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Mekhanik [1.2K]
3 years ago
14

Given that two tangent lines are constructed from the shared point A outside a circle with the center O and points of tangency B

and C, what is the measure of ∠OAB if ∠OAC measures 30°?
Mathematics
2 answers:
vlabodo [156]3 years ago
8 0

Answer:

OAC =30

Step-by-step explanation:

Given that for a circle there are two tangents at points of contacts B and C meet at A

The centre of the circle is O.

By tangents theorem for circles, OAB and OAC are congruent

Hence angle OAB = angle OAC

Angle OAB is given to be 30 degrees

Hence angle OAC is equal to 30 degrees

ololo11 [35]3 years ago
5 0
∠OAB = ∠OAC

∠OAB = 30°
You might be interested in
N divided Into 8 is what
Goryan [66]

Answer:

\frac{N}{8}

Dividing is the same as putting numbers into a fraction. This is N/8. We don't get the answer until we figure out what N is equal to.

7 0
4 years ago
The box plot show the weights in ounces of 15 different bags of almonds. About how many bags contained less than 27 ounces:
andre [41]

Answer:

See explanation

Step-by-step explanation:

The question is incomplete, as the box plot is not given. A general approach to the question, is as follows:

First, identify the 27 mark on the box plot.

Next, count the number of data less than 27.

Take, for instance, there are 6  dots or marks before 27;

This means that 6 bags contain  less than 27 ounces

4 0
3 years ago
find the equation of a circle which passes through the point (2,-2) and (3,4) and whose centre lies on the line x+y=2
Nadusha1986 [10]

Answer:

Equation of the circle

(x - 0.7)² + (y - 1.3)² = 12.58

Step-by-step explanation:

The formula for the equation of a circle is given as:

(x - a)² + (y - b)² = r²,

where(a, b) is the center of the circle and r = radius of the circle.

a) We are told in the question that the equation of the circle passes through point(2, -2)

Hence,

Substituting 2 for x and -2 for y in the equation of the circle.

(x - a)² + (y - b)² = r²

(2 - a)² +(-2 - b)² = r²

Expanding the bracket

(2 - a) (2 - a) + (-2 - b)(-2 - b) = r²

4 - 2a - 2a +a² +4 +2b +2b +b² = r²

4 - 4a + a² + 4 + 4b + b² = r²

a² + b² -4a + 4b + 4 + 4 = r²

a² + b² -4a + 4b + 8 = r²............Equation 1

We are also told that the equation of the circle also passes through point (3,4) also, where 3 = x and 4 = y

Hence,

Substituting 3 for x and 4 for y in the equation of the circle.

(x - a)² + (y - b)² = r²

(3 - a)² +(4 - b)² = r²

Expanding the bracket

(3 - a) (3 - a) + (4 - b)(4- b) = r²

9 - 3a - 3a +a² +16 -4b -4b +b² = r²

9 -6a + a² + 16 -8b + b² = r²

a² + b² -6a -8b + 9 + 16 = r²

a² + b² -6a -8b + 25 = r²..........Equation 2

The next step would be to subtract Equation 1 from Equation 2

a² + b² -4a + 4b + 8 - (a² + b² -6a -8b + 25) = r² - r²

a² + b² -4a + 4b + 8 - a² - b² +6a +8b - -25= r² - r²

Collecting like terms

a² - a² + b² - b² - 4a + 6a + 4b + 8b +8- 25 = 0

2a + 12b -17 = 0

2a + 12b = 17...........Equation 3

Step 2

We are going to have to find the values of a and b in other to get our equation of the circle.

Since the center of the circle(a, b) lies on x + y = 2

Therefore, we have

a + b = 2

a = 2 - b

2a + 12b = 17 ..........Equation 3

Substituting 2 - b for a in

2(2 - b) + 12b = 17

4 - 2b + 12b = 17

4 + 10b = 17

10b = 17 - 4

10b = 13

b = 13/10

b = 1.3

Substituting 1.3 for b in

a + b = 2

a + 1.3 = 2

a = 2 - 1.3

a = 0.7

hence, a = 0.7, b = 1.3

Step 3

We have to find the value of r using points (2, -2)

(x - a)² + (y - b)² = r²

Where x = 2 and y = -2

(-2 - 0.7)² + (-2 - 1.3)² = r²

(-2.7)² + (-3.3)² = r²

1.69 + 10.89 = r²

r² = 12.58

r = √12.58 = 3.55

Step 4

The formula for the equation of a circle is given as:

(x - a)² + (y - b)² = r²,

where(a, b) is the center of the circle and r = radius of the circle

a = 0.7

b = 1.3

r² = 12.58

Equation of the circle =

(x - 0.7)² + (y - 1.3)² = 12.58

7 0
4 years ago
The drama club was selling ticketsto the school play. Adult ticketscost $8.00 each, and studenttickets cost $5.00 each. The litt
BlackZzzverrR [31]

We are given a problem that can be solved using a system of linear equations. Let A, be the number of adults, and S the number of students. Since there are in total 142 people and there were two days, this means that the sum of the number of adults and the number of students must be 284, which can be written mathematically as follows:

A+S=284,(1)

This is our first equation. The second equation is found using the total sales of $1948. Since the ticket per adult is $8 and per student is $5, we have the following equations:

8A+5S=1948,(2)

To solve this equation we will solve for A in equation (1), by subtracting S to both sides;

\begin{gathered} A+S-S=284-S \\ A=284-S \end{gathered}

Now we will replace this value in equation (2):

8(284-S)+5S=1948

Now we will apply the distributive property:

2272-8S+5S=1948

Addins like terms:

2272-3S=1948

Subtracting 2272 to both sides;

\begin{gathered} 2272-2272-3S=1948-2272 \\ -3S=-324 \end{gathered}

Dividing both sides by -3:

S=-\frac{324}{-3}=108

Now we replace this value in equation (1), where we have already solved for A:

\begin{gathered} A=248-108 \\ A=140 \end{gathered}

Therefore, there were sold 108 student tickets and 140 adult tickets.

3 0
1 year ago
Help please if u can answer!:)
pentagon [3]

Answer:

ANGLE K IS 75 DEGREES

All the interior angles of a triangle ADD up to 180 degrees

lets add the angles!

6x-11+8x-29+3x-1

add like terms. all the x terms add up and all the constants as well

8x+6x+3x = 17x

-29-1-11 = -41

17x-41= 180 (-41 + 41 = 0 we do this to remove -41 from the left side of the equation to isolate x)

41+180 = 221

17x=221

221/17 = 13

x=13

so..

8 * 13 - 29 is the angle..

8*13 = 104

and 104-29 = 75

Angle K is 75 degrees! hope that helps..

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
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