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:
[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]
Related Questions
The length of a planet's orbit around a star is approximately 24,130,000 km.
It takes the planet about 1440 Earth days to complete a full orbit.
What is the planet's average speed in kmh-1 to 3sf?
Answers
hii I am enter in wrong serve ....
Answer:
have u goa answer
Step-by-step explanation:
Consider two people where one person is 25% taller than the other but proportion in exactly the same way That the taller person looks like a lager version of the shorter person Suppose the shorter person has a 36%-inch waist what size is the the taller person's waist?
Answers
Answer:
46.8 inches
Step-by-step explanation:
Taller person = 30% more than height of shorter individual
Waist size of shorter person = 36 inches
Since they are proportioned in the same way:
Waist size of the taller person will be 30% larger than the waist size of the shorter person :
30% increase in size 36
(100 + 30)% of 36
130% of 36
(130 / 100) * 36
1.3 * 36
= 46.8 inches
Kristen invested $1,800 in an account paying 6.5% simple interest. After 5 years, what is the balance of her account?
Answers
Answer: 2,385
Step-by-step explanation:
Identify the correct Triangle Congruence Theorem that describes the figure below.
A. SAS
B. ASA
C. AAS
D. SSS
E. HL
Answers
Answer:
ASA
Step-by-step explanation:
Don't worry I just know
1) Ben has 15 coins, all dimes and quarters, worth $2.55. How
many dimes and how many quarters does Ben have?
Answers
Answer:
Ben has 8 dimes and 7 quarters.
Step-by-step explanation:
Given that:
Number of coins = 15
Worth of coins = $2.55 = 2.55 * 100 = 255 cents
Let,
x be the number of dimes
y be the number of quarters
According to given statement,
x+y=15 Eqn 1
10x+25y=255 Eqn 2
Multiplying Eqn 1 by 10
10(x+y=15)
10x+10y=150 Eqn 3
Subtracting Eqn 3 from Eqn 2
(10x+25y)-(10x+10y) = 255 - 150
10x+25y-10x-10y=105
15y=105
Dividing both sides by 15
[tex]\frac{15y}{15}=\frac{105}{15}\\y=7\\[/tex]
Putting y=7 in Eqn 1
x+7=15
x=8
Hence,
Ben has 8 dimes and 7 quarters.
Use the replacement set {4, 8, 21} to find the solution of the equation
7n - 4 = 24.
Answers
Answer:
n=4
Step-by-step explanation:
7n - 4 = 24
24 + 4 = 28
7n = 28
n = 4
OR plug in the sets you gave and see if they equal 24
Help it's due in 20 minutes !!
Answers
Answer:
ok
Step-by-step explanation:
hmm chemistry nice bro
Aileen has a total debt of $45. She is trying to pay back $6 each week for the next 4 weeks. If Aileen is successful, which amount will represent the change in the amount of her debt?
Answers
Answer:
$-21
Step-by-step explanation:
Since she is paying $6 for 4 weeks, in total she will pay:
6 x 4 = $24
She has an initial balance of $-45 Because she is in debt
Therefore you just need to add it all up
-45 + 24 = $-21
Answer:
-24
Step-by-step explanation:
6 x (-4) = 24
simplify it using order of operations
Answers
Answer:
=106
Step-by-step explanation:
PMDAS
First thing you do is the parenthesis
6+4(5)^2
then the exponent
6+4(25)
then multiply
6+100
then add
106
Hope this helps (:
Answer:
150
Step-by-step explanation:
First do what is in the parenthesis:
(2+3)
(6)
Then exponents:
[tex](6)^{2}[/tex]
(36)
Then Multiplication:
4(36)
144
Then Add:
144+6
150
Please help ASAP!!!!
