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nata0808 [166]
2 years ago
6

Fill in the blanks to complete this proof of theorem 2-3.

Mathematics
1 answer:
Basile [38]2 years ago
6 0

Answer:

Therefore.

angle 1 is congruent to angle 3 ...Proved

The proof with steps are below with Fill in the blanks

Step-by-step explanation:

Complementary Angles:

Two angles are Complementary when they add up to 90 degrees.

Example 40° and 50° are Complementary Angles.

If 'x' and 'y' are Complementary Angles the we have

x+y=90\°

Here,

Given:

angle 1 and angle 2 are complementary

angle 3 and angle 2 are complementary

To Prove:

angle 1 is congruent to angle 3

Proof:

Step 1:

angle 1 and angle 2 are complementary and angle 3 and angle 2 are complementary because it is Given.

Step 2:

By the definition of complementary angles,

m of angle 1 + m of angle 2 = _90°__ and m of angle 3 + m of angle 2 = _90°_.

Step 3:

Transitive Property of Equality.

Then m of angle 1 + m of angle 2 = m of angle 3 + m of angle 2 by the Transitive Property of Equality.

Step 4:

Subtract m of angle 2 from each side. By the Subtraction Property of Equality, you get

m\angle 1 +m\angle 2-m\angle 2=m\angle 3+m\angle 2-m\angle 2

m\angle 1=m\angle 3

m of angle 1 = _measure of angle_3_.

Step 5:

Angles with the same measure are _Congruent__,

Step 6:

so angle 1 is congruent to angle 3.

Therefore.

angle 1 is congruent to angle 3 ...Proved

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two arcs of concentric circles are intercepted by the same central angle. the resulting arc length of the arc of the larger circ
Bond [772]
the complete question in the attached figure

Let
A°-----------> <span>the same central angle

</span><span>For the larger circle
length of larger circle=2*pi*r-------> 2*pi*12-----> 75.36 m

360</span>°<span> (full circle) has a length of------------> 75.36 m 
 A</span>°-----------------------------------> 16 m
A°=(16)*360/75.36--------> A=76.43°

For the smaller circle
length of smaller circle=2pi*r-------> 2*pi*7.5-----> 47.1 m

360° (full circle) has a length of------------> 47.1 m 
 76.43°-----------------------------------> X
X=76.43*47.1/360-----> X=10 m ----> length arc of the smaller circle

the answer is
the length arc of the smaller circle is 10 m

3 0
2 years ago
Help please need help with this stuff thank you again for helping
Alex777 [14]
Slope intercept form: y = mx + b

Where m = slope and b = y-intercept.

By looking at the graph, we can see that the line cuts at 1/2 on the y-axis, therefore eliminating option D.

So now we have: y = mx + 1/2

Next, we'll find the slope. \frac{y_2-y_1}{x_2-x_1}

Plug the coordinates into the formula.

\frac{3-(-2)}{4-(-4)}= \frac{5}{8}

So our slope is 5/8 and the y-intercept is 1/2.

Option A is the answer.
6 0
3 years ago
Which of the following is an example of normal data?​
saveliy_v [14]

Answer:

1. heights

2. blood pressure

3 . measurement error

4. IQ scores

Step-by-step explanation:

hope this will help you

5 0
3 years ago
Read 2 more answers
The two pyramids are similar. Find the volume of the smaller pyramid. Round your answer to the nearest hundredth.
mihalych1998 [28]

Answer:

A) 5.12mm³

Step-by-step explanation:

Step 1

Find the volume of the bigger pyramid

This is a triangular based pyramid.

The formula to use is given as Volume of Pyramid =

1/3 × Area of the triangle × Height

Area of the triangle = 1/2 × 3 mm × 4mm = 6mm²

Volume of the large pyramid = 1/3 × 6mm² × 5mm

= 10mm³

We are given the length of the small pyramid as 4mm

We would be using was is known as scale factor to find the volume of the small pyramid

The scale factor k = (Height of the small pyramid)³/ (Height of the Large pyramid)³

k = 4³/5³

k = Volume of small pyramid/ Volume of large pyramid

Volume of small pyramid = X

Volume of large pyramid = 10mm³

Hence,

4³/5³ = X/10

Cross Multiply

= 4³ × 10 = 5³ × X

X = (4³ × 10)/ 5³

X = 5.12mm³

5 0
3 years ago
Write five fractions that each simplify to one-ninth
egoroff_w [7]
2/18
3/27
4/36
5/45
6/54

Take any number let's say 9
Then 9/9 = 1
Or 9/9 = 1/1
Then if you multiply the bottom half of those by 9, you get
9/9 becomes 9/81
and
1/1 becomes 1/9

So to generate any fraction equivalent to 1/9
take any number and write it as one, i.e. 5/5 = 1 (or 1/1)
and then multiply the bottom part by 9 = 5/45
3 0
3 years ago
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