MAKING AN ARGUMENT In an aerial ski competition, you perform two acrobatic ski jumps. The scores on the two jumps are then added together.

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.

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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Answer:

8 feet

Step-by-step explanation:

Since it is 2 inches and 1 inch is equal to 4 feet, you just multiply 2 inches by 4 feet which will give you 8 feet.

Hope that helps

Answer:

Blank 1: 97

Blank 2: 73

Step-by-step explanation:

This equation is shown on a straight line, which equals 180.

We can start by adding the two equations which together are equal to 180.

15x + 2 + 10x + 3 = 180

We can simplify it to 25x + 5 = 180

Now we can subtract 5 from both sides to get

25x = 175

Then we can divide both sides by 25 to get x = 7

Now we can plug in x for both angles

Angle RQS is 15x + 2, so 15*7=95 and the +2 is 97.

Angle TQS is 10x + 3 so 10*7=79 and the + 3 is 73

:D

Answer:

f(-2) = -1

Step-by-step explanation:

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Answer: f(-2) = 5

Step-by-step explanation: In this piecewise function, when x is less than -1, the equation is -3x-1. -2 is less than -1 so we use the first equation. -3(-2)-1= 6-1 = 5.

a-/ |-5-10| = 15 ; |-2√2-√12|=2√3+√12 ; |-π-4π|=5π

Answer: a=-0.75

Step-by-step explanation:

14a - (2a +9)=2/3 (12a-18)​

14a - 2a -9=2/3 * 6(2a-3)​

12a-9=2*6/3 (2a-3)​

12a-9=2*2(2a-3)​

12a-9=4(2a-3)​

12a-9=8a-12

4a-9=-12

4a=-3

a=-3/4

a=-0.75

Scale factor 1.5

Let O (0,2)  as the centre of enlargement

A (0, 0)

B (-2, 0)

C (-2, 4)

Step 1:

First draw lines from point O through A, B and C, as shown in the image attached below

Step 2:

Measure the length O A and multiply it by 1.5 to get the distance from O of the image point A';

<=> O A' = 1.5 × O A.

<=> OA' = 1.5 * [tex]\sqrt{2^2}[/tex]

<=> OA' = 1.5*2

<=> OA' = 3

Mark the point A' on the diagram

Step 3:

The images B' and C' can then be marked in a similar way and the enlarged triangle A' B' C' can then be drawn.

OB' = 1.5OB

<=> OB' = 1.5 *[tex]\sqrt{( 2^2+2^2}[/tex]

<=>  OB' = 1.5*2[tex]\sqrt{2}[/tex]

<=> OB' = 3[tex]\sqrt{2[/tex]

OC' = 1.5*[tex]\sqrt{2^2+2^2}[/tex]

<=> OC' = 1.5*2[tex]\sqrt{2[/tex]

<=> OC' = 3[tex]\sqrt{2}[/tex]

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The perimeter of the right triangle is 30 units.

The shorter leg of the right triangle is 8 less than the hypotenuse. The longer leg is one less than the hypotenuse.

Let's break the information into smaller chunk.

The shorter leg of a right triangle is 8 less than the hypotenuse.

The longer leg is one less than the hypotenuse.

The hypotenuse is the longest side of a right triangle.

Therefore,

let

the hypotenuse = x

short leg = x - 8

long leg = x - 1

Applying Pythagorean theorem in the given right triangle.

c² = a² + b²

where

(x - 1)² + (x - 8)² = x²

(x - 1)(x - 1) + (x - 8)(x - 8) = x²

x² - x - x + 1 + x² - 8x - 8x + 64 = x²

2x² - 18x + 65 = x²

x² - 18x + 65 = 0

(x - 13)(x - 5) = 0

Therefore,

x = 5 and x = 13

13² - 5² = a²

169 - 25 = a²

a = √144

a = 12

So, the hypotenuse is 13, the shorter leg is 5 and the longer leg is 12.

perimeter of the right triangle = 13 + 5 + 12 = 30

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Answer: 1

I did this problem a couple times and got 1 every time

The value of x based on the information given about the circumference is 2.24.

It should be noted that the circumference is calculated as:

= 2πr

where

π = 3.142

r = radius = 4x - 5.

Circumference = 25

Therefore, circumference = 2πr.

(2 × 3.142)(4x - 5) = 25

6.284(4x - 5) = 25.

25.136x - 31.42 = 25

Collect like terms

25.136x = 25 + 31.42

25.136x = 56.42

x = 56.42 / 25.136

x = 2.24

Therefore, the value of x based on the information given about the circumference is 2.24.

