Show Work to factor the binomials.

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Explanation:

Check out the diagram below.

We have the following points

Let x be the length of segments DE and EC. Note how segment AB bisects segment DC. Whenever the radius is perpendicular to the chord like this, the radius will bisect the chord.

We're told that the chord length CD is the same as the radius AD, since CD = CE+ED = x+x = 2x, this means AD = 2x as well.

At this point, you probably can recognize we have a 30-60-90 triangle. One useful property of such triangles is that the hypotenuse is double the length of the short leg. The long leg is [tex]x\sqrt{3}[/tex] which is the length of segment EA. You can use the pythagorean theorem to confirm this.

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To summarize that last section, we formed triangle DAE and this triangle is a 30-60-90 triangle as shown in the diagram below.

Notice how the segments EA and FA span the entire width of the square. That width being [tex]EA+FA = x\sqrt{3}+x\sqrt{3} = 2x\sqrt{3} = EF[/tex]

The square has side lengths of [tex]2x\sqrt{3}[/tex] while the circle has radius 2x.

Use these two facts to find the area of each in terms of x.

[tex]A_1 = \text{area of square} = (\text{side})^2 = (2x\sqrt{3})^2 = 12x^2[/tex]

[tex]A_2 = \text{area of circle} = \pi*r^2 = \pi*(2x)^2 = 4\pi x^2[/tex]

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The last step is to divide the two results. The x^2 terms cancel out.

We'll be left with...

[tex]\frac{A_1}{A_2} = \frac{12x^2}{4\pi x^2} = \frac{12}{4\pi} = \frac{3}{\pi} \approx 0.9549[/tex]

There are many ways to express this ratio. One way we could write it is to say 3:pi to indicate that if the area of the square is 3, then the circle has area of pi (approximately 3.14). No matter what the square's area is, the circle is always slightly larger in area.

Answer:

f(-2) = -2

Step-by-step explanation:

f(-2)  means find the y value when x = -2

The y value when x = -2 is-2

f(-2) = -2

Answer: 18:23

Step-by-step explanation:

i have to write 20 characters so there is ur answer

The zero of the equation [tex]6 = -16x^2 + 24x + 1[/tex] represents the moment when the ball is 6 ft above the ground.

Given that,

The height y, in feet, of a football x seconds, after it is thrown is modeled by the equation,

[tex]\rm y = -16x^2 + 24x + 1.[/tex]

We have to determine,

What information does the zero of the equation [tex]6 = -16x^2 + 24x + 1[/tex] represent?

According to the question,

In the quadratic equation for the ball's height, it is found that the zero of the equation represents,

[tex]\rm 6 = -16x^2 + 24x + 1[/tex]

The instant of the time x is when the ball is 6 ft above the ground.

The height of the ball is y(x), after x seconds, is modeled by:

[tex]\rm y = -16x^2 + 24x + 1.[/tex]

The equation given is,

[tex]\rm 6 = -16x^2 + 24x + 1[/tex]

In which the height is 6 feet above the ground, and the zeroes are the instants of time when the ball is 6 ft above the ground.

Hence, These points represent the moment when the ball is 6 ft above the ground.

For more details about the Quadratic equation refer to the link given below.

https://brainly.com/question/25960606

Answer:

3d+4

Step-by-step explanation:

(5d+6)–(2d+2)

To find the opposite of 2d+2, find the opposite of each term.

5d+6−2d−2

Combine 5d and −2d to get 3d.

3d+6−2

Subtract 2 from 6 to get 4.

3d+4

Hope this helps! :)

The graph must pass through the y-axis at y = -4 with a positive slope of 3

Given the expression

Write the given equation in standard form to have:

7x+y=10x-4.

y = 10x - 7x - 4

y = 3x - 4

From the equation, the slope is 3 and the y-intercept is -4

The graph must pass through the y-axis at y = -4 with a positive slope of 3.

