1answer.
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
Papessa [141]
3 years ago
8

Please help.. with 6 & 15 ​

Mathematics
1 answer:
Black_prince [1.1K]3 years ago
3 0

Answer:

6. C: {x^2 +(y-1)^2 =2; x+y = 3}

15. C: The line does not intersect the circle.

Step-by-step explanation:

The formula for the distance (d) from a point (x, y) to a line ax+by=c is ...

d = |ax+by-c|/√(a^2+b^2)

The formula for a circle centered at (h, k) with radius r is ...

(x -h)^2 +(y -k)^2 = r^2

___

6. Comparing the circle equation to the generic equation, we find (h, k) = (0, 1) and r = √2. Then we want to find the line that is distance √2 from the center of the circle. Our line equation is x+y=c for some value of c that we want to find.

d = √2 = |0 +1 -c|/√(1^2+1^2)

2 = |1-c|

±2 = 1-c

c = 1±2 = -1 or 3

The line that is tangent to the circle is the one of choice C: x+y = 3

__

The attached graph shows the lines for all 4 answer choices. The point of tangency is (1, 2), so x+y=1+2=3.

___

15. The circle is centered at (4, 1) and has radius 3. The distance from the circle center to the line is ...

d = |2(4) -(1)|/√(2^2+(-1)^2) = 7/√5 ≈ 3.13

The distance from the circle center to the line is more than the radius of the circle, so there can be no points of intersection.

__

Alternate solution

You can substitute for y using the equation of the line. Then the circle equation becomes ...

(x -4)^2 + (2x -1)^2 = 9

x^2 -8x +16 +4x^2 -4x +1 = 9

5x^2 -12x +8 = 0

The discriminant of this quadratic is ...

b^2 -4ac = (-12)^2 -4(5)(8) = 144-160 = -16

Since this value is negative, there can be no real solutions, meaning the line does not intersect the circle.

You might be interested in
Please please Help me!!!!!
pav-90 [236]

Answer:

19,23

Step-by-step explanation:

9+x-7≥ 21

Combine like terms

2+x≥21

Subtract 2 from each side

2+x-2 ≥21-2

x≥19

Any number greater than or equal to 19

3 0
3 years ago
Inga divided two identical rectangles into equal parts. She colored one part of each rectangle.
likoan [24]

Answer:

The areas are equal.

Step-by-step explanation:

Let the first rectangle be R and

the second rectangle be R'.

Sine R and R' are identical, their lengths are equal and their breadths are equal.

So, if Inga divided each into equal parts, then each part of both rectangles are equal.

Hence, the colored parts of both rectangles are equal.

8 0
2 years ago
7x/2+5=8<br><br> solve for x
ANEK [815]

Answer:

X= 6/7

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
According to the US government, you need to drink 5 cups of beer per day to be considered an alcoholic. If Jimmy drinks 1652 cup
vlada-n [284]

Answer:

no close but he is not he drinks 4.5 a year

Step-by-step explanation:

5 0
2 years ago
Read 2 more answers
How to find the perimeter of a octagon
Morgarella [4.7K]

If you know the radius <span>RR</span> of the circle that inscribes a regular polygon having <span>nn</span>sides, the side of the regular polygon can be easily found with trigonometry.

The polygon is composed by <span>nn</span> identical triangles having a common vertex in the center of this circle, therefore this angle is <span><span>2π/n.</span></span>

4 0
3 years ago
Read 2 more answers
Other questions:
  • Will give brainlist**** What is the slope-intercept equation for the cost of a sub at Fred’s Sub Shop?
    9·1 answer
  • Find the sum of an AP sequence 6,2,-2,-6,-10..... up to 20 terms
    5·1 answer
  • Plz help me, URGENT!! 15 points!
    7·1 answer
  • Suzie went to a candy shop. The candy shop has a sign that shows the cost of the candies at the shop. The sign is below:
    9·2 answers
  • Help plz!!!!!!!!!!!!!!!!!!!!
    13·2 answers
  • Systems of equations<br> y=2x+3<br> y=-x-9
    5·2 answers
  • I need help?? I don’t understand thanks!!
    8·1 answer
  • Which expression can be used to find the slope of a line containing the points (–3, 2) and (7, –1)?
    5·1 answer
  • Find the surface area of the triangular prism (above) using its net (below).
    11·2 answers
  • If f(x) = 2x + 3, what is f(-2)?
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!