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

help me please ! !!!!!

Answers

Answer:

24

Step-by-step explanation:

[tex]m < a = \frac{mde - mbc}{2} [/tex]

[tex] = \frac{119 - 71}{2} [/tex]

[tex] = \frac{48}{2} [/tex]

[tex]answer = 24[/tex]

hope it helps you

have a great day!!

Determine the number of zeros of the polynomial function
F(x) = x^4 - x^7

Answers

Answer:

7

Step-by-step explanation:

Using fundamental theorem of algebra, there should be 7 roots, if you count multiplicity.

If you're only counting distinct roots, then there should be 4 roots.

A limo weighs 3 tons, 1,000 pounds. How many pounds does the limo weigh?

Note: 1 ton = 2,000 pounds

Answers

Answer:

2000 times 3 = 6000 + 1000 = 7000 pounds

pls help with math that’s attached

Answers

Answer:

TU = 28.5

Step-by-step explanation:

The triangles are congruent because of side-angle-side

TU = VU because corresponding sides of congruent triangles are congruent.

so:

3x + 9 = 7x - 17

simplify:

4x = 26

x = 6.5

TU = 3(6.5 + 9) = 19.5 + 9 = 28.5

Answer:

3x+9=7x-17

26 = 4x

x=6.5

TU:28.5

Which expression is equal to 97/33 ?

Answers

Answer:

2 31/33

Step-by-step explanation:

Answer:

=2.93939393

Step-by-step explanation:

97/33

=2.93939393

Is 2(6 - 3x) + x equivalent to 2(3x) + x?

Answers

Answer:

No.

Step-by-step explanation:

2(6-3x)= 12-6x and 2(3x)+x= 7x

The tables below show the values of Y for different values of X

Answers

Answer:

Option D

Step-by-step explanation:

Rate of change of a linear function between two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is given by,

Rate of change 'm' = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

From the given table,

Rate of change of the function between (-2, 6) and (-4, 9),

Rate of change 'm' = [tex]\frac{9-6}{-4-(-2)}[/tex]

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

Initial value = y-intercept

Let the equation of the line passing through a point (h, k) is,

y - k = m(x - h)

If a point (-2, 6) is lying on the graph of the function,

y - 6 = [tex]-\frac{3}{2}(x+2)[/tex]

y = [tex]-\frac{3}{2}x-3+6[/tex]

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

Y-intercept of the function = 3

Therefore, initial value of the function = 3

Option D is the answer.

write the following mathematical expressions in simplest form 3.5 m + 2 (0.6 M - 5) + 4​

Answers

Answer:hamburger

Hamburger

Step-by-step explanation:hamburger

Hamburger

Two lines are represented by equations: 10x – 15y = 21 and y = kx + 5.What value of will make lines perpendicular? ​

Answers

Answer:

is this what u wanted? if no can u write on paper what u wanted and send me


1. Find the degree measure and the length of arc AB:

120°
20 in.

Answers

Answer:

Degree measure of arc AB = 120°

Length of arc = 41.9 in.

Step-by-step explanation:

✔️Measure of Central angle is the same as Measure of the intercepted arc

Therefore,

Degree measure of arc AB = 120°

✔️Length of arc = [tex] \frac{\theta}{360} * 2 \pi r [/tex]

[tex] \theta = 120 [/tex]

r = 20 in.

Length of arc = [tex] \frac{120}{360} * 2 \pi * 20 [/tex]

= 41.887902

Length of arc = 41.9 in. (Nearest tenth)

Which number line represents the solution to 5x < 30?

Answers

Answer:

x < 6

Step-by-step explanation:

6 * 5 = 30

done

Hope this helped! Have a nice day! Plz mark as brainliest!!!

-XxDeathshotxX

Answer: It's B

<---|-----|-----|-----●-----|-----|--->

Arrow goes this way →

In ΔKLM, l = 7 inches, k = 9.5 inches and ∠K=54°. Find all possible values of ∠L, to the nearest 10th of a degree.

Answers

Answer: 36.6

Step-by-step explanation: did on delta math

Whoever responds first will get marked Best.
The amount of wallpaper needed to cover the wall is an example of which
A: area
B: volume
C:perimeter
D:length

Answers

Answer:

A area

Step-by-step explanation:

the measures of the angles of a triangle are shown below. solve for x ​

Answers

Answer is in the file below

tinyurl.com/wpazsebu

Answer:

X = 3

Step-by-step explanation:

All you do is add the angles up and set them equal to 180.

solution to 3x+4=3x+4

Answers

The results can be shown in multiple forms;

4 = 4, All real numbers, Always true, Interval notation: (-∞,∞).

Move all terms containing [tex]x[/tex] to the left side of the equation.

[tex]Subtract\\3x+4-3x=4\\[/tex]

Combine the opposite terms in [tex]3x+4-3x[/tex]

[tex]Subtract\\3x from 3x.\\\\0+4=4\\\\Add\\0+4=4 \\4=4*[/tex]

Since [tex]4=4[/tex] the equation will always be true.

Find the missing angle.
120°
30°
N
Z=
Enter the number that belongs in the green box,
[?]
please help this is urgent

Answers

Answer:

missing angle = 30 degrees

Step-by-step explanation:

all triangles have an interior angle or 180 degrees.

to find the missing angle, just take the know angles and add them together:

120 + 30 = 150

then take the sum and subtract it from 180:

180 - 150 = 30

Answer:

120° +30° +z=180°150° +z =180°z= 180°-150°z=30°

The height (in inches) of males in the United States is believed to be Normally distributed. The average height of a random sample of 50 American adult males is 69.72 inches and the standard deviation of the 50 heights is s = 4.23. The best pint estimate for the average height if males in the United States is_____inches. Give answer to the hundredths place.

