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3 years ago

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.

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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

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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

A = pi r^2

We use pi = 3.14 and the radius is 3

A = 3.14 * (3)^2

A = 3.14 *9

A =28.26

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3 years ago

Rewrite the expression ln(33^3)+ln(9^4) so that it includes the expressions ln(3) and 33 and 9 do not appear inside a natural lo

krok68 [10]

Answer:

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analogs of all of the properties of exponents you learned in Elementary and Intermediate Algebra.

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

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3 years ago