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zlopas [31]
3 years ago
6

The difference of two supplemtary angles is 58 degrees. Find the measures of the angles

Mathematics
1 answer:
erik [133]3 years ago
4 0

Answer:

The measure of the angles are 61° and 119°

Step-by-step explanation:

Let the first angle = x°

let the second angle = y°

The sum of two supplementary angles = 180°

x° + y° = 180° ----- equation (1)

based on the given question; "the difference of two supplementary angles is 58 degrees."

x° - y° = 58° ------- equation (2)

from equation (2), x° = 58° + y°

Substitute the value of x into equation (1)

(58° + y°) + y° = 180°

58 + 2y = 180

2y = 180 -58

2y = 122

y = 122 / 2

y = 61°

The second angle is given by;

x° = 58° + y°

x = 58° + 61°

x = 119°

Thus, the measure of the angles are 61° and 119°

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Complete the proof for the following conjecture.
Ray Of Light [21]

Answer:

Statements                                                      Reasons

AC+CD=AD and AB+BD=AD         Segment Addition Postulate

AC+CD=AB+BD                            Transitive/Substitution Property

AC=BD                                         Given

BD+CD=AB+BD                            Substitution Property

CD=AB                                         Subtraction Property

AB=CD                                         Symmetric Property

Step-by-step explanation:

By segment addition postulate, we can say the following two equations:

AC+CD=AD and AB+BD=AD.

By either substitution/transitive property, you can say AC+CD=AB+BD.

You are given AC=BD, so we use substitution and write AC+CD=AB+AC.

After using subtraction property (subtracting both sides by AC), you obtain CD=AB.

By symmetric property, you may say AB=CD.

So let's write it into the 2 column-proof you have there:

Statements                                                      Reasons

AC+CD=AD and AB+BD=AD        Segment Addition Postulate

AC+CD=AB+BD                            Transitive/Substitution Property

AC=BD                                          Given

BD+CD=AB+BD                             Substitution Property

CD=AB                                          Subtraction Property

AB=CD                                          Symmetric Property

Properties/Postulates used:

Transitive property which says:

If a=b and b=c, then a=c.

Substitution property which says:

If a=b, then b can be substituted(replaced with) for a.

Subtraction property which says:

a=b implies a-c=b-c.

Segment Addition Postulate says:

If you break a segment into two smaller pieces then the measurement of that segment is equal to the sum of the smaller two segments' measurements.

3 0
3 years ago
Aaron’s room has a perimeter of 96 feet. The length of the room is 23 feet. How wide is Aaron’s room?
SIZIF [17.4K]

Answer:

The length is also 25 feet.

Step-by-step explanation:

23+23+25+25=96

5 0
3 years ago
Read 2 more answers
A manufacturer knows that their items have a normally distributed length, with a mean of 15.4 inches, and standard deviation of
Masteriza [31]

Answer:

0.9452 = 94.52% probability that their mean length is less than 16.8 inches.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

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

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

The Z-score 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. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Mean of 15.4 inches, and standard deviation of 3.5 inches.

This means that \mu = 15.4, \sigma = 3.5

16 items are chosen at random

This means that n = 16, s = \frac{3.5}{\sqrt{16}} = 0.875

What is the probability that their mean length is less than 16.8 inches?

This is the p-value of Z when X = 16.8. So

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

By the Central Limit Theorem

Z = \frac{X - \mu}{s}

Z = \frac{16.8 - 15.4}{0.875}

Z = 1.6

Z = 1.6 has a p-value of 0.9452.

0.9452 = 94.52% probability that their mean length is less than 16.8 inches.

5 0
3 years ago
3(x – 2) – 2x + 3 = -12
enyata [817]
X = 9 sorry if x isnt what youre looking for
6 0
3 years ago
8.35x - 1.5 = 71.98<br> (a) 8.6<br> (b) 8.8<br> (c) 9<br> (d) 10.3
prisoha [69]
<h3>  Hola! :D ¡te invito a recibir ayuda de un latinoamericano puto!</h3><h2><u> _____________________________________ </u></h2><h2>                        8.35x - 1.5 = 71.98</h2><h2> - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -</h2>

                           <u>El -1,5 qlero pasaría al otro lado positivo</u>

<h3>                                     8.35x = 71.98 + 1.5</h3><h2> - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -</h2>

                              <u>Ahora, se suma 71.98 + 1.5 = 73,48</u>

<h3>                                         8.35x = 73,48</h3><h2> - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -</h2>

    <u>El 8.35 qlero que está multiplicando, pasa al otro lado pero dividiendo</u>

<h3>                                       x = 73,48 ÷ 8.35</h3><h2> - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -</h2>

                                                    <u>Dividimos</u>

<h3>                                               x = 8,8</h3><h2> - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -</h2><h2>                 <u>(b) 8,8</u>  es la opción correcta</h2>
3 0
3 years ago
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