Answers

Answer:

69.72 inches.

Step-by-step explanation:

The best point estimate for the average height if males in the United States is...

For large samples, as we have here, the best point estimate is the sample mean. In this question, the sample mean is of 69.72 inches, so the answer is 69.72 inches.

Assume v is a vector in R^5. You wish to compute a vector w such that the th entry of w, denoted wi, is the sum of vi-1,vi, vi+1. For example wi is the sum of ,vo,v1 and v2. For elements at the endpoints of w, you will only account for two elements in your sum. For example wo, (assuming zero-based indexing) is the sum of vo and v1. Construct a matrix A such that Av=w.

Answers

Answer:

Use the drawing tools to form the correct answer on the graph.

Graph the line that represents this equation:

Step-by-step explanation:

pls help i need answer

Answers

Answer:

109 degrees

Step-by-step explanation:

23 + 48 = 71

180 - 71 = 109 :)

Answer:

i think the answer is 109 im not sure

Step-by-step explanation:

48+23=71 180-72=109

Tyler has to savings accounts that his grandparents opened for him . One of the accounts Pay 8% annual interest Where as the other pay 10% annual interest. If you have $700 more invested at 10% then you invested at 8%, how much do you have invested in each account If the total amount of interest You earn in a year is $106?

Tyler invested $___at 8%, and $___at 10%

Answers

Thank you hope this helps see photo

3 |a| +5 |b| if a = −2; b = −1
WILL AWARD BRAINLIEST

Answers

Answer:

-11

Step-by-step explanation:

[tex]3( - 2) + 5( - 1)[/tex]

[tex] - 6 + ( - 5)[/tex]

[tex] - 11[/tex]

100
400 people were surveyed
about their eye color. 8% of
the people surveyed have
green eyes. How many
people had green eyes?

Answers

Answer:

32 people

Step-by-step explanation:     If there are 400 people and there is 8% of that, then first convert 8% to a decimal so its easier to work with. The multiply with 400:

0.08 * 400 = 32

Answer: 32 people have green eyes

32 people have green eyes

Solve
9+1/5b=3/10b
what is b

Answers

Answer:

b = 90

Step-by-step explanation:

Answer:

[tex] \huge\sf \colorbox{pink}{hey \: there}[/tex]

Step-by-step explanation:

[tex] \underline \red{given:- \: 9 \frac{1}{5b} = \frac{3}{10b} }[/tex]

[tex]b = 70[/tex]

HELPP ASAPPP
The rectangular prism shown is made up of cubes that measure 1/8 inch on each side. What is the volume, in cubic inches, of the rectangular prism?

Answers

Answer:

3/8

Step-by-step explanation:

3/4*1/2=3/8

3/8*1=3/8

*=multiply

Estimate 4/5x6/7
I WIL MARK BRAINLIEST IF ITS THE BEST ANSWER

Answers

Answer:

Simplify x6/7

4/5 x x6/7

Simplify 4/5

4/5 x x6/7

Finally the answer

4x6/35

Write the factored form of the third-degree polynomial
function that has a positive leading coefficient and a
zero at x= -3 with a multiplicity of 3.

Answers

Answer:

[tex]a(x+3)^3, a \neq 0[/tex]

Step-by-step explanation:

Zeros of a function:

Given a polynomial f(x), this polynomial has roots [tex]x_{1}, x_{2}, x_{n}[/tex] such that it can be written as: [tex]a(x - x_{1})*(x - x_{2})*...*(x-x_n)[/tex], in which a is the leading coefficient.

Zero at x= -3 with a multiplicity of 3.

This means that:

[tex]x_1 = x_2 = x_3 = -3[/tex]

So

[tex]a(x - (-3))*(x - (-3))*(x-(-3)) = a(x+3)(x+3)(x+3) = a(x+3)^3[/tex]

Positive leading coefficient

[tex]a(x+3)^3, a \neq 0[/tex]

A circle has a diameter of 7 inches. Find the radius

Answers

Answer:

radius= 3.5 in

Step-by-step explanation:

Answer: 3.5

Step-by-step explanation:

The diameter is the length from one side of the circle to the other the radius is half that

how many meters are equal to 5,253 centimeters? use how the placement of the decimal point changes when dividing by power of 10 to help you​

Answers

Answer:

[tex]52.53\ \text{meters}[/tex]

Step-by-step explanation:

[tex]1\ \text{meter}=100\ \text{centimeter}[/tex]

[tex]1\ \text{centimeter}=\dfrac{1}{100}\ \text{meter}[/tex]

In the question the quantity that is required to be converted to meters is 5253 centimeters.

[tex]5253\ \text{cm}=5253\times \dfrac{1}{100}\\ =52.53\ \text{meters}[/tex]

So, the required measurement in meters is [tex]52.53\ \text{meters}[/tex].


x2 – 12x = 39

Please help me solve this! I need the answer ASAP

Answers

Answer:

x = 6 ± 5[tex]\sqrt{3}[/tex]

Step-by-step explanation:

Given

x² - 12x = 39

Using the method of completing the square

add ( half the coefficient of the x- term)² to both sides

x² + 2(- 6)x + 36 = 39 + 36

(x - 6)² = 75 ( take the square root of both sides )

x - 6 = ± [tex]\sqrt{75}[/tex] = ± 5[tex]\sqrt{3}[/tex] ( add 6 to both sides )

x = 6 ± 5[tex]\sqrt{3}[/tex] ← solutions in exact form

Answer:

x = 6 ± 5* OR 6 - 5*

Step-by-step explanation:

In decimal form it would be either 14.66025403... or -2.66025403

Hope this helps!

what is this figure ?

Answers

that figure is B. a parallelogram
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