In a certain triangle, the measure of the largest angle is 20 degrees more than twice the measure of the smallest angle. Five times the measure of the smallest angle equals the sum of the measures of the other two angles. Find the measures of the three angles.

Answers

Answer 1

Answer: Let the medium angle be B degrees the small angle be A degrees the large angle be C degrees Then C = 2 B + 20 ..................X 5 B = A + C ..................Y Sum of all angles A + B + C = 180 .............Z Applying Y in Z 5 B + B = 180 6 B = 180 B = 30 From X C = 2 x 30 + 20 = 60 + 20 = 80 From Y 5 x 30 = A + 80 150 = A + 80 150 - 80 = A = 70 Hence medium angle B = 30 degrees the small angle A = 70 degrees the large angle C = 80 degrees

Answer 2

Answer:

Final answer:

To solve the problem, we apply the properties of a triangle and make a system of linear equations. Setting up appropriate mathematical expressions for angles and solving the equation gives the angles as 30, 80 and 70 degrees.

Explanation:

This problem involves angles in a triangle and can be solved through linear equations. We know from the problem that the largest angle is 20 degrees more than twice the smallest angle, and 5 times the smallest angle equals the sum of the measures of the other two angles.

Let's denote the smallest angle as x. Thus the largest angle becomes 2x + 20.
The third angle, due to the property that the sum of angles in a triangle equals 180, would be 180 - x - (2x + 20).
You can insert the expression of the third angle into the second equation from problem statement, which gives: 5x = x + 2x + 20. Solving this equation gives x = 30.
Therefore, the angles are: 30 degrees, 2*30 + 20 = 80 degrees and 180 - 30 - 80 = 70 degrees.

Solution verification:

The sum of all angles is indeed 180 degrees.
The largest angle is indeed 20 degrees more than twice the smallest one.
Five times the smallest angle is indeed equal to the sum of the two other angles.

Learn more about Triangle Angles here:

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Is 9 rational or irrational?

Answers

Answer:

9 is a rational number.

Step-by-step explanation:

Answer:

irrational

Step-by-step explanation:

How the number 9 is irrational is that irrational numbers are numbers that are not expressed as fractions or decimals. So some examples of irrational numbers is 1,2,6,22,12,9

can I get brainlest?

A survey was conducted that asked 1003 people how many books they had read in the past year. Results indicated that x overbar equals 12.8 books and sequels 16.6 books. Construct a 99% confidence interval for the mean number of books people read. Interpret the interval.

Answers

Answer:

The 99% confidence interval would be given (11.448;14.152).

Step-by-step explanation:

1) Important concepts and notation

A confidence interval for a mean "gives us a range of plausible values for the population mean. If a confidence interval does not include a particular value, we can say that it is not likely that the particular value is the true population mean"

$s=16.6$ represent the sample deviation

$\bar X=12.8$ represent the sample mean

n =1003 is the sample size selected

Confidence =99% or 0.99

$\alpha=1-0.99=0.01$ represent the significance level.

2) Solution to the problem

The confidence interval for the mean would be given by this formula

$\bar X \pm z_(\alpha/2) (s)/(√(n))$

We can use a z quantile instead of t since the sample size is large enough.

For the 99% confidence interval the value of $\alpha=1-0.99=0.01$ and $\alpha/2=0.005$ , with that value we can find the quantile required for the interval in the normal standard distribution.

$z_(\alpha/2)=2.58$

And replacing into the confidence interval formula we got:

$12.8 - 2.58 (16.6)/(√(1003))=11.448$

$12.8 + 2.58 (16.6)/(√(1003)) =14.152$

And the 99% confidence interval would be given (11.448;14.152).

We are confident that about 11 to 14 are the number of books that the people had read on the last year on average, at 1% of significance.

I need an answer fast

Answers

Answer:

y=5x/6-10/6

y=5x/6-5/3 ( simplified)

Step-by-step explanation:

5x-6y=10

slope intercept form :

-6y=-5x+10

y=-5x/-6 +10/-6

y=5x/6-10/6

y=5x/6-5/3

Given that f(x)=x+3 and g(x) = x^2 - x, find (f+g)(4)

Answers

The answer is 19

Check out the attached images for the steps. They are slightly different approaches that lead to the same answer.

A cup of brewed tea has 54 milligrams less caffeine than a cup of brewed coffee. If a cup of tea has 66 milligrams of caffeine, how much caffeine is in a cup of coffee? Write this problem in an equation.