Answers
The proof of the inequality → (a + b)²/2 ≥ 2ab, is given below -
We have the following inequality -
(a + b)²/2 ≥ 2ab
We have to prove it.
What is inequality ?An inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions.
According to the question, we have -
Inequality -
(a + b)²/2 ≥ 2ab
Proof -
Starting from the inequality - (a - b)² ≥ 0
(a - b)² ≥ 0
a² + b² - 2ab ≥ 0
a² + b² - 2ab + 2ab ≥ 2ab
a² + b² ≥ 2ab
Add - 2ab on both sides, we get -
a² + b² + 2ab ≥ 4ab
(a + b)² ≥ 4ab
Divide both sides by 2, we get -
(a + b)²/2 ≥ 2ab
Hence Proved.
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Related Questions
what is the answer for b?
Answers
Answer:
4
Step-by-step explanation:
2+2=4 dummy
Do you think it would be better to use breaking apart in the distributive property or compensation to find the product of five times 328? explain why and show how to find the product.
Answers
Yes it would be better to use breaking apart in the distributive property or compensation to find the product of 5 x 328 .
what is distributive property?
This property states that multiplying the total of two or more addends by a number will produce the same outcome as multiplying each addend by the number separately and then adding or substracting the results together .like in subtraction A(B-C)= AB-AC
In other words, an equation of the type A (B+C) can be solved as A (B+C) AB+AC in accordance with the distributive property.
This characteristic also holds for subtraction.
5 x 328
= 5(300+28)
= 5 x 300 + 5 x 28
= 1500 + 140
= 1640
Hence, it would be better to use breaking apart in the distributive property or compensation to find the product of 5 x 328 .
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A town's population is 42,975 . About 125 people move out of the town each month. Each month, 175 people on average move into town. A nearby town has a population of 45,225. It has no one moving in and an average of 175 people moving away every month. In about how many months will the populations of the towns be equal? Write an equation to model the situation. Then solve the equation and answer the question.
Answers
The number of months when they will be equal is 45 months.
How to calculate the equation?The equation for the first town will be:
= 42975 + 125x
The equation for the second town will be:
= 45225 + 175x
The number of months when the populations of the towns will be equal will be:
42975 - 125x = 45225 - 175x
- 125x + 175x = 45225 - 42975
50x = 2250
x = 2250 / 50
x = 45
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what’s the answer to this???
you have to find where it increases, decreases, and where it’s constant….
help..
Answers
We know that since there's an arrow pointing
to the left of the line that it goes on infinitely
Same thing when the arrow is going to the
right
Then we can just looking at the x-values on
the graph for the intervals where it starts and
stops
-3,3
inf, -3
3,inf
i hope this helps
8. Mason read 12 books in 4 months. If he reads at a
constant rate, how many books did he read each month?
Give your answer as a whole number or a FRACTION in
simplest form.
Answers
What is the remainder for 3,167 / 28
45 POINTS!!!
Answers
Answer:
113 with a remainder of 3
Step-by-step explanation:
Watch help video
Adriel drove 216 miles in 8 hours. If he continued at the same rate, how far would he
travel in 3 hours?
Answer:
miles Submit Answer
SAMSUNG
attempt 1 out of 2
Answers
Answer:
bkjjb.l kkllkk kk. lkm j. km j. kk. k mgdv. nutdc
The quotient of 24 and d
Answers
Answer:
The quotient of 24 and d would be [tex]\frac{24}{d}[/tex]
Step-by-step explanation:
Quotient is the answer of a division problem. So, you would divide 24 by d.
The diameter of a cylindrical container is 22cm. If the volume of the container is 1331cm³, calculate its height.
Answers
Answer:
3.5cm
Step-by-step explanation:
Vol=πr²h
Transposing for h,=vol÷πr²
where r=22/2=11cm and taking π=3.142
h=1331/(3.142×(11)²)=3.5cm
Step by step
For cylinders we know
Volume = pi x radius ^2 x height
We know volume is 1331
We know pi = 3.14
We know radius is 11 (diameter is 22, so radius is 1/2 of that, so r=11)
We are looking for height “H”
Fill in the numbers into the formula
1331 = 3.14 x 11^2 x H
1331 = 3.14 x 121 x H
1331 = 380 H
Divide both sides by 380 to solve for H
1331/ 380 = 380/ 380 H
3.5 = Height
Problem solved!
What are the values of (-2)^4 and -2^4?
8 and -8
16 and 16
-8 and -8
16 and -16
Answers
16 and - 16
Determine the sign
24
Write as a multiplication
2×2×2×2
Multiply
Solution
16
-24
Write as a multiplication
-2×2×2×2
Multiply
Solution
-16
the teacher separated her class of fifty-eight students into two groups. one group has 6 more than thrice as many students as the other group. how many students are in each group?