Answers
Answer:
(-2, 0, 1, 3)
Step-by-step explanation:
From the given graph, there are four x-intercepts, which are the points the graph crosses the x-axis
Taking the y-axis as the given vertical line, and each demarcation as representing one unit division, we have;
The x coordinates of the x-intercepts are given as follows;
1) Two lines to the left of the origin which represents "-2"
2) Through the origin, which represents "0"
3) One line to the right of the origin which represents "1"
4) Three lines to the right of the origin which represents "3"
The set of values that represents the x-intercepts of the function are;
(-2, 0, 1, and 3)
X^3 + 4x^2 - 11x - 30 = (x+2) (x-3) (x+5)=0
Answers
Answer:
STEP 1
Equation at the end of step 1
(((x3) - 22x2) - 11x) + 30
STEP 2
Checking for a perfect cube
2.1 x3-4x2-11x+30 is not a perfect cube
Trying to factor by pulling out :
2.2 Factoring: x3-4x2-11x+30
Thoughtfully split the expression at hand into groups, each group having two terms :
Group 1: -11x+30
Group 2: x3-4x2
Pull out from each group separately :
Group 1: (-11x+30) • (1) = (11x-30) • (-1)
Group 2: (x-4) • (x2)
need help solving a practice question
Answers
look at the step by step explanation.
Step-by-step explanation:
Triangle inequality theorem - the sum of the two shorter sides has to be greater than the longest side, which is 8. This is not possible because the sum of the two shorter sides is 8 which is not greater than the longest side.
Answer:
Complicated answer.
Step-by-step explanation:
So, if one side length is 8 the perimeter of a triangle cannot be 16 this is because a triangle has three sides and 8 multiplied by three would not be 16 so we have two possible conclusions.
1. The perimeter is actually 24
2. The side lengths are actually 4
Hope I helped! Have a silver dollar day! :) Please give me brainliest! Thanks Adios!
Which gives the prices in order, from least to greatest
Answers
Answer:
is there a picture to go with the problem?
Hi another math question please help:)
Answers
Answer:
1). Yes
2). Yes
3). No
Step-by-step explanation:
1). y = 3
We can rewrite this equation in the slope-intercept form as,
y = 0.x + 3
Here, slope = 0
y-intercept = 3
Therefore, it's a linear relation.
YES.
2). 2x - 5y = 10
5y = 2x - 10
y = [tex]\frac{2}{5}x-2[/tex]
Therefor, it's a linear function.
YES
3). y = x(x + 3)
y =x² + 3x
Since, this equation is a quadratic equation,
It's not a linear function.
NO
ARE ON
1. Which of the following is most likely a graph of y=-2x +3?
Answers
Round off 3.447 g to the nearest 1/100 g
pls help
Answers
Answer: 3.55 g
Step-by-step explanation: 3.447 g rounded to the nearest 1/100 g is 3.55 g.
Hint: nearest 1/100 g also means nearest hundredth!
For what value of x must ABCD be a parallelogram?
Answers
Answer:
yes it could be
Step-by-step explanation:
Answer:
5x = 6x-7 subtract 6x from each side-x=-7x=7
Select ALL the correct answers.
Which equations have a greater unit rate than the rate represented in the table?
Y= 5/7x
Y= 3/4x
Y= 1/3x
Y= 7/9x
Y= 7/11x
Answers
Answer:
y = 5/7 x
y = 7/9 x
y = 3/4 x
Step-by-step explanation:
Firstly, let us get the unit rate on the table
That would be;
y/x = 2/3
y = (2/3)x
so the fractions greater than 2/3 will
be our answer
3/4 is greater
7/9 is greater
5/7 is greater
v / -0.8 +14=39 plssss help this is literally so hard
Answers
______________________________
1.) Subtract 14 from both sides:[tex]14-14=[/tex] Cancels Out[tex]39-14=25[/tex]- We do this because we have to get 2 variables/numbers on each side of the equals, and the only way to do so is to cancels other numbers out by doing the opposite of what we see.
