answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Mrrafil [7]
2 years ago
12

25 points ! Circle B is Internally tangent to circle A at point p. Likewise, circle C is internally tangent to circle D at point

P. If BD=AC , AB=4, and SD=2, find the length of diameters for circles C and D. Be sure to justify your work. The Picture is the diagram

Mathematics
1 answer:
Greeley [361]2 years ago
3 0
All the given points are collinear, so we have ...
  AB +BC = AC
  BC +CS +SD = BD
The problem statement tells us
  BD = AC
  BC +CS +SD = AB +BC . . . . . substituting for BD and AC
  BC +CS +2 = 4 +BC . . . . . . . . substituting given lengths
  CS = 2 . . . . . . . . . . . . . . . . . . . subtract (2+BC)

CS is the radius of Circle C, so its diameter is twice that: 4. The radius of Circle D is the diameter of Circle C plus SD, so is 4 +2 = 6. The diameter of Circle D is twice that: 12.

The diameter of Circle C is 4.
The diameter of Circle D is 12.
You might be interested in
If the squared difference of the zeroes of the quadratic polynomial x2+kx+30 is equal to 169 find the value of k and the zeroes
anyanavicka [17]

ANSWER

x  =  2 \: \: or \:  \:  x  =  15

Or

x  =   - 2 \: \: or \:  \:  x  =   -  15

EXPLANATION

The given polynomial is

f(x) = {x}^{2}  + kx + 30

where a=1,b=k, c=30

Let the zeroes of this polynomial be m and n.

Then the sum of roots is

m + n =  -  \frac{b}{a}  =  -k

and the product of roots is

mn =  \frac{c}{a}  = 30

The square difference of the zeroes is given by the expression.

( {m - n})^{2} =  {(m + n)}^{2} - 4mn

From the question, this difference is 169.

This implies that:

( { - k)}^{2}  - 4(30) = 169

{  k}^{2}  -120= 169

k^{2} = 289

k=  \pm \sqrt{289}

k=  \pm17

We substitute the values of k into the equation and solve for x.

f(x) = {x}^{2}   \pm17x + 30

f(x) = (x  \pm2)(x  \pm 15)

The zeroes are given by;

(x  \pm2)(x  \pm 15) = 0

x  =  \pm2 \: \: or \:  \:  x  =  \pm 15

5 0
2 years ago
A standard six-sided die is rolled $6$ times. You are told that among the rolls, there was one $1,$ two $2$'s, and three $3$'s.
Alex777 [14]

Answer:

Sequence = 120

Step-by-step explanation:

Given

6 rolls of a die;

Required

Determine the possible sequence of rolls

From the question, we understand that there were three possible outcomes when the die was rolled;

The outcomes are either of the following faces: 1, 2 and 3

Total Number of rolls = 6

Possible number of outcomes = 3

The possible sequence of rolls is then calculated by dividing the factorial of the above parameters as follows;

Sequence = \frac{6!}{3!}

Sequence = \frac{6 * 5 * 4* 3!}{3!}

Sequence = 6 * 5 * 4

Sequence = 120

Hence, there are 120 possible sequence.

7 0
2 years ago
Carly will be going to college in 3 years. She anticipates that she will need $12,000 to pay for the first year. She currently h
kupik [55]
<span>Carly needs to deposit  $350 into the savings account per month over the next 3 years to be able to pay for her first year of college</span>
4 0
2 years ago
1. What is m∠CAD?
bulgar [2K]
< CAD = 100....if u add < ACB + < CBA u get < CAD
================
< DAB = 125 and < ACB = 30

if DAB = 125.....then BAC = 180 - 125 = 55
and all 3 interior angles of a triangle = 180
< BAC + < ACB + < ABC = 180
55 + 30 + < ABC = 180
85 + < ABC = 180
< ABC = 180 - 85
< ABC = 95 <===


6 0
2 years ago
Read 2 more answers
You get a large ice-cream cone for $2.99 and a bottle of water for $1.07 . You pay with a 10 -dollar bill. How much change will
Igoryamba
10 - 2.99 = 7.01 and 7.01 - 1.07 = 5.94 so you will get 5.94 in change 
5 0
2 years ago
Read 2 more answers
Other questions:
  • The lines graphed below are perpendicular. The slope of the red line is -1/3. What is the slope of the green line?
    15·1 answer
  • Compare the two functions described below.
    15·1 answer
  • Find sec θ if θ is in Quadrant IV and sinθ=-1/5
    11·2 answers
  • PLEASE !!! don’t want to sound rude but I could really, really use some help. thank you so much if you answer !
    8·2 answers
  • Sabrina has a rug with a perimeter of 18 feet. She decides to place a border around the rug so that the new length of the rug is
    15·2 answers
  • Brad buys a pack of 12 bottles of energy drink for £9.25 he then sells all bottles for £1 each. Work out brads percentage profit
    8·1 answer
  • The Post Office has established a record in a major midwestern city for delivering 90 percent of its local mail the next working
    11·1 answer
  • Consider the following hypothesis: "There is no relationship between income and amount of money spent on food." If the hypothesi
    11·1 answer
  • Mrs.thapa bought 150 kg of oranges.18 kg of oranges were rotten and not fit for selling.If she sold the remaining quantity of or
    6·2 answers
  • The value of a tractor decreases over time and is given by
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!