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Tamiku [17]
2 years ago
11

Heya! ツ

Mathematics
2 answers:
fiasKO [112]2 years ago
5 0

Answer:

See Below.

Step-by-step explanation:

In the given figure, O is the center of the circle. Two equal chords AB and CD intersect each other at E.

We want to prove that I) AE = CE and II) BE = DE

First, we will construct two triangles by constructing segments AD and CB. This is shown in Figure 1.

Recall that congruent chords have congruent arcs. Since chords AB ≅ CD, their respective arcs are also congruent:

\stackrel{\frown}{AB }\, \cong\, \stackrel{\frown}{CD}

Arc AB is the sum of Arcs AD and DB:

\stackrel{\frown}{AB}=\stackrel{\frown}{AD}+\stackrel{\frown}{DB}

Likewise, Arc CD is the sum of Arcs CB and DB. So:

\stackrel{\frown}{CD}=\stackrel{\frown}{CB}+\stackrel{\frown}{DB}

Since Arc AB ≅ Arc CD:

\stackrel{\frown}{AD}+\stackrel{\frown}{DB}=\stackrel{\frown}{CB}+\stackrel{\frown}{DB}

Solve:

\stackrel{\frown}{AD}\, \cong\,\stackrel{\frown}{CB}

The converse tells us that congruent arcs have congruent chords. Thus:

AD\cong CB

Note that both ∠ADC and ∠CBA intercept the same arc Arc AC. Therefore:

\angle ADC\cong \angle CBA

Additionally:

\angle AED\cong \angle CEB

Since they are vertical angles.

Thus:

\Delta AED\cong \Delta CEB

By AAS.

Then by CPCTC:

AE\cong CE\text{ and } BE\cong DE

stepladder [879]2 years ago
3 0

Answer:

this is your answer. look it once.

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James was trying to sleep one night but there was too much noise around him. His clock ticked every
g100num [7]

Answer:

<em>It will occur zero times between midnight and one o'clock.</em>

Step-by-step explanation:

<u>Least Common Multiple (LCM)</u>

Three events keep James from sleeping: his clock ticking every 20 seconds, a tap dripping every 15 seconds, and his dog snoring every 27 seconds.

All three events happened together at midnight. They will happen together again the first time the numbers 20, 15, and 27 have a common multiple. This is the LCM.

List the prime factors of each number:

20: 2,2,5

15: 3,5

27: 3,3,3

Now multiply all the factors the maximum number of times they appear:

LCM=2*2*3*3*3*5=540

(a) All the events will happen together again after 540 minutes.

(b) Since 540 minutes = 9 hours, this event won't happen again until 9 am. Thus, it will occur zero times between midnight and one o'clock.

4 0
3 years ago
4-inch by 6-inch what is the width of 15 inches for a ratio table
quester [9]

This is a ratio problem; the ratio of the length to width is constant (and therefore equal):

4 /6 = 15 / x

Now, with a ratio, we may do any allowable algebra operation: cross-multiply, invert both sides, multiply or divide both sides by the same amount, etc.

Let's cross-multiply:

4x = (15)(6)

x = 90/4

x = 22.5 in.

3 0
3 years ago
The formula for the slant height of a cone is , where S is surface area of the cone. Use the formula to find the slant height, l
liq [111]

we know that

The formula of the surface area of the cone is equal to

SA=\pi r^{2}+\pi rl

where

SA is the surface area

r is the radius of the cone

l is the slant height

in this problem we have

SA=500\pi\ ft^{2}\\r=15\ ft\\l=?

Solve the formula for l

SA=\pi r^{2}+\pi rl\\ \\\pi rl=SA-\pi r^{2} \\ \\l=\frac{SA-\pi r^{2} }{\pi r}

substitute the values

l=\frac{500\pi -\pi 15^{2} }{\pi15}\\ \\l=\frac{275}{15}\ ft\\ \\l=\frac{55}{3}\ ft\\ \\l=18\frac{1}{3}\ ft

therefore

<u>the answer is</u>

The slant height is 18\frac{1}{3}\ ft

7 0
3 years ago
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Please help me, its due today
nasty-shy [4]

Answer:

No, u keep going around and answering questions with sorry i don't know the answer and its pising me off, so just stop before you get your account reported too many times and end up getting banned from answering questions.

7 0
3 years ago
Jessica and Patricia finished 2/5 of their group project in 4/5 hour. If Jessica and Patricia's rate stayed the same, how much o
kvv77 [185]

Answer:

1/3

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A because it thev anwser

3 0
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