the probability of rolling a regualr 6-sided die and flipping a coun. He wants to know the probability if rolling a 4, then landing on heads twice Find P(4 and H and H). Which of the following is true of adaptive traits? they give organisms an advantage when it comes to survivalorganisms with adaptive traits survive longerorganisms with adaptive traits produce more offspring all of the above PLS HELP (MARKING BRAINLIEST) Rewrite the number in Standard form6 x 10^8 They are out of order. Tell me what you think of the story. Felipe planted some seeds for a science project. One of his plants grew 6 1/2 inches in the first week, and then it grew 5 3/4 inches during the second week. How much did the plant grow during these two weeks? The answer should be written as a proper mixed number and should be simplified, if possible. *ill give brainliest* What is happening in Posey's poem? They knew that all of Oz, including their own territory, was ruled by abeautiful Princess named Ozma, who live in the splendid Emeralddityapter the simple folk of Oogaboo never visited Ozma....The King of Oogaboo used to be a man named Jol Jemkiph Soforth,who for many years did all the drudgery of deciding disputes andtelling his people when to plant cabbages and pickle onions. But theKing's wife had a sharp tongue and small respect for the King, herhusband; therefore one night King Jol crept over the pass into the Landof Oz and disappeared from Oogaboo for good and all. The Queenwaited a few years for him to return and then started in search of him.-L. Frank Baum, Tik-Tok ofOz Monthly grocery cost based on the average number of shopping trips is predicted using the least-square regression line, = 275.3 + 90.7x, where represents the predicted monthly expense and x represents the average number of trips. A shopper visits the grocery store an average of 3.2 times and has a monthly cost of $520. What is the residual for the shopper? 45.54 76.47 45.54 76.47 90.7 8How does a corporate How does a corporate monopoly impact the economy?OA.' A monopoly decreases the amount of competition.OB. A monopoly helps create new markets.OC. A monopoly increases the amount of production.OD. A monopoly helps reduce unemployment. MUCH ADO ABOUT NOTHING WHEN THE UPROAR OVER HERO'SINFIDELITY IS OVER, NO ONE SEEMSUPSET WITH MARGARET'S BEHAVIORWHY DO YOU THINK THAT IS? Will give Brainlyist Compare and contrast how the characters or settings are developed in Antigone and "The Game" and how they create meaning in each play. Use specific textual evidence from both plays to support your answer. The sum of three consecutive positive numbers is 147. Find the product of the greatest and thesmallest number. 4. 3a+6+5a A)16 B)8a C)85. 8b+8-4b A)20 B)28 C)12b6. 5c-4c+c A)9c B)0 C)-6