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Mathematics

1 answer:

tatuchka [14]2 years ago

3 0

Answer:

Linear Pair Theorem

m∠2

∠3

definition of congruent angles

Step-by-step explanation:

1. ∠1 and ∠2 form a linear pair of angles, so ∠1 and ∠2 are supplementary by the Linear Pair Theorem.

2. Therefore, m∠1 + m∠2 = 180°, by the definition of supplementary angles.

3. It is given that ∠2 ≅ ∠3, so m∠2 = m∠3 by the definition of congruent angles.

4. By substitution, m ∠1 + m∠3 = 180°, so ∠1 and ∠3 are supplementary by the definition of supplementary angles.

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MAVERICK [17]

Answer:

y=-x-2

Step-by-step explanation:

To find the slope of the line, you can use the slope formula. I did this with (-3,1) and (2,-4) to get: (1+4)/(-3-2). This ends up as -5/5, which simplifies to -1.

next I plugged in the slope and one point into the line equation: y=mx+b. I plugged in (-4)=(-1)(2)+b. This equated to b=-2.

Check Work:

The equation -4=(-1)(2)-2 is true

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3 years ago

The radioactive isotope radium has a half-life of 1,600 years. The mass of a 100-gram sample of radium will be______ grams after

Olenka [21]

To solve this we are going to use the half life equation $N(t)=N_{0} e^{( \frac{-0.693t}{t _{1/2} }) }$
Where:
$N_{0}$ is the initial sample
$t$ is the time in years
$t_{1/2}$ is the half life of the substance
$N(t)$ is the remainder quantity after $t$ years

From the problem we know that:
$N_{0} =100$
$t=200$
$t_{1/2} =1600$

Lets replace those values in our equation to find $N(t)$ :
$N(200) =100e^{( \frac{(-0.693)(200)}{1600}) }$
$N(200)=100e^{( \frac{-138.6}{1600} )}$
$N(200)=100e^{-0.086625}$
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We can conclude that after 1600 years of radioactive decay, the mass of the 100-gram sample will be 91.7 grams.

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2 years ago

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natita [175]

Mark and Don have to sell 11 and 59 marbles respectively.

Explanation

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