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3 years ago

∠1 and ∠2 are supplementary angles.

Mathematics

1 answer:

Phoenix [80]3 years ago

7 0

∠1 and ∠2 are supplementary angles, and so they will equal 180°

note that:

m∠1=4x+3

m∠2=3x−5

Plug in the corresponding expression for the angle

(4x + 3) + (3x - 5) = 180

Simplify. Combine like terms

7x - 2 = 180

Isolate the x. Note the equal sign. What you do to one side you do to the other.

Add 2 to both sides

7x - 2 (+2) = 180 (+2)

7x = 182

Divide 7 from both sides

7x/7 = 182/7

x = 182/7

x = 26

26 is your answer for x.

hope this helps

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Ede4ka [16]

Answer:AB=15 ,angle A=53.1°,angle B=36.9°

Step-by-step explanation:

AB=√(12^2+9^2)

AB=√(12x12+9x9)

AB=√(144+81)

AB=√(225)

AB=15

TanA=12/9

TanA=4/3

A=Tan(inverse)(4/3)

A=53.1° angle A=53.1°

angle B=180-(90+53.1)

angle B=180-143.1

angle B=36.9°

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4 years ago

Halloween Candy Halloween is Kelly's favorite holiday of the year! Based on experience, Kelly knows that on average, each house

LuckyWell [14K]

Using the <u>normal distribution and the central limit theorem</u>, it is found that there is an approximately 0% probability that the total number of candies Kelly will receive this year is smaller than last year.

Normal Probability Distribution

In a normal distribution with mean $\mu$ and standard deviation $\sigma$ , the z-score of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

It measures how many standard deviations the measure is from the mean.
After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.
By the Central Limit Theorem, for n instances of a normal variable, the mean is $n\mu$ while the standard deviation is $s = \sigma\sqrt{n}$ .

In this problem:

Mean of 4 candies, hence $\mu = 4$ .
Standard deviation of 1.5 candies, hence $\sigma = 1.5$ .
She visited 35 houses, hence $n = 35, \mu = 35(4) = 140, s = 1.5\sqrt{4} = 3$