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
denis23 [38]
3 years ago
15

A secant and a tangent to a circle intersect in a 42-degree angle. The two arcs of the circle intercepted by the secant and the

tangent have measures in a 7:3 ratio. Find the measure of the third arc
Mathematics
1 answer:
Amanda [17]3 years ago
3 0

Answer:

The measure of the third arc is 150\°

Step-by-step  explanation:

step 1

we know that

The measurement of the external angle is the semi-difference of the arcs which comprises

in this problem

Let

x----> the greater arc of the circle intercepted by the secant and the tangent

y----> the smaller arc of the circle intercepted by the secant and the tangent

42\°=\frac{1}{2}(x-y)

84\°=(x-y) ----> equation A

\frac{x}{y}=\frac{7}{3}

x=\frac{7}{3}y -----> equation B

Substitute equation B in equation A and solve for y

84\°=(\frac{7}{3}y-y)

84\°=(\frac{4}{3}y)

y=3*84\°/4=63\°

Find the value of x

x=\frac{7}{3}(63\°)=147\°

step 2

Find the measure of the third arc

Let

z------> the measure of the third arc

we know that

x+y+z=360\° -----> complete circle

substitute the values and solve for z

147\°+63\°+z=360\°

z=360\°-(147\°+63\°)=150\°

You might be interested in
A classroom has 3 rows of desks. There are 5 desks in each row. How many desks are there altogether?
kicyunya [14]
The answer is 15 because you multiply 5×3=15
4 0
3 years ago
Read 2 more answers
Michael lives in the northwest corner of Clark County. Clara
timama [110]

Answer:

About 0.41 hours

Step-by-step explanation:

THe distance between Michael and Clara is 44 km.

We know D = RT,

Where

D is distance

R is rate (speed)

T is time

For Michael, we can write:

D = 47t

For Clara, we can write:

D = 61t

If we let michael's distance be x, Clara's distance would be 44 - x

So, we can say:

x = 47t

and

44 - x = 61t

Putting first equation into 2nd, we get:

44 - 47t = 61t

SOlving:

44 - 47t = 61t

44 = 61t + 47t

44 = 108t

t = 44/108 = 0.41 hours

The commute took 0.41 hours

7 0
3 years ago
12x + 2y = 112<br> What does x equal???<br> What does y equal???
Schach [20]
12x+2y=112
6x+y=56
6x=56-y

x=(56-y)/6
y=(56-6x)
4 0
3 years ago
Read 2 more answers
An angle measures 152° less than the measure of its supplementary angle. What is the measure of each angle?
GrogVix [38]

Two supplementary angles when added together need to equal 180 degrees.

Let the first angle = X

The second angle would then be X - 152

Add them together to equal 180:

X + X - 152 = 180

Simplify:

2X -152 = 180

Add 152 to each side:

2X = 332

Divide both sides by 2:

X = 332 / 2

X = 166

The first angle = X = 166 degrees.

The second angle = X - 152 = 166 - 152 = 14 degrees.

The angles are 166 and 14

5 0
3 years ago
Find the vertices and foci of the hyperbola with equation x squared over nine minus y squared over sixteen = 1.
Arisa [49]
<em>Standard equation of hyperbola is </em>\frac{x^{2} }{ a^{2} } -  \frac{ y^{2} }{ b^{2} } = 1.

<em>Comparing given info with standard equation, we get 
</em>a(vertices)= +3 and -3
foci = \sqrt{ a^{2} + b^{2} } =  \sqrt{9+16} =  \sqrt{25} =5.
7 0
3 years ago
Other questions:
  • 1/1×3 + 1/3×5 + ... + 1/47×49 HELP PLZ
    8·1 answer
  • I hate math can someone please help me
    15·2 answers
  • What is the hypothesis in the following conditional
    15·1 answer
  • What is the value of 111=14g
    6·2 answers
  • Which segment is parallel to FE?
    7·1 answer
  • Can someone help pls​
    6·1 answer
  • After ordering the data set, what is the next step in drawing a box plot that shows the distribution of the amounts spent? 1. Ma
    14·1 answer
  • Solve for r.<br><br> 19 = 7 − –3r
    5·2 answers
  • Can someone help me answer this question plz and thank you
    15·2 answers
  • Urgent help……………………:::::::::::
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!