Find the length of the tangent segment AB to the circles centered at O and O' whose radii are a and b respectively when the circles touch each other

Answers

Answer 1

Answer:

[tex]AB=2\sqrt{ab}[/tex]

Step-by-step explanation:

From figure,

[tex]OA=a, \quad \quad O'B=b\\\Rightarrow OO'= (a+b) \quad \quad \text{and}\quad OD=(a-b)[/tex]

In triangle [tex]OO'D[/tex]

  [tex](OO')^2=(OD)^2+(O' D)^2[/tex]

[tex]\Rightarrow (a+b)^2=(a-b)^2+(O' D)^2\\\Rightarrow a^2+b^2+2ab-a^2-b^2+2ab=(O' D)^2\\\Rightarrow 4ab=(O' D)^2\\\Rightarrow O'D=2\sqrt{ab} \\\Rightarrow O' D=2\sqrt{ab}=AB \quad \quad [\because O' DAB\;\; \text{is a rectangle.}][/tex]

Hence, [tex]AB=2\sqrt{ab}[/tex]

Find The Length Of The Tangent Segment AB To The Circles Centered At O And O' Whose Radii Are A And B

Related Questions

HELP!!!!!!! Solve the equation |x-1|+3=2

Answers

|x-1| + 3=2
The absolute value of x-1 is x+1

Our new equation: x+1+3=2

X+4=2
Then you have to isolate the variable
X+(-4+4)=(2-4)


Answer: X=-2

What is the equation of the line that passes through the point (4,-3)(and has a slope of 11?

Answers

Answer: -3 = 11(4) + b

Step-by-step explanation: y = mx + b, -3 is the y, 11 is the slope (m), 4 is the x, b is the y-intercept which is unknown unless you solve for it.

3х +2у = -5
Чx - Зу = 16

Answers

3х +2у = -5 Xx - Pe = 16

Dominic buys a 64-ounce container of salad mix. About how many ounces of romaine lettuce does the container have? 6 ounces 12 ounces 18 ounces 27 ounces Please help cuz im in a pretest and my brain is ded

Answers

Complete question :

The graph below shows the percentages of ingredients in a salad mix.

A pie chart titled Percentages in salad mix. 40 percent is iceberg, 27 percent is romaine, 15 percent is spinach, 12 percent is arugula, 6 percent is carrots.

Dominic buys a 64-ounce container of salad mix. About how many ounces of romaine lettuce does the container have?

Answer:

18 ounces

Step-by-step explanation:

From the pie chart ;

The percentage of each Salad mixture in the mix is given ;

Romaine lettuce occupies 27% of the total salad mix ;

The total of amount of ounce of the entire salad mix is 64 ounce

Therefore, number of ounces of Romaine lettuce in the salad mix is ;

27% of 64

0.27 * 64

17.28

= 18 ounces

Alfredo has 3 times as many sneakers as Jessy. Lucia has 5 more sneakers than Jessy. Together they have 20 pairs. Find the number of sneakers each person has.
please show work

Answers

Answer:

Step-by-step explanation:

H

Answer:

15

Step-by-step explanation: 3x5=15

so thx 4 the points

Hard Equation that equals 1-25

Answers

Answer:

8000000000000000000000000000000000

Answer:

5X5=

-X4=

-+25=

-divide by 5=

Step-by-step explanation:

hope thats ok for you please mark me as brainliest

At T-Shirts R Us, the cost to make new shirts is $1.50 per shirt plus a $50 set-up fee. At T-Shirt Planet, the set-up fee is $75 and $1 per shirt. Find the number of shirts you can order so that the cost at both companies is the same.

Answers

Answer: The number of shirts you can order = 40

Step-by-step explanation:

Let x = Number of shirts

At T-Shirts R Us,

Total cost = 50+1.50x

At T-Shirt Planet,

Total cost = 75+x

As per given, when the cost at both companies is the same then

[tex]1.50x+50=x+70\\\\\Rightarrow\ 1.50x-x=70-50\\\\\Rightarrow 0.50x=20\\\\\Rightarrow\ x=\dfrac{20}{0.50}=40[/tex]

Hence, the number of shirts you can order = 40

PLZ: show work, solve for x:

Answers

x+11/-2=-8

x+11/-2 x -2= -8 x -2

x+11= 16

X+11-11=16-11

x = 5

Jake said he can find 630 ÷ 10 by taking the 0 off of 630 to get 63. Jake finds 35.270 ÷ 10 using the same method and gets 35.27. Use the drop-down menus to complete the statement about why Jake is correct or incorrect.