Learn more on equation of a line here: https://brainly.com/question/13763238

Answer:

0.677

Step-by-step explanation:Add up the values in the plan A column. There are 10+12+16 = 38 people who prefer plan A.

Add up the values in the "40-49" row to find that 16+8 = 24 people are ages 40 to 49.

We have 38+24-16 = 46 people who either prefer plan A, are aged 40-49, or fit both descriptions. I subtracted off 16 because those 16 people were counted twice when adding 38 and 24.

An alternative way to get this value of 46 is to add up everything that is in column1 or row 3 (or both). So that would get 10+12+16+8 = 46.

Now add up everything in the table to find out how many people were surveyed total. That would be 10+7+12+15+16+8 = 68 people overall.

The probability of someone liking plan A, or being age 40-49, or both is 46/68 = 0.6765 approximately. Rounding to 3 decimal places gives 0.677

Answer:

Step-by-step explanation:

A. x is negative infinite to positive infinite

b. Y=3

c. Yes

reasoning

a. It’s asking what can x equal Be used domain is like another name for x and of you look on thw graph the arrow is crossing all the x points

B. It’s asking for y since range is another name for y and you see on the y axis, y is only interacts with three and no other point so it’s just y=3

C. It’s a function because it passes the vertical line tes!

Answer:

Salmat po sa lahat

Step-by-step explanation:

ako ay from pilipinas na padpad lng dito ^_^

Answer:

Undefined

Step-by-step explanation: Because the pints are a line so there isnt a slope unless ther is a shape.

I'm saying positive. I don't think you need a shape to find the slope

Hello there! :)

We are given that the line passes through the point (4,5) and that it's perpendicular to the line y=2x-3.

Perpendicular lines have slopes that are opposite reciprocals.

This means we take a number, make it negative, and flop it over:

2

-2

-1/2

So the slope of the line perpendicular to y=2x-3 is -1/2.

Now, we have the slope and a point that the line passes through, so we can write the equation in point-slope form, which looks like so:

y-y1=m(x-x1)

Where

y1 is the y-coordinate of the point

m is the slope

x1 is the x-coordinate of the point

Now, let's plug our values into the equation:

y-y1=m(x-x1)

y-5=-1/2(x-4)

y-5=-1/2x+2

y=-1/2x+2+5

y=-1/2x+7

Hence, that is the equation of the line.

Hope it helps.

~A lonely teen who helps others with a smile

-Grace :-)

Good luck.

Answer:

12 cm^2

Step-by-step explanation:

The area of the rhombus is 12 cm².

Given that, a rhombus has a side length of 6 centimetres, and a height of 2 centimetres.

We need to find the area of the rhombus, in centimetres.

The formula for the area of the rhombus when base and height are known.

The rhombus is a parallelogram. We know that the area of a parallelogram is given by multiplying base and height sq units. The same is applied to the rhombus as well. Area of a rhombus = Base × Height sq units.

Now, the area of a rhombus= 6×2=12 cm²

Therefore, the area of the rhombus is 12 cm².

To learn more about the area of the rhombus visit:

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Answer:

OK so a triangle has 3 sides and the perimeter around it is 20.6 cm to find the unknown for the length of a side it would be 20.6 ÷3 which is = to 6.86 to 2 decimal places

Step-by-step explanation:

20.6÷3

= 6.86 cm to 2 dp

The life expectancies of residents of a country for which the average annual income is $80,000 for the three models are 12309.9352, 172.2436 and 4828.1393

The life expectancies of the models are given as:

[tex]y =69.9352 + 0.1530\times (income)[/tex] --- model 1

[tex]y =4.2436 + 0.0021\times (income)[/tex] --- model 2

[tex]y =4.1393 + 0.0603\times (income)[/tex] --- model 3

Given that the average annual income is $80,000;

We simply substitute 80000 for income in the equations of the three models.

