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3 years ago

A and b are complementary and congruent. what is the measure of each of these angles?

Mathematics

1 answer:

Nadya [2.5K]3 years ago

8 0

Answer: The required measures of angles A and B is 45°.

Step-by-step explanation: Given that the angles A and B are complementary and congruent.

We are to find the measure of angles A and B.

Let x and y represents the measures of angles A and B respectively in degrees.

According to the given information, we have

$x+y=90^\circ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\x=y~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)$

From equations (i) and (ii), we get

$x+x=90^\circ\\\\\Rightarrow 2x=90^\circ\\\\\Rightarrow x=\dfrac{90^\circ}{2}\\\\\Rightarrow x=45^\circ.$

Therefore, from equation (ii), we get

$x=y=45^\circ.$

Thus, the required measures of angles A and B is 45°.

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3 years ago

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Consider the following sets of sample data: A: $29,400, $30,900, $21,000, $33,200, $21,300, $24,600, $29,500, $22,500, $35,200,

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Answer:

CV for A = 21.8%

CV for B = 15.5%

Step-by-step explanation:

The formula for coefficient of variation is:

CV = Standard Deviation / Mean

So,

For A:

Mean = Sum/No. of items

= 391300/14

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CV for A = 6085.31/27950 * 100

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Rounding off to one decimal

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3 years ago

A company has 10 men qualified to run a machine that requires 3 operators at a time. find how many groups of 3 operators are pos

anzhelika [568]

The number of possible groups or combination of three men can be formed from 10 is 120.

According to the given question.

Total number of men in a company, n = 10.

Number of men to be selected, r = 3

As we know that, What is a combination in math?

Image result for what is combination

A combination is a mathematical technique that determines the number of possible arrangements in a collection of items where the order of the selection does not matter.

Therefore, the number of possible groups or combination of three men can be formed from 10

= $^{10} C_{3}$

= 10!/ 3!7!

= 10(9)(8)/3(2)

= 5 × 3 × 8

= 120

The number of possible groups or combination of three men can be formed from 10 is 120.

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1 year ago

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Couldn’t quite read everything, the writing is very light. But from what I could read, it was correct for the most part. :)

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3 years ago

Mr. and mrs. lorenzo want to buy a home valued at $213,500. if they have 18% of this amount saved for a down payment, how much h

Vesnalui [34]

Option d is the correct answer. $38,430.00 is the amount saved for a down payment given that Mr. and Mrs. Lorenzo want to buy a home valued at $213,500 and they have 18% of this amount saved for the down payment. This can be obtained by using percentage formula.

<h3>How much have they saved?</h3>

The percentage of a number can be obtained using percentage formula,

If P% of X is Y then it can be denoted using the formula of percentage as,

⇒ P% of X = Y

⇒ P% × X = Y (where P% is P/100)

Here in the question it is given that,

Mr. and Mrs. Lorenzo want to buy a home valued at $213,500

They have 18% of this amount saved for a down payment

We have to find the amount they saved for the down payment.

Given that the total amount = $213,500

Percentage they are saving = 18%

The amount they saved for the down payment,

18% of the total amount = 18% of $213,500

Using the percentage formula we get,

18% of $213,500 = 18% × $213,500

18% of $213,500 = 18/100 × $213,500

18% of $213,500 = $ 38,430.00

Hence Option d is the correct answer. $38,430.00 is the amount saved for a down payment given that Mr. and Mrs. Lorenzo want to buy a home valued at $213,500 and they have 18% of this amount saved for the down payment.

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