All categories

3 years ago

In the diagram A, B, and C are the points on the circle. Use the diagram to prove the theorem which states that:

Mathematics

1 answer:

nevsk [136]3 years ago

8 0

9514 1404 393

Explanation:

Here's one way to go at it.

Draw segments AB and CO. Define angles as follows. (The triangles with sides that are radii are all isosceles, so their base angles are congruent.)

x = angle OAB = angle OBA

y = angle OAC = angle OCA

z = angle OBC = angle OCB

Consider the angles at each of the points A, B, C.

At A, we have ...

angle CAB = x + y

At B, we have ...

angle CBA = x + z

At C, we have ...

angle ACB = y + z

The sum of the angles of triangle ABC is 180°, as is the sum of angles in triangle ABO. This gives ...

x + x + ∠AOB = (x+y) +(x+z) +(y+z)

∠AOB = 2(y+z) = 2∠ACB

This shows ∠AOB = 2×∠C, as required.

You might be interested in

Pls explain for each answer you pick pls

Igoryamba

All except the third selection are 0.

-12+12= 0
8+(-8)=0
-5+-5= -10
-20+20=0
-2,000+2,000=0

follow the the rules of integers

7 0

3 years ago

Read 2 more answers

What is the area of this trapezoid?

lilavasa [31]

Well you 86 + 63 = 149 • 4 = 596 divide 2 = 298ft2

8 0

3 years ago

Read 2 more answers

“The line that passes through point H has the equation y=-2x -3”

Katena32 [7]

Answer:

Step-by-step explanation:

Generally

The equation of a line is given as

y = mx + c

Where

m is the slope

c is the intercept on y axis

Note: if two lines are parallel, their slopes are equal

I.e M1 = M2 =m

If two lines are perpendicular, then, their slopes are given as

M2 = - 1/M1

Given that,

The line that pass through the point H has an equation

y = -2x-3

From equation of a line, we know that, the slope of the line that passes through H is -2

m = -2

We want to find the equation of a line parallel to line that passes through H

If the line we want to find is parallel to the given line, then, their slope are equal,

So, the slope of line that passes through point G is m=-2

So, the equation of the line that passes through point G is

y = mx + c, m=-2

y = -2x + c

So, we need to find c, so, using the point G it passes through,

G = (2,1) I.e x = 2 and y = 1

y = -2x + c.

1 = -2(2) + c

1 = -4 + c

1+4 = c

c = 5

So, the equation of the line that passes through G becomes

y = -2x + 5

3 0

3 years ago

Suppose that 1 month before the election a random sample of 500 registered voters are surveyed. From this sample 270 indicate th

Aleonysh [2.5K]

Answer:

[ 0.4964, 0.5836 ]

Step-by-step explanation:

Data provided in the question:

Total sample size = 500

person voting for smith = 270

thus,

P( person voting for smith ), p = $\frac{270}{500}$ = 0.54

Confidence level = 95%

now,

standard error, SE = $\sqrt{\frac{p(1-p)}{n}$

SE = $\sqrt{\frac{0.54(1-0.54)}{500}$

SE = 0.0223

now,

Confidence interval = p ± ( z × SE )

here,

z value for 95% confidence interval is 1.96

Confidence interval = [ 0.54 - ( 1.96 × 0.0223 ), 0.54 + ( 1.96 × 0.0223 ) ]

= [ 0.54 - 0.0436 , 0.54 + 0.0436 ]

= [ 0.4964, 0.5836 ]

8 0

2 years ago

PLEASE HELP!! NEED ASAP 100 POINTS!!

Leto [7]

Answer:

See Below.

Step-by-step explanation:

Remember that the maximum account balance Ebony had was $400.

We can see that her bank balance first reached $400 on Day 4 and continued until Day 8.

Part A)

Since the maximum amount is $400, it is whenever the graph reaches (and stays) at its maximum, or the highest points on the graph.

We can see that at around Day 4, she first reached her maximum of $400 since that is the highest point of the graph.

And this continues until approximately Day 8.

Therefore, Ebony first reached $400 on Day 4 and stayed at $400 until Day 8.

Part B)

Refer above. The explanation is the same.

Part C)

Jade is says that the amount Ebony is depositing per day from Days 0 to 4 is the same as the amount Ebony is withdrawing per day from Days 8 to 12.

We also know that Day 12 is when Ebony’s account first reached 0.

Essentially, Jade is saying that the slope of the line from Days 0 to 4 is the same as the slope of the line from Days 8 to 12.

Ignoring the negative, we can immediately see that this is not true without calculating.

This is because the slope of the line from Days 8 to 12 is much steeper than than slope of the line from Days 0 to 4.

So, the two slopes are not equal since they are not the same steepness.

Therefore, this means that from Days 8 to 12, Ebony withdrew money at a faster rate per day than she had been depositing from Days 0 to 4.

Hence, Jade’s statement cannot be true.

3 0

3 years ago

Read 2 more answers