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The equations that match the diagram are 18 ÷ 3 = x + 5 and 3(x + 5) = 18

The given parameters are

Expression = x+5\x+5\x+5

Value = 18

The above means that

Expression = Value

So, we have

x + 5 + x + 5 + x + 5 = 18

Evaluate the sum

So, we have

3x + 15 = 18

Factor out 3

So, we have

3(x + 5) = 18

Divide both sides by 3

So, we have

x + 5 = 18 ÷ 3

Hence, the equations that match the diagram are 18 ÷ 3 = x + 5 and 3(x + 5) = 18

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The amount borrowed by the print shop: $5700

Time for which loan is taken: 193 days

Rate of interest: 12%

Day in terms of year is given by: 1/365

The formula for simple interest:

Simple interest = P*R*T/100

where P = principal amount invested

R = rate of interest

T = time in years

Solving the question using the formula we have:

Simple interest = (5700*12*193)/(100*365)

= 13201200/36500

= 361.67 or $362

Interest that will be owed after 193 days will be $362

Amount owed after 193 days will be $5700 + $362 = $6062

Although a part of your question is missing, you might refer to this full question: A print shop borrows $5700 from a credit union for 193 days. The credit union charges simple interest at an annual rate of 12% for this loan. Assume 1/365 each day of a year. Find the interest that will be owed after 193 days. If no payments are made on the loan find the amount owed after 193 days.

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Answer:

38 degrees

Step-by-step explanation:

Angle 38 and b are the same.

The angle x will be 98 ⁰  

What are alternate interior angle ?

An alternate interior angle is one formed on the inside side of two parallel lines and opposite on the outer side of the transversal when those two parallel lines are intersected by a transversal and they are equal.

Alternate angles between a transverse and parallel lines are equal .

Let the lines are AB and CD and let us draw a transverse line HI parallel to AB and CD, then the angle FEI will be 62 degree as alternate interior angle are equal. and also angle EPC will be supplementary angle of 144 degree that is 36 degree thus forming angle GEI to be 36 degree also as shown in figure below :

Now calculating angle x :

x = 62+ 36

x = 98 ⁰

Therefore, the angle x will be 98 ⁰  

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Answer:

y = -1/2 x + 1.

Step-by-step explanation:

The slope is -1/2.

The y intercept is at y = 1

So, it's

y = -1/2 x + 1.

Answer:

5

Step-by-step explanation:

Both answers equal 25.

The dimensions of the rug which Abdul would use in discuss as described in the task content are; 21.84 ft by 21.84 ft.

It follows from the task content that the dimensions of the rug which Abdul would use in the room in discuss are to be determined.

Since the room Abdul wants to put a rug on is; 775 ft² and the room is a square room.

It follows that all sides of the room are equal and the length of each side can be determined as;

s = √Area; since Area = s².

s = √775

s = 27.839 ft.

Hence, the dimensions of the room is; 27.839 ft by 27.839 ft.

However, since he wants to leave a 3-foot border of bare floor on each side, it follows that the dimensions of the rug on each axis would be;

= 27.839 - 3 -3 = 21.839 ft on all sides.

Consequently, the dimensions of the rug rounded to the nearest hundredth are; 21.84 ft by 21.84 ft.

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A=9, B=5 and D=7 are the correct options.

In the *Geometry*, a *triangle* is a closed 2-dimensional figure with 3 angles, 3 sides and 3 vertices. Triangles are considered as a *polygon* with the least number of sides.

a,b and c are the sides of a triangle if it satisfies:

a<b+c  , b<a+c and c<b+a

Here, a=4 and b=7

We have to find c

i.e. all those c which satisfies:

4<7+c , 7<4+c and c<4+7=11

AAAAAA. 9 it is true

B.5   it is true

C.17   This is clearly false, since it doesn't satisfies inequality third.

D.7   it is true

EE. 3  it is not true since it doesn't satisfies second inequality.

F.11 This is clearly false, since it doesn't satisfies inequality third

Hence, The correct answer of the given question is A,B and D.

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Answer:

almost.

Step-by-step explanation:

You can write almost every linear equation in slope-intercept form.

Slope-intercept form is:

y = mx + b

So every line except a vertical line can be written in the form y=mx+b.

This form cannot be used when m is undefined.

It should be noted that based on the information given, the square root of 225 will be A. 15.

