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3 years ago

An acute, isosceles triangle has a vertex angle measuring 78 degrees. What are the measures of the other two angles?

Mathematics

2 answers:

kumpel [21]3 years ago

8 0

Answer: the other 2 angles are 51 degrees

Step-by-step explanation: since it is an isoceles triangle two sides are equal thus 2 angles are equal.

Therefore, let's take the two angles as x

78+ x+x = 180 ( angle sum property)

Thus , 2x= 180-78

X = 102/2

X= 51 degrees

Hope I helped you !!

mixas84 [53]3 years ago

6 0

Answer:

Step-by-step explanation:

180-78=102

102/2=51

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(3x+13)+(x-8)+(x)=180

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Answer:

Step-by-step explanation:

3x+13+x-8+x=180

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3 years ago

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3 years ago

The gypsy moth is a serious threat to oak and aspen trees. A state agriculture department places traps throughout the state to d

k0ka [10]

Part A:

From the central limit theorem, since the number of samples is large enough (up to 30), the mean of the the mean of the average number of moths in 30 traps is 0.6.

Part B:

The standard deviation is given by the population deviation divided by the square root of the sample size.

$standard \ deviation= \frac{\sigma}{\sqrt{n}} = \frac{0.4}{\sqrt{30}} = \frac{0.4}{5.477} =0.073$

Part C:

The probability that an approximately normally distributed data with a mean, μ, and the standard deviation, σ, with a sample size of n is greater than a number, x, given by

$P(X\ \textgreater \ x)=1-P(X\ \textless \ x) \\ \\ =1-P\left(z\ \textless \ \frac{x-\mu}{\sigma/\sqrt{n}} \right)$

Thus, given that the mean is 0.6 and the standard deviation is 0.4, the probability that <span>the average number of moths in 30 traps is greater than 0.7</span> given by:

$P(X\ \textgreater \ 0.7)=1-P(X\ \textless \ 0.7) \\ \\ =1-P\left(z\ \textless \ \frac{0.7-0.6}{0.073} \right)=1-P(z\ \textless \ 1.369) \\ \\ =1-0.91455=\bold{0.0855}$

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4 years ago

How do I solve this system of equations by substitution? <br> y - 3x = 2, y=(x + 1)^2 - 5

Arada [10]

Hello,

y-3x=2==>x=(y-2)/3
==>(x+1)²=((y-2)/3+1)²=(y+1)²/9

y=(x+1)²-5
==>y=(y²+2y1)/9 -5
==>y²-7y-44=0 ; Δ=7²+4*44=225=15²
==>y=(7+15)/2 or y=(7-15)/2

==>y =11 and x=(11-2)/3=3
or y=-4 and x=(-4-2)/3=-2

sol={(3,11);(-2,-4)}

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3 years ago