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Marrrta [24]
3 years ago
9

URGENT HELP NEEDED WITH TRIANGLES/CIRCLES! IF ET = 31, DE = 65, AND DC= 74, FIND THE PERIMETER OF DCE.

Mathematics
1 answer:
snow_tiger [21]3 years ago
6 0

ES = ET

and

DS = DR

and

CR = CT ( because each pair are tangents to the circle)


So ES = 31 and Ds = 65-31 = 34

and DR = 34 and CR = 74- 34 = 40.

CT = CR = 40

Therfore the line EC = 31 + 40 = 71


Finally the perimeter = 65 + 74 + 71 = 210 (answer)

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The amount of polonium-210 remaining, p(t), after t days in a sample can be modeled by the exponential function p(t) = 100e−0.00
Archy [21]

Answer:

% Po lost = 100[1 - e^(-0.005t)]  %; 73.0 g

Step-by-step explanation:

p(t) = 100e^(-0.005t)

Initial amount:        p(0) = 100

Amount remaining: p(t) = 100e^(-0.005t)

Amount lost: p(0) – p(t) = 100 - 100e^(-0.005t) = 100[1 - e^(-0.005t)]

% of Po lost  = amount lost/initial amount × 100 %

= [1 - e^(-0.005t)]  × 100 % = 100[1 - e^(-0.005t)]  %

p(63) = 100e^(-0.005 × 63) = 100e^(-0.315) = 100 × 0.730 = 73 g

The mass of polonium remaining after 63 days is 73 g.

4 0
3 years ago
Based on the information given say whether or not △ABC∼△FED. Explain your reasoning.
GalinKa [24]

Answer:

Yes, △ABC ∼ △FED by AA postulate.

Step-by-step explanation:

Given:

Two triangles ABC and FED.

m∠A = m∠B

m∠C = m∠A + 30°

m∠E = m∠F = x

m∠D = 2x-20°.

Now, let m∠A = m∠B = y

So, m∠C = m∠A + 30° = y+30

Now, sum of all interior angles of a triangle is 180°. Therefore,

m∠A + m∠B +  m∠C = 180

y+y+y+30=180\\3y=180-30\\3y=150\\y=\frac{150}{3}=50

Therefore, m∠A = 50°, m∠B = 50° and m∠C =  m∠A + 30° = 50 + 30 = 80°.

Now, consider triangle FED,

m∠D+ m∠E + m∠F = 180

2x-20+x+x=180\\4x=180+20\\4x=200\\x=\frac{200}{4}=50

Therefore,  m∠F = 50°  

m∠E = 50° and  

m∠D =  2x-20=2(50)-20=100-20=80\°

So, both the triangles have congruent corresponding angle measures.

m∠A = m∠F = 50°

m∠B = m∠E = 50°

m∠C = m∠D = 80°

Therefore, the two triangles are similar by AA postulate.

5 0
3 years ago
if the length of a rectangle is increased by 30% and the width of the same rectangle is decreased by 30% what is the effect on t
faltersainse [42]

Answer:60

Step-by-step explanation:30%+30%=60% since it is a rectangle i thing this is the answer

6 0
3 years ago
Find the area of a circle with a radius of 3.
TiliK225 [7]

Answer:

A =28.26

Step-by-step explanation:

Using the area formula

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We use pi = 3.14 and the radius is 3

A = 3.14 * (3)^2

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krok68 [10]

Answer:

In Section 6.1, we introduced the logarithmic functions as inverses of exponential functions and

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development of our society since, among other things, they were used to develop analog computing

devices called slide rules which enabled scientists and engineers to perform accurate calculations

leading to such things as space travel and the moon landing. As we shall see shortly, logs inherit

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We first extract two properties from Theorem 6.2 to remind us of the definition of a logarithm as

the inverse of an exponential function.

Step-by-step explanation:

Hope this helps

4 0
3 years ago
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