Answers

Answer:

Jake is incorrect with his methodology for solving these problems

Step-by-step explanation:

Jake is incorrect with his methodology for solving these problems. This is because dividing a number by 10 requires moving the decimal point one digit to the left. When dividing 630 by 10, removing the zero works because by moving the decimal one digit to the left we would simply drop the zero and the decimal would not be needed leaving the answer as 63. However, this does not work on numbers that already have a decimal such as 35.270. This number divided by 10 would be 3.527 but simply removing the 0 like Jake states would give us the incorrect answer of 35.27

Answer:

Step-by-step explanation:

Which one of these transformations would produce an image that is not congruent to its pre-image? (4 points)


A translation of (x − 1, y − 3)
A rotation of 90 degrees about the origin
A rotation followed by a translation
A dilation followed by a reflection

Answers

Answer:

A dialation followed by a reflection

Step-by-step explanation:

When you dialate a shape it changes the size which makes the shape similar but not congrouent.

The option “a dilation followed by a reflection” will produce an image that is not congruent to its pre-image option, fourth is correct.

What is geometric transformation?

It is defined as the change in coordinates and the shape of the geometrical body. It is also referred to as a two-dimensional transformation. In the geometric transformation, changes in the geometry can be possible by rotation, translation, reflection, and glide translation.

As we know, the translation will shift the object.

If rotate the image with 90 degree about origin will change the orientation of the image but shape will remains same.

A dilation followed by reflection will change the image because the transformation dilation is used to resize an item. Dilation is a technique for making items appear larger or smaller.

Thus, the option "a dilation followed by a reflection" will produce an image that is not congruent to its pre-image option fourth is correct.

Learn more about the geometric transformation here:

brainly.com/question/16156895

#SPJ2

PLEASE help, i’ll give brainliest

Answers

Step-by-step explanation: I think it is 18 tell me if I am wrong

what is the answer ?

Answers

Answer:

4

......................

anyone know this? I need help with this badly

Answers

Answer:

Step-by-step explanation:

no

whats 4 +4

guys pls help

Answers

Answer:

8

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

the 2 triangles are similar. if the perimeter of triangle abc is 28, find the value of x​

Answers

given the sides 8 and 10 are similar we can assume that triangle abc is 80% as large. meaning the perimeter of triangle rst is 35.
so 10 + x - 4 + x - 1.5 = 35
4.5 + 2x = 35
2x = 30.5
x = 15.25

A person can bike 48 miles in 2 hours. At this rate how long will it take this person to travel 66 miles? Show work please!!!

Answers

Answer:

Convert to a decimal by dividing the numerator by the denominator.

2.75  hours

someone please help!

Answers

IT IS THE THIRD ONE:

3+8.486

because I find it like that

A school purchases a used van that costs $10,000. The value, V(t), in dollars, of the van t years since its purchase is modeled by the exponential function V(t)=10,000(0.8)^t . Select ALL statements that are true regarding the value of the van. a.The value of the van decreases by 20% each year since its purchase. b.The value of the van decreases by 80% each year since its purchase. c.The value of the van decreases by $2,000 each year since its purchase. d.Each year since its purchase, the value of the van is 80% of the value of the previous year. e.Each year since its purchase, the value of the van is 0.8 times the value of the previous year.

Answers

Answer:

a.The value of the van decreases by 20% each year since its purchase.

b.The value of the van decreases by 80% each year since its purchase.

d.Each year since its purchase, the value of the van is 80% of the value of the previous year.

Step-by-step explanation:

From the above question, we are given the Exponential function

V(t)=10,000(0.8)^t

Verifying the given options:

a.The value of the van decreases by 20% each year since its purchase.

Option a is correct , this is because, the Exponential function above is and Exponential Decrease.

The formula is given as:

V(t) = 10000(1 - r) ^t

Where r = Decreasing rate

Comparing

= 1 - r = 0.8

= 1 - 0.8 = r

r = 0.2

Converting to percentage

= 0.2 × 100 = 20%

Option a is correct

b.The value of the van decreases by 80% each year since its purchase.

Let solve for t = 1 and t = 2

V(t) = 10000(0.8) ^t

When t = 1

= 10000× 0.8¹

= 8000

When t = 2

= 10000× 0.8²

= 6400

Confirming option d

For year 2

= 80% × year 1

Year 1 = 8000

= 80% × 8000 = 6400

Option b is correct

c.The value of the van decreases by $2,000 each year since its purchase.

Option C is incorrect

d.Each year since its purchase, the value of the van is 80% of the value of the previous year.

Option d is correct because

Let solve for t = 1 and t = 2

V(t) = 10000(0.8) ^t

When t = 1

= 10000× 0.8¹

= 8000

When t = 2

= 10000× 0.8²

= 6400

Confirming option d

For year 2

= 80% × year 1

Year 1 = 8000

= 80% × 8000 = 6400

Option d is correct

e.Each year since its purchase, the value of the van is 0.8 times the value of the previous year.

