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3 years ago

How do you solve a proof?

1 answer:

6 0

To solve a proof, you need to distinguish which is the hypothesis and which is the conclusion. The hypothesis is the starting point and the conclusion is the ending point. We go from hypothesis to conclusion. A conditional statement can be written as If A, then B. Where A is the hypothesis and B is the conclusion.

For example, take this theorem.

If two sides of a triangle are congruent, then the angles opposite those sides are congruent.

We go from Two sides of a triangle are congruent to the angles opposite those sides are congruent.

The first statement's reason is pretty much always Given.

Statement | Reason
1. Two sides of a triangle are congruent 1. Given
.... After a bunch of steps
3. the angles opposite those sides are congruent. 3. Your postulate of definition of what reason you need to complete the last step.

Sorry if this is a little confusing.

You might be interested in

In Spetember of 2013, Mario The Baker introduced a new chocolate cake and hired Doug and Jeremy to bake these cakes. Every custo

professor190 [17]

Answer:

There is a 90.32% probability that the cake was baked by Doug.

Step-by-step explanation:

We have these following probabilities:

A 70% probability that Doug bakes the cake.

A 30% probability that Jeremy bakes the cake.

A 40% probability that a cake baked by Doug gets a thumbs up.

A 10% that a cake baked by Jeremy gets a thumbs up.

One cake was selected at random on 10/01/2014 and got a "thumbs up".

1. Find the probability that the cake was baked by Doug.

The probability that a baked cake gets a thumbs up is:

$P = 0.7*0.4 + 0.3*0.10 = 0.31$

Of those, 0.7*0.4 = 0.28 are baked by Doug.

So the probability is:

$P = \frac{0.28}{0.31} = 0.9032$

There is a 90.32% probability that the cake was baked by Doug.

4 0

3 years ago

What is the value of cos θ given that (-2, 9) is a point on the terminal side of θ?

liq [111]

Answer:

a) cosθ = $\frac{-2\sqrt{85} }{85}$

Step-by-step explanation:

Step(i):-

Given point ( x , y ) = ( - 2 , 3 )

We know that the polar co-ordinates

x = r cos θ and y = r sinθ

where $r = \sqrt{x^{2} +y^{2} }$

$r = \sqrt{(-2)^{2} +(9)^{2} } = \sqrt{4+81} = \sqrt{85}$

Step(ii):-

x = r cos θ

cosθ $= \frac{x}{r}$

cosθ = $\frac{-2}{\sqrt{85} } = \frac{-2}{\sqrt{85} } X \frac{\sqrt{85} }{\sqrt{85} }$

cosθ = $\frac{-2\sqrt{85} }{85}$

3 0

3 years ago

The population of rabbits in a national forest is modeled by the formula P= 12,000 + 1000 (t+1) where t is the number of years f

V125BC [204]

In this formula, 1000(t+1) represents the growth rate of the rabbits. We want the number right now, so sub in 0 for t.

P=12,000+1000(0+1)
P=12,000+1000
P=13,000 rabbits.
Hope this helps!!!

4 0

3 years ago

Situation:A researcher in North America discoversa fossile that contains 65% of its originalamount of C-14..-ktN=NoeNo inital am

zheka24 [161]

SOLUTION

We have been given the equation of the decay as

$\begin{gathered} N=N_0e^{-kt} \\ where\text{ } \\ N_0=initial\text{ amount of C-14 at time t} \\ N=amount\text{ of C-14 at time t = 65\% of N}_0=0.65N_0 \\ k=0.0001 \\ t=time\text{ in years = ?} \end{gathered}$

So we are looking for the time

Plugging the values into the equation, we have

$\begin{gathered} N=N_0e^{-kt} \\ 0.65N_0=N_0e^{-0.0001t} \\ e^{-0.0001t}=\frac{0.65N_0}{N_0} \\ e^{-0.0001t}=0.65 \end{gathered}$

Taking Ln of both sides, we have

$\begin{gathered} ln(e^{-0.000t})=ln(0.65) \\ -0.0001t=ln(0.65) \\ t=\frac{ln(0.65)}{-0.0001} \\ t=4307.82916 \end{gathered}$

Hence the answer is 4308 to the nearest year

8 0

10 months ago

triangle LMN is similar to triangle FGH and LN/FH= 7/4. What is the ratio of the area of triangle LMN to the area of triangle FG

jeyben [28]

Answer:

Step-by-step explanation:

6 0

2 years ago