Answers
Students in one group is 45
Students in another group is 13
teacher separated her class of fifty-eight students into two groups
Number of groups =2
one group has 6 more than thrice as many students as the other group
Let one group has x students
another group has y students
x+ y = 58 . . . . . 1
x= 6+3y
Substitute x= 6+3y in . . . 1
6+3y +y = 58
4y=52
y=13
x=6+3y=6+3(13)
= 6+39
= 45
Students in one group is 45
Students in another group is 13
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A portion of the periodic table is shown below. Which column of elements would be most likely to chemically combine with sodium in a 1:1 ratio?
Answers
Step-by-step explanation:
chlorine cl when combines with sodium na
Nacl will form so chlorine
HELPP PLEASE 70 POINTS
Answers
At 9:00 AM the temperature was -15°C in Anchorage. The
proceeded to rise 4°C each hour. What was the
at 2:00PM.
CAN SOMEONE HELP ME WITH THIS QUESTION
Answers
Answer:
5°C
Step-by-step explanation:
(add 4 each hour)
9AM:-15°C
10AM:-11°C
11AM:-7°C
12AM:-3°C
1AM:1°C
2AM:5°C
On a shopping trip, Jeffery buys 3 sweaters and 5 pairs of jeans for $160. Eric also purchases 6 sweaters and two pairs of jeans for the same price. What is the difference in price of a sweater and one pair of jeans?
Answers
Answer:
Step-by-step explanation:
It would most likely be 0, but I am not sure.
Convert 5.764764764 ... to a rational expression in the form of a over b , where b ≠ 0
Answers
If x = 5.764764764…, then 1000x = 5764.764764764…, so that
1000x - x = 5764.764764764… - 5.764764764…
999x = 5759
x = 5759/999
33/25 as a decimal rounded to the nearest tenth
Answers
Answer:1.3
Step-by-step explanation:
33/22=1.32
Round to nearest 10th
1.32=1.3
Type the correct answer in each box. Use numerals instead of words.
This graph represents a quadratic function. What is the function’s equation written in factored form and in vertex form?
Answers
The equation of the parabola in vertex form is y + 8 = 2 · (x - 2)². The factored form of the equation of the parabola is y = 2 · x · (x - 4).
What is the equation of the parabola seen in a graph?
Herein we find a representation of a quadratic function on a Cartesian plane, whose formula in vertex form is presented below:
y - k = C · (x - h)²
Where:
(h, k) - Vertex of the parabola.C - Vertex constantBy direct inspection we find that the equation of the parabola has a vertex at (h, k) = (2, - 8) and the point (x, y) = (4, 0). Then, the vertex constant is:
C = (y - k) / (x - h)²
C = (0 + 8) / (4 - 2)²
C = 8 / 4
C = 2
Then, the equation of the parabola in vertex form is y + 8 = 2 · (x - 2)². The factored form of the equation is determined by algebra:
y + 8 = 2 · (x - 2)²
y = 2 · (x - 2)² - 8
y = 2 · (x² - 4 · x + 4) - 8
y = 2 · x² - 8 · x + 8 - 8
y = 2 · x² - 8 · x
y = 2 · x · (x - 4)
The factored form of the equation of the parabola is y = 2 · x · (x - 4).
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Important Please Help!!!!
Answers
Answer:
angle bisector
Step-by-step explanation:
the construction shows an angle bisector.
the line EG bisects ∠ FED
Which of the following describes a situation in which the total distance a baseball player travels is zero meters from his starting point? (5 points)
Answers
Situation (B) best describes how a baseball player travels a total distance of zero meters from his starting point, that is, the player runs 3 meters forward and then 3 meters in the opposite direction.
What is the distance?Distance is a numerical or quantifiable measurement of the distance between two objects or points. The distance can refer to a physical length or an estimate based on other criteria in physics or everyday usage (e.g. "two counties over"). Because spatial thinking is a rich source of conceptual metaphors in human thought, the term is also frequently used figuratively to mean a measurement of the amount of difference between two common pieces (such as statistical distance between probability distributions or edit distance between text strings) or a degree of detachment (as exemplified by the distance between people in a social network). The concept of a metric space is used in mathematics to formalize most such notions of distance, both physical and metaphorical.According to the options:
Options (A), (C), and (D) is wrong as there the basketball travels some sought distance from the starting point. It is only in option (B) in which the total distance of the baseball player comes to 0 as he runs 3 meters forward and then runs 3 meters in the opposite direction.Therefore, situation (B) best describes that the total distance a baseball player travels is zero meters from his starting point that is, the player runs 3 meters forward and then runs 3 meters in the opposite direction.
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The complete question is given below:
Which of the following describes a situation in which the total distance a baseball player travels is 0 meters from his starting point? (5 points)
a) The player runs 4 meters forward and then runs 3 meters in the opposite direction.
b) The player runs 3 meters forward and then runs 3 meters in the opposite direction.
c) The player runs 3 meters forward and then runs 4 meters in the opposite direction.
d) The player runs 3 meters forward and then runs 0 meters in the opposite direction.