So, we have:

Model 1

[tex]y =69.9352 + 0.1530\times (income)[/tex]

[tex]y =69.9352 + 0.1530\times 80000[/tex]

[tex]y =12309.9352[/tex]

Model 2

[tex]y =4.2436 + 0.0021\times (income)[/tex]

[tex]y =4.2436 + 0.0021\times 80000[/tex]

[tex]y =172.2436[/tex]

Model 3

[tex]y =4.1393 + 0.0603\times (income)[/tex]

[tex]y =4.1393 + 0.0603\times 80000[/tex]

[tex]y =4828.1393[/tex]

Hence, the life expectancies are 12309.9352, 172.2436 and 4828.1393

Read more about linear models at:

https://brainly.com/question/8609070

Answer:

  Y = 62°

Step-by-step explanation:

The sum of angles in a triangle is 180°.

  W + X + Y = 180°

  (4n -9°) + (7n -16°) +(6n -16°) = 180°

  17n -41° = 180° . . . . . . . . . . simplify

  17n = 221° . . . . . . . . . . add 41°

  n = 13° . . . . . . . . . . divide by 17

Then the measure of Y is ...

  Y = 6n -16° = 6(13°) -16° = 78° -16°

  Y = 62°

_____

The other angles are W = 43°, X = 75°.

Angles of a triangle adds to 180° .

=> W + X + Y = 180°

=> (4n-9°) + (7n-16°) + (6n-16°) = 180°

=> 17n-41° = 180°

=> 17n = 180° + 41°

=> 17n = 221°

=> n = 221/17

=> n = 13°

=> 6n-16° = 6(13°) -16° = 62°

Y = 62°

Answer:

$62,900

Step-by-step explanation:

Answer:

Graph C

Step-by-step explanation:

Answer:

In other words, x = r x = r is a root or zero of a polynomial if it is a solution to the equation P (x) =0 P ( x) = 0.

Step-by-step explanation:

Answer:

The answer would be 5 Girls and 4 Boys.

Step-by-step explanation:

15 Girls divided by 3 groups= 5 girl groups

12 boys divided by 3= 4 boy groups

Answer:

3+3=6

the answer is 6 many groups created

Answer:

61 minutes and 36 seconds

Step-by-step explanation:

150 mph is equal to 2.5 miles per minutes divide miles by 2.5

Step-by-step explanation:

it's option D (x³)

hope this helps you.

Answer:

Step-by-step explanation:

Conclusion:

Therefore, n = 20.

Hoped this helped.

[tex]GeniusUser[/tex]

Answer:

A. 2 units

Step-by-step explanation:

took the test and got it right

The radius of the circle is r = 2 units

A circle is a closed figure in which the set of all the points in the plane is equidistant from a given point called “center”. Every line that passes through the circle forms the line of reflection symmetry. Also, the circle has rotational symmetry around the center for every angle

The circumference of circle = 2πr

The area of the circle = πr²

where r is the radius of the circle

The standard form of a circle is

( x - h )² + ( y - k )² = r²,

where r is the radius of the circle and (h,k) is the center of the circle.

The equation of circle is ( x - h )² + ( y - k )² = r²

For a unit circle , the radius r = 1

x² + y² = r² be equation (1)

Now , for a unit circle , the terminal side of angle θ is ( cos θ , sin θ )

Given data ,

Let the equation of the circle be represented as A

Now , the value of A is

( x - 7 )² + ( y - 10 )² = 4

The equation ( x - 7 )² + ( y - 10 )² = 4 represents a circle in standard form, where the center of the circle is located at the point (7, 10) and the radius is the square root of the number on the right side of the equation

Taking the square root of 4, we find that the radius of the circle is 2 units

Hence , the radius is r = 2 units

To learn more about circle click :

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Answer:

130

Step-by-step explanation:

Step 1: write equations:

Company A: y = 0.20x + 110

Company B: y = 0.50x + 80

Step 2: graph your lines

Step 3: Find your intersect point

Step 4: find the points: (100,130)

The number of miles is y, so at 130 miles, both trucks are the same cost

Hope that helps

Answer:

x-intercept = 3, 0

y-intercept = 0, -4

Step-by-step explanation: