Pherris is graphing the function f(x) = 2(3). He begins with the point (1,6). Which could be the next point on his graph?

Which statements are true regarding the relationships between central, inscribed, and circumscribed angles of a circle? Check al

mamaluj [8]

Answer:

# A circumscribed angle is created by two intersecting tangent segments ⇒ true (1st answer)

# The measure of a central angle will be twice the measure of an inscribed angle that intercepts the same arc ⇒ true (3rd answer)

# The measure of a central angle will be equal to the measure of an inscribed angle when the arc intercepted by the inscribed angle is twice as large as the arc intercepted by the central angle ⇒ true (6th answer)

Step-by-step explanation:

* Lets revise the types of angles in a circle

- A circumscribed angle is the angle made by two intersecting

tangent lines to a circle (it's out side the circle)

- Its measure is half the difference of the measures of the two

intercepted arcs

- Ex:

∵ AB and AC are tangent to circle M at B and C

∴ ∠A is a circumscribed angle

∴ m∠A = 1/2(m major arc BC - m minor arc BC)

- An inscribed angle is an angle formed by two chords in a circle

which have a common endpoint, this common endpoint is the

vertex of it

- Its measure is half the measure of the intercepted arc

Ex:

∵ XY and XZ are two chords in circle M

∴ ∠YXZ is an inscribed angle subtended by arc YZ

∴ m∠YXZ = 1/2 (m arc YZ)

- A central angle is an angle with endpoints located on the

circumference of the circle and its vertex is the center of the circle

- Its measure is the measure of the intercepted arc

- Ex:

∵ MA and MB are two radii of circle M

∴ ∠AMB is a central angle subtended by the opposite arc AB

∴ m∠AMB = m of arc AB

- The measure of an inscribed angle is half the measure of the

central angle which subtended by the same arc

- Ex:

∵ ∠ABC is an inscribed angle in circle M subtended by arc AC

∵ ∠AMC is a central angle subtended by arc AC

∴ m∠ABC = 1/2 m∠AMC

∴ m∠AMC = 2 m∠ABC

* Lets solve the problem

- From the facts above:

# A circumscribed angle is created by two intersecting tangent

segments ⇒ true

# The measure of a central angle will be twice the measure of an

inscribed angle that intercepts the same arc ⇒ true

- Lets prove the last statement

∵ AMC is a central angle of circle M subtended by arc AC

∴ m∠AMC = m of arc AC ⇒ (1)

∵ XYZ is an inscribed angle of circle M subtended by arc XZ

∴ m∠XYZ = 1/2 m of arc XZ

∵ m of arc XZ is twice m of arc AC

∴ m∠XYZ = m of arc AC ⇒ (2)

- From (1) and (2)

∴ m∠AMC = m∠XYZ

∴ The statement down is true

# The measure of a central angle will be equal to the measure of

an inscribed angle when the arc intercepted by the inscribed

angle is twice as large as the arc intercepted by the central

angle ⇒ true

8 0

2 years ago

Read 2 more answers

Your tutor asks you to record the time you spend using IT during the week. You have recorded this time below: Day Time Monday 0.

NikAS [45]

Let us convert all figures into decimals so that we can compare them easily.

Monday 0.3

Tuesday 15% = 0.15

Wednesday 1/6 = 0.1666

Thursday 0.2

Friday 1/8 = 0.125

Clearly, I spent the least amount of time on Friday using IT and the time is 0.125 or 1/8.

7 0

2 years ago

A boat travels at constant speed. After 20 minutes the boat had traveled 2.5 miles. How long does it take the boat to reach the

schepotkina [342]

120 minutes

Step by step:

divide 20 by 2.5 to find how many minutes it takes to drive 1 mile, then multiply that by 15 miles

7 0

2 years ago

Find the limits of integration ly, uy, lx, ux, lz, uz (some of which will involve variables x,y,z) so that ∫uyly∫uzlz∫uxlxdxdzdy

motikmotik

Answer:

Hello your question is incomplete attached below is the complete question

Ix = 0 Ux = $\sqrt{y-9z^2}$

Iz = 0 Uz = $\frac{\sqrt{y} }{3}$

Iy = 5 Uy = 10

Step-by-step explanation:

Ix = 0 Ux = $\sqrt{y-9z^2}$

Iz = 0 Uz = $\frac{\sqrt{y} }{3}$

Iy = 5 Uy = 10

attached below is the detailed solution

4 0

2 years ago

The following graph shows the consumer price index (CPI) for a fictional country from 1990 to 2000.For which of these time perio

KatRina [158]

Answer:

Option B. 1990 - 1992

Step-by-step explanation:

If we have to calculate inflation rate in year 2000 from 1990, we use the formula

$inflation=\frac{C.P.I. 2000-C.P.I. 1990}{C.P.I 1990}\times 100$

which means if consumer price index is increasing year by year the inflation rate will increase.

Now we analyse our options given with the help of graph given.

A. from 1994 - 2000

Consumer price index increased from year 1994 to 1998 but decreased between 1998 to 2000.

So this option doesn't show the continuous inflation.

B. Year 1990 - 1992

We find a continuous increase in C.P.I. therefore there will be a continuous increase in inflation.

So this option is correct.

C. Year 1992 - 1996

In this gap we see deflation from year 1992 to 1994 then inflation between 1994 - 1996.

So there is ups and downs in this period showing discontinuity in inflation.

D. 1992 - 1994

There is continuous decrease in C.P.I. so continuous deflation is reported between this period.

It's not the correct option.

Answer is Option B.

4 0

2 years ago