Option e is incorrect

From the options given in the question, the correct statements are,

Options a, b, and d.

The regular price of a skateboard is p. Which expression represents the price of the skateboard when it is on sale for 25% off? Select all that apply.

Answers

Answer:   The expression represents the price of the skateboard when it is on sale for 25% off = 0.75p

Step-by-step explanation:

Given: Regular price of a skateboard is p.

Discount = 25% off = 0.25p

Now, the  price of the skateboard when it is on sale for 25% off = p - Discount

= p -0.25p

= (1-0.25)p

= 0.75p

Hence, the expression represents the price of the skateboard when it is on sale for 25% off = 0.75p

Answer: The expression represents the price of the skateboard when it is on sale for 25% off = 0.75p

Step-by-step explanation:

Find the simple interest for 3 years at a rate of 5% on $200

Answers

Answer:

The simple interest is $30

Step-by-step explanation:

To find this, we use the simple interest formula

Mathematically, this is;

I = PRT/100

P is the principal = $200

R is the rate = 5%

T is the time = 3 years

Substituting these values, we have;

I = (200 * 5 * 3)/100

I = $30

On a certain hot summer's day, 263 people used the public swimming pool. The daily prices are $1.25 for children and $2.50 for adults. The receipts for admission totaled $437.50. How many children and how many adults swam at the public pool that day?

Answers

Answer:

The number of children = x = 176

The number of Adults = y = 87

Step-by-step explanation:

Let us represent

The number of children = x

The number of Adults = y

On a certain hot summer's day, 263 people used the public swimming pool.

x + y = 263.... Equation 1

x = 263 - y

The daily prices are $1.25 for children and $2.50 for adults. The receipts for admission totaled $437.50.

$1.25 × x + $2.50 × y = $437.50

1.25x + 2.50y = 437.50.....Equation 2

We substitute 263 - y for x in Equation 2

1.25(263 - y) + 2.50y = 437.50

328.75 - 1.25y + 2.50y = 437.50

- 1.25y + 2.50y = 437.50 - 328.75

1.25y = 108.75

y = 108.75 ÷ 1.25

y = 87

Solving for x

x = 263 - y

x = 263 - 87

x = 176

Therefore:

The number of children = x = 176

The number of Adults = y = 87

can someone pls help!!!

Answers

3n+4=10

answer= n=2

c+2=18

PLEASE HELLPPP MEEEEE

Answers

Answer:

2x - 3y = 24

Step-by-step explanation:

You use the formula Ax ± By = C.

This is the standard linear equation form.

NEED HELP ASAP PLS HELP WILL GIVE BRAINLIEST
A triangle has side lengths of 1512, 223, and 314. What is the perimeter of the triangle? Remember that the perimeter of a triangle is the sum of its side lengths.

Answers

Answer:

Step-by-step explanation:

P= a+b+c

P= 1512+223+314

=2049

What percent of 18 is 24?

Answers

Answer:

133.33%

Step-by-step explanation:

you can find this by doing 24/18x100, which is equal to 133.33

Answer:

133%

Step-by-step explanation:

We're going to divide [tex]\frac{24}{18}[/tex].

That equals about 1.33 repeating.

Next, we're multiplying that decimal by 100.

That gets us 133.

1/3 divided by 4
2/5 divided by 4
4/7 divided by 4
2/5 divided by 3
5/6 divided by 5
5/8 divided by 10

Answers

1. 1/3 divided by 4 is 0.0833
2. 2/5 divided by 4 is 0.1
3. 4/7 divided by 4 is 0.1428
4. 2/5 divided by 3 is 0.1333
5. 5/6 divided by 5 is 0.1666
6. 5/8 divided by 10 is 0.0625

Answer:

1. 0.0833

2. 0.1

3.  0.1428

4.  0.1333

5. 0.1666

6.  0.0625

14 m
4m
What is the area of the figure to the nearest hundredth? Enter the answer in the box.
square meters

Answers

Answer:

Step-by-step explanation:

we have a rectangle and a semicircle,

area rectangle=14*4=56

area of semicircle

diameter is 4, than r=2

A of the circle=3.14*r^2=3.14*4=12.56

we have a semicircle so we will divide the area by 2

A=12.56/2=6.28

total area=56+6.28=62.28

IM BEING TIMED PLZ HURRY AND THANKS What is the sum of a° + c°

Answers

Answer:

300°

Step-by-step explanation:

a° is 180°

c° is 120° (from 180° = 60° + c°)

Pleeease help meeeeee​

Answers

Answer:

It would have to either be A or B

Step-by-step explanation:

Please help as soon as possible

Answers

Answer:

Step-by-step explanation:

the answer is No its not similar

because the factors don't work

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