It should be noted that a number y such that y² = x, or a number y whose square is x, is referred to as the square root of a number x in mathematics. For instance, since 4² = 16, 4 and -4 are the square roots of 16.

It should be noted that in this case, the square root of 225 will be:

= ✓225

= 15

Therefore, it should be noted that based on the information given, the square root of 225 will be 15.

In conclusion, based on the information, the correct option is A.

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According to the given statement this is a type of stratified sampling.

Stratified random sampling is often when researchers want to know about different subgroups or based on the entire population being studied. For instance, if one is interested in differences between groups based on race, gender, or gender.

she measures her blood sugar level at 3 randomly selected times during each part of the day.

So,

This is a type of stratified sampling.

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I understand that the question you are looking for is :

To determine her blood sugar level, charlotte divides up her day into three parts: morning, afternoon, and evening. She then measures her blood sugar level at 3 randomly selected times during each part of the day.

What type of sampling is used?

Answer:

  11

Step-by-step explanation:

You want to simplify (2x+7) - (2x - 4).

The distributive property tells you the factor outside parentheses applies to every term inside parentheses. It is used for the purpose of removing parentheses.

  (2x+7) - (2x - 4) = 2x +7 -(2x) -(-4) = 2x +7 -2x +4

Terms that have the same variable (or product of variables) are "like terms." Their coefficients can be combined. (This is another use of the distributive property.)

  2x +7 -2x +4 = 2x -2x +7 +4 = (2 -2)x +(7 +4) = 0x +11

  = 11 . . . . simplified form of the given expression

By solving a quadratic equation we can see that the width of the path measures 20 meters.

We know that the pool measures 18 meters by 20 meters, then the area of the pool alone is:

A = 18m*20m = 360 m^2

Now, if the path has a width x, then the rectangle that includes the path and the pool has dimensions:

(18m + 2x) and (20m + 2x)

And its area is given by:

(18m + 2x)*(20m + 2x)

And we know it is equal to 1520 m^2, then (i'm not writting the units in the computation):

(18 + 2x)*(20 + 2x) = 1520

360 + 4x^2 + 76x = 1520

Now we just need to solve that quadratic equation:

4x^2 + 76x - 1520 + 360 = 0

4x^2 + 76x - 1160 = 0

The solutions are:

x = (-76 ± √(76^2 - 4*4*(-1160))/(2*4)

x = (-76 ± 156)/4

We only care for the positive solution, which gives:

x = (-76 + 156)/4 = 20

We conclude that the width of the path measures 20 meters.

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Answer:

1 & 4

Step-by-step explanation:

because 3 & 5 is a reflection, 2 & 6 is a translation.

Answers:

A ' = (-3, -3)

B ' = (1, 0)

C ' = (2, -6)

=====================================================

Explanation:

To translate 6 units to the left, we subtract 6 from each x coordinate.

For point A, we have x = 3 become 3-6 = -3 as the new x coordinate.

Point A also goes down 7 units, in which we subtract 7 from the y coordinate. So the y coordinate of point A, which is 4, becomes 4-7 = -3 as the new y coordinate.

This is how we can write out the work shown for moving point A

[tex](\text{x},\text{y})\to(\text{x}-6,\text{y}-7)\\\\(3,4)\to(3-6,4-7)\\\\(3,4)\to(-3,-3)[/tex]

Point A is at (3,4) and moves to A ' which is at (-3, -3)

Do similar steps for points B and C to get the answers shown above.

Answer:

1 3/4

Step-by-step explanation:

OK but what if brainliest instead

Answer:1 3/4

Step-by-step explanati

The car's average acceleration is 8.44 ft/s².

Acceleration is defined as the rate of change of velocity per unit time. It is usually denoted by the letter a.

Here, we are given that a car travels on a straight road. Starting from rest, the car is going at 38 ft/s (26 mi/h) at the end of 4.5 s.

Acceleration of an object can be calculated using the given formula-

acceleration = velocity/ time

Here, the velocity of the car will be 38 ft/s

and the time is equal to 4.5 seconds.

Thus, putting these formulas in the equation, we get-

acceleration of the car = 38/ 4.5

= 380/ 45

= 8.44

Thus, the car's average acceleration is 8.44 ft/s².

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The resulting product of the expression is 13 1/8

Fractions are written as a ratio of two integers

Given the following expression

-4 1/6 * -3 15/100

Convert to improper fraction to have:

-25/6 * -315/100

-1/6 * -315/4

315/24

13 1/8

Hence the resulting product of the expression is 13 1/8

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