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2 years ago

Solve the following inequality. 2x + 2(x+5) <+4(8 – 20)

Mathematics

1 answer:

Ilia_Sergeevich [38]2 years ago

3 0

Answer:

x <-14.5

Step-by-step explanation:

2x + 2(x+5) <+4(8 – 20)

Distribute

2x+2x+10 < 4 (-12)

4x +10 < -48

Subtract 10 from each side

4x+10-10 <-48-10

4x< -58

Divide each side by 4

4x/4 < -58/4

x <-14.5

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Find the measure of the exterior angles of the following regular polygons: a triangle, a quadrilateral, a pentagon, an octagon,

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Answer:

Triangle: 120

Quadrilateral: 90

Pentagon: 72

Octagon: 45

Decagon: 36

30-gon: 10

50-gon: 7.2

100-gon: 3.6

Step-by-step explanation:

360/n = the measure on the exterior angle

n = the number of sides

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2 years ago

Is 14/18 greater then, less then, or equal to 7/9

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Answer:

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Step-by-step explanation:

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valentina_108 [34]

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2 years ago

Of the students in Rosalie's dance class, 29 out of 59 have participated in dance class before. About how many of her students h

Harrizon [31]

Answer:

Step-by-step explanation:

half of 59 is 29.5, which is very close to 29. this indicates that this fraction (29/59) is the closest to one half, which is answer choice B.

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2 years ago

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A sample of a radioactive substance decayed to 97% of its original amount after a year. (Round your answers to two decimal place

Andrej [43]

Answer:

a) The half life of the substance is 22.76 years.

b) 5.34 years for the sample to decay to 85% of its original amount

Step-by-step explanation:

The amount of the radioactive substance after t years is modeled by the following equation:

$P(t) = P(0)(1-r)^{t}$

In which P(0) is the initial amount and r is the decay rate.

A sample of a radioactive substance decayed to 97% of its original amount after a year.

This means that:

$P(1) = 0.97P(0)$

Then

$P(t) = P(0)(1-r)^{t}$

$0.97P(0) = P(0)(1-r)^{0}$

$1 - r = 0.97$

$P(t) = P(0)(0.97t)^{t}$

(a) What is the half-life of the substance?

This is t for which P(t) = 0.5P(0). So

$P(t) = P(0)(0.97t)^{t}$

$0.5P(0) = P(0)(0.97t)^{t}$

$(0.97)^{t} = 0.5$

$\log{(0.97)^{t}} = \log{0.5}$

$t\log{0.97} = \log{0.5}$

$t = \frac{\log{0.5}}{\log{0.97}}$

$t = 22.76$

The half life of the substance is 22.76 years.

(b) How long would it take the sample to decay to 85% of its original amount?

This is t for which P(t) = 0.85P(0). So

$P(t) = P(0)(0.97t)^{t}$

$0.85P(0) = P(0)(0.97t)^{t}$

$(0.97)^{t} = 0.85$

$\log{(0.97)^{t}} = \log{0.85}$

$t\log{0.97} = \log{0.85}$

$t = \frac{\log{0.85}}{\log{0.97}}$

$t = 5.34$

5.34 years for the sample to decay to 85% of its original amount

8 0

3 years ago