Please help me it doesn't have to be quickly just help
Answers
Answer:
3 to the power of 3
Step-by-step explanation:
Answer:
1. 8x
2.4x^2
3.3^x
Step-by-step explanation:
I took the test
√-100=____ + _____i
Answers
Answer:
[tex]10 + 1i[/tex]
Step-by-step explanation:
[tex]i = \sqrt{-1}[/tex]
[tex]\sqrt{-100} = \sqrt{100} * \sqrt{-1}[/tex]
[tex]\sqrt{-100} = 10 + 1i[/tex]
Fill in the missing amounts (do not use commas or decimal points.)
Answers
Here are the missing amounts :
A = $2100
B = $300
C = $50
D = $270
E = $945
F = $1,345
What are the missing amounts?
Receipts represents income to the company. It is a source of cash inflow. Expenses represents cash outflow. Net cash flow is the difference between receipts and expenses. Cumulate balance is the sum of the net cash flow of the previous periods and the net cash flow of the present period.
A = Net cash flow + expenses
1975 + 125 = 2100
B = Receipts - expense
$2225 - $1925 = $300
C = Receipts - expense
$2050 - $2000 = $50
D = Net cash flow = $270
E = cumulative balance in April + net cash flow in May
$570 + $375 = $945
F = = cumulative balance in July + net cash flow in August
$1120 + $225 = $1,345
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PLEASE PLEASE PLEASE ANSWER CONFIDENTLY
Evaluate the expression when p = 5
-|-3p|
Answers
Answer:
-15
Step-by-step explanation:
p = 5
- | -3(5 | = - | -15 | = - | 15 | = -15
find the absolute value |-2|
Answers
Answer:
2.
Step-by-step explanation:
The absolute value is the distance between a number and zero. The distance between −2 and 0 is 2.
Hope this helps.
Answer:
2
Step-by-step explanation:
Let's solve the equation step by step
|-2|
= 2
A rectangular hotel room has a perimeter of 72 feet. Its area is 320 square feet. What are the dimensions of the room?
Answers
Answer
Step-by-step explanation:
BE is the perpendicular bisector of AD. Find the value of each variable.
14. AC = 5x - 7 and DC = 8x - 28
15. m/ACB = (7y - 8)°
Answers
Answer:
ac =13x-35
m/abc = 7y-8
Step-by-step explanation:
in first to minus of same base
second it remain same because it can't be subracted with different base
m/abc = 7y-8
The width of a rectangle measures (10p - 9q) centimeters, and its length measures
(7p+8q) centimeters. Which expression represents the perimeter, in centimeters,
of the rectangle?
Answers
The expression represents the perimeter, in centimeters, of the rectangle is P = 30q + 2p
Perimeter of a rectangleThe formula for calculating the perimeter of a rectangle is expressed as:
P = 2(l+w)
l = (7p+8q) cm
w = (10p - 9q) cm
Substitute
P = 2(7p+8q+10p-9q)
P = 2(15q+p)
P = 30q + 2p
Hence the expression represents the perimeter, in centimeters, of the rectangle is P = 30q + 2p
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four points, a, b, c, and d, lie on a circle having a circumference of 17 units. b is 5 units counterclockwise from a. c is 3 units clockwise from a. d is 11 units clockwise from a and 6 units counterclockwise from a. what is the order of the points, starting with a and going clockwise around the circle?
Answers
The order of the points starting with a and going clockwise around the circle is;
a ⇒ c ⇒d ⇒b
Here,
Four points, a, b, c, and d, lie on a circle having a circumference of 17 units.
b is 5 units counterclockwise from a.
c is 3 units clockwise from a.
d is 11 units clockwise from a and 6 units counterclockwise from a.
We have to find, The order of the points starting with a and going clockwise around the circle.
What is Circumference of circle?
The circumference is the distance around a circle or any curved geometrical shape.
Now,
b is 5 units counterclockwise from a.
b ⇒ a
c is 3 units clockwise from a.
b ⇒ a ⇒ c
d is 11 units clockwise from a and 6 units counterclockwise from a.
d ⇒ b ⇒a ⇒ c ⇒d
So, when we draw all points on circle we get;
The order of the points starting with a and going clockwise around the circle is;
a ⇒ c ⇒d ⇒b
This is shown in figure.
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The function y = f(x) is graphed below. What is the average rate of change of the function f(x) on the interval -2 ≤ x ≤ 3? -10 Go -8 -6 -4 -2 100 80 60 20 -20 -40 -60 -80 -100 2 8 10
Answers
Answer:
1 + 1 = 2 a i esta la respjesta
Step-by-step explanation:jijiji