Equation at the end of Step 1:
[tex]v[/tex] ÷ [tex]-0.8=25[/tex]2.) Multiply both sides by −0.8:[tex]-0.8[/tex] × [tex]-0.8=[/tex] Cancels Out[tex]25[/tex] × [tex]-0.8=-20[/tex]______________________________
marking Brainlist 7-9g+3g
Answers
Answer:
7-6g
Then you do the 1 step equation.
Divide both sides by 6.
1.16=g
I'm not sure if it's right.
The table shows the amount of apple sauce made from one apple of each size. Patrice has 17 medium apples and 23 large apples. What is the total amount of apple sauce that she can make with these apples? here's the table:
Apple size: small medium large
1/3 cup 1/2 cup 3/4 cup
Answers
Answer:
uhhhhh 75
Step-by-step explanation:
find f(-3) f(x) = 4x+7
Answers
Answer:
-5
Step-by-step explanation:
4(-3) + 7
-12+7
Answer:
f(-3) = -5
Step-by-step explanation:
f(x) = 4x + 7
f(-3) = 4(-3) + 7
f(-3) = -12 + 7
f(-3) = -5
A livestock pen is built in the shape of a rectangle that is four times as long as is wide. The total perimeter is 60 ft. Write an equation that models the perimeter in terms of width and/or length, find the length and width.
Answers
Answer:
Perimeter = 60ft = 2(4x + x)
breadth = 6ft
length = 24ft
Step-by-step explanation:
Perimeter = 2 (L + B)
L =length
B = Breadth
x= breadth
4x = length
Perimeter = 60ft = 2(4x + x)
Dividing both sides by 2 :
30ft= 4x + x
30ft = 5x
divide both sides by 5
6ft= x
breadth = 6ft
length = 4x= 4 x 6 = 24ft
Merry has a pipe that she wants to cut into 4 pieces. If the pipe is 26 2/3 feet long, how long should she cut each piece?
Answers
Answer: 6 2/3 ft
Explanation:
1. Turn the mixed number (26 2/3) into an improper fraction by multiplying 26 by 3 and then adding 2. (26x3=78)(78+2=80=80/3)
2. Now divide 80 by the number of pieces she’s cutting (4). (80÷4=20)
3. Now divide 20 by the denominator (3) to convert it back into a mixed number. (20÷3=6 2/3)
45% of a number is 34. Find the number.
if you could explain that would be great thx!!!
Answers
Step-by-step explanation:
45% of number = 34
100% of number = 34 * (100/45) = 680/9.
The number is 680/9.
Can someone help w this
Answers
PLZ HELP ME
saeszxdrctfvgybhunjimkoploihuy7gt5rdesxrdfghbinug 6frbed46c5rtf
Answers
Answer:
Sorry just trying to get pts
Step-by-step explanation:
A House needs to some maintenance one sink is dripping water every 10 minutes and the other sink is dripping every 12 minutes if both sink dripped at the same time how many minutes until they both drip at the same time again
Answers
Answer:
60 minutes
Step-by-step explanation:
We solve this question using Lowest Common Factor method
Find and list multiples of each number of minutes( 12 and 10 minutes) until the first common multiple is found. This is the lowest common multiple.
Multiples of 10:
10, 20, 30, 40, 50, 60, 70, 80
Multiples of 12:
12, 24, 36, 48, 60, 72, 84
Therefore,
LCM(10, 12) = 60
The number if minutes until they both drip again is 60 minutes
HELP ME IM USING ALL MY POINTS MULTIPLE QUESTONS PLZ
Answers
hope it will help you.........
Answer:
UV=UZ+ZV
Step-by-step explanation:
UV=3y-5+2z+2
=3y+2y-3
but UV =27=3y+2y-3
30 =3y+2y
bisect means cut in to two equal parts so
3x+3=3y+6
3x-3y=6-3
3x-3y=3
then combine the two equation
30 =3y+2y this is 30=5y which is y=6
3 = 3x-3y so enter y=6 into this equation
3=3x-3*6
3=3x-18
3x=21
x=7
does this graph represent a function? if yes why?
