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Fed [463]
3 years ago
5

in a triangle, the measure of the first angle is three times the measure of the second angle. The measure of the third angle is

55 more than the measure of the second angle. Use the fact that the sum of the measures of the three angles is 180 to find the measure of each angle to find the measure of each angle.
Mathematics
2 answers:
Deffense [45]3 years ago
6 0
Let the angles be A, B, C where B is the second angle.

"measure of the first angle is three times the measure of the second angle" =>
A=3B
 
"T<span>he measure of the third angle is 55 more than the measure of the second angle</span>" =>
C=B+55
 
We know that A+B+C=180, =>
A+B+C=180=(3B+B+B+55)
=>
5B=180-55=125
B=25 degrees
A=3*25=75
C=25+55=80
Check: A+B+C=75+25+80=180 ok!


allochka39001 [22]3 years ago
6 0
The second angle = 25 , the third angle= 75.
the equation i used was 3X + X + X + 55 = 180
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ArbitrLikvidat [17]

<em>Y</em>₁ and <em>Y</em>₂ are independent, so their joint density is

f_{Y_1,Y_2}(y_1,y_2)=f_{Y_1}(y_1)f_{Y_2}(y_2)=\begin{cases}\frac1{49}e^{-\frac{y_1+y_2}7}&\text{for }y_1\ge0,y_2\ge0\\0&\text{otherwise}\end{cases}

By definition of conditional probability,

P(<em>Y</em>₁ > <em>Y</em>₂ | <em>Y</em>₁ < 2 <em>Y</em>₂) = P((<em>Y</em>₁ > <em>Y</em>₂) and (<em>Y</em>₁ < 2 <em>Y</em>₂)) / P(<em>Y</em>₁ < 2 <em>Y</em>₂)

Use the joint density to compute the component probabilities:

• numerator:

P((Y_1>Y_2)\text{ and }(Y_1

=\displaystyle\frac1{49}\int_0^\infty\int_{\frac{y_1}2}^{y_1}e^{-\frac{y_1+y_2}7}\,\mathrm dy_2\,\mathrm dy_1

=\displaystyle-\frac17\int_0^\infty\int_{-\frac{3y_1}{14}}^{-\frac{2y_1}7}e^u\,\mathrm du\,\mathrm dy_1

=\displaystyle-\frac17\int_0^\infty\left(e^{-\frac{2y_1}7} - e^{-\frac{3y_1}{14}}\right)\,\mathrm dy_1

=\displaystyle-\frac17\left(-\frac72e^{-\frac{2y_1}7} + \frac{14}3 e^{-\frac{3y_1}{14}}\right)\bigg|_0^\infty

=\displaystyle-\frac17\left(\frac72 - \frac{14}3\right)=\frac16

• denominator:

P(Y_1

(I leave the details of the second integral to you)

Then you should end up with

P(<em>Y</em>₁ > <em>Y</em>₂ | <em>Y</em>₁ < 2 <em>Y</em>₂) = (1/6) / (2/3) = 1/4

5 0
2 years ago
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m_a_m_a [10]

Answer:

Slope=3/4

Step-by-step explanation:

1) Label all values with x1 y1, x2 y2

Then, plug jn each value into this equation:y2-y1/x2-x1

Remember that negative values will become positive when dealjng with a subtraction sign.

5-(-1)=5+1.

---------------= 6/8

6-(-2)=6+2

After getting 6/8, simplify by the gcf (2) to get 3/4

Answer:3/4

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butalik [34]

Answer:

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6 0
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Monica [59]

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Answer:

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6 0
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