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3 years ago

5

Let PQR be a triangle such that angle P = angle Q + angle R. Among all three exterior angles of triangle PQR, what is the smalle

st exterior angle, in degrees?

1 answer:

Phantasy [73]3 years ago

7 0

Answer:

The smaller exterior angle is the exterior angle in the vertex P, and it measures 90°

Step-by-step explanation:

The sum of the internal angles of a triangle needs to be 180 degrees, so we have two equations:

$mP = mQ + mR$

$mP + mQ + mR = 180\°$

Substituting $mQ + mR$ by $mP$ in the second equation, we have:

$mP + mP = 180\°$

$mP = 90\°$

The other two angles need to be lesser than mP, and the exterior angle is the supplement of the internal angle, so the bigger the internal angle, the smaller the exterior angle.

So if the bigger internal angle in this triangle is mP, the smaller exterior angle is also the angle in the vertex P:

$exteriorP = 180\° - mP$

$exteriorP = 90\°$

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maks197457 [2]

Answer:

1. $n=\pm7$

2. $x=\pm7i[tex]3.[tex]\pm 12x =a$

4. 22

Step-by-step explanation:

1. $n^2 - 49 = 0$

$n^2 =49$

$n= \sqrt{49}$

$n=\pm7$

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$x^2 =-64$

$x= \sqrt{49}$

$x=\pm7i[tex]3. Area of square = [tex]a^{2}$

Where a is the side

We are given an area o square = $144x^{2}$

So, $144x^{2}=a^{2}$

$\sqrt{144x^{2}}=a$

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So, equation becomes:

$(x+9)(x-9)=0$

$x^2- 81=0$

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z should be the number from which if we subtract 103 so we get 81

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3 years ago

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Find the equation of the line. <br> Use exact numbers.

AlekseyPX

The slope of the line (m) = 3/1 = 3
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3 years ago

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3 years ago

A gambler has a fair coin and a two-headed coin in his pocket. He selects one of the coins at random. (a) When he flips the coin

Aleks04 [339]

Answer:

a) probability of choosing heads= 1/2 (50%)

b) probability of choosing the fair coin knowing that it showed heads is= 1/3 (33.33%)

Step-by-step explanation:

Since the unfair coin can have 2 heads or 2 tails , and assuming both are equally possible . then

probability of choosing the fair coin (named A)= 1/2

probability of choosing an unfair coin with 2 heads (named B)= (1-1/2)*1/2= 1/4

probability of choosing an unfair coin with 2 tails (named C)= (1-1/2)*(1-1/2)= 1/4

then

probability of choosing heads= probability of choosing A * probability of getting heads from A + probability of choosing B * probability of getting heads from B + probability of choosing C * probability of getting heads from C =

1/2*1/2 + 1/4*1 + 1/4*0 = 2/4 = 1/2

the probability of choosing the fair coin knowing that it showed heads is

P(A/B) = P(A∩B)/P(B)

denoting event A= the coin is fair and event B= the result is heads

P(A∩B) = 1/2*1/2 = 1/4

but since we know now that that the unfair coin is not possible , the probability of choosing heads is altered:

P(B)=probability of choosing heads= probability of choosing A * probability of getting heads from A + probability of choosing B * probability of getting heads from B = 1/2*1/2+1/2*1 = 3/4

then

P(A/B) = P(A∩B)/P(B) = (1/4)/(3/4) = 1/3

then the probability is 1/3

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beks73 [17]

Answer:

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Step-by-step explanation:

Divide term by term.

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= -x +5 -5/(3x)

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3 years ago