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Here I labeled angle 3 .

Since  l₁  and  l₂  are parallel...

m∠2  =  m∠1 + m∠3          Imagine "sliding over"  l₂  onto  l₁ to see why this is.

                                         The problem says that  m∠1 = 50°  .

m∠2  =   50°  + m∠3          l₁  and  l₂  are parallel, and  m₂  is perpendicular to  l₂  .

                                          So... m₂  is perpendicular to l₁ . This means  m∠3 = 90º  .

m∠2  =   50°  +  90º

m∠2  =  140°

incorrect

Here's a method that you can utilize

If the ratio of the triangle's angle is 2:3:4, that means that the there is an angle with the value 2y, 3y, and 4y. Of course, by the triangle sum theorem, all the angles in a triangle must equal 180 degrees. Now, let's solve for y:

To find the measure of the largest angle, substitute the value for x and plug it into the largest angle, which is 4x since 4 multiplied by a natural number is greater than one multiplied by three:
 

2)

This problem is very similar to the one above. This time, however, we must know that the sum of all the exterior angles in any polygon is equal to 360 degrees. We'll use y again and solve just like before:

Ok, we want the smallest exterior angle to get the largest interior angle:

Therefore, the largest interior angle is 100 degrees.

This is a binomial probability problem.......the probability is given by :

C (7, 2) * ( 1/4)^5 (3/4)^2  = 189 / 16384  ≈ .0115   ≈  1.15%

I'm no Chemist, but will give it a go!.

1 molecule of methane is: CH4. This means that 1 molecule of methane consists of 1 atom of Carbon 6 and 4 atoms of Hydogen 1. Since 1 atom of Carbon 6 has 6 protons and, therefore, 6 electrons. And since 1 atom of Hydrogen 1 has 1 proton and 1 electron, therefore 4 Hydrogen atoms have 4 electrons.

So, 6 electrons from the Carbon atom + 4 electrons from 4 Hydrogen atoms = 10 electrons in 1 molecule of methane, CH4.

Since 1 mole of methane has =6.023 x 10^23 molecules, therefore 1 mole of methane has:

10 x [6.023 x 10^23] =6.023 x 10^24 electrons.

x + 4y = n and 5x - 2y = 10 

If we let x =  0 in the second equation, the y intercept is at  (0, -5)

Then, subbing these values into the first equation for x and y we have that   (0) + 4(-5)  = n  =   -20

The graph here confirms this : https://www.desmos.com/calculator/dcugsajo7a

but in 2 we are asking still for the answer to be the largest interior angle

1. Suppose that in a certain triangle, the degree measures of the interior angles are in the ratio 2:3:4.If the largest interior angle measures x degrees, what is the value of ?

I'm assuming that you want the value of the largest angle....the sum of the interior angles of a triangle = 180° ... and the ratio of 2:3:4 indicates that there there are 9 equal parts of the180°......the largest angle is 4/9ths of this = (4/9) (180)  = 80°

2.Suppose that in a certain triangle, the degree measures of the exterior angles are in the ratio 2:3:4.

If the largest interior angle measures x degrees, what is the value of ?( x degrees)

The sum of the exteriior angles of any regular polygon total 360°.......as before, there are 9 equal parts of the 360°....the largest interior angle will be supplementary to the smallest exterior angle.......the smallest exterior angle  =  (2/9) (360)   = 80°....so the greatest interior angle will   = 180 - 80  = 100°

Proof of this is that the next greatest exteriior angle = (3/9)(360)  =   120°  and the interior angle supplementary to this = 180 - 120  = 60°

And the greatest exterior angle  = ( 4/9) (360)  = 160°....and the interior angle supplementary to this = 180 - 160  = 20°

And the sum of the interior angles is  100 + 60 + 20  = 180°

Thanks to the guest for spotting my previous error.....!!!!!

It is possible, though.

(2,2,2,3) is a solution. 

Ok thanks ginger ale 

In order to do this problem, you must understand not slope-intercept form but point-slope form.

Point-slope form is the following equation:
 

\(y-k=m(x-h)\)

m = slope of the line

(h,k) is a point (any point will do) on the line.

We already have all of this information given to us already, so this problem is relatively easy. m = -2 and (h,k) is (4,7). Let's plug this in:

There is NO such thing !!!.

\(\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{(8*5)^2-10(8*5)+8*6-5*4+0.8}{2}}{2}}{2}}{2}}{2}}{2}}{2}}{2}}{2}}{2}}{2}\)

The above equals 0.6. 

Graphing is technically not necessary to solve the problem as you could be aware of the conditions of the different types of quadrilaterals, but doing so helps the solving process immensely.

To figure this problem out, let's first take a look at all the natural numbers up to 20.

The question asks for the probability for a number to be divisible by 2, 3, or 4. However, 2 is a factor of 4, so any number divisible by 4 is already divisible by 4, so there is no need to ever check for divisibility by 2. Also, if you prove a number is divisible by 2, you do not need to check if a number is divisible by 3.Let's take a look:

Now, let's count how many numbers are divisible by either 2 or 3. There are 13 numbers that divisible by either 2 or 3.

Therefore, there is a \(\frac{13}{20}\) chance that a number selected at random from the natural numbers 1 to 20 is divisible by either 2 or 3.

0.6, 3/5,6/10,12/20

There are infinite possibilities...for example....

a  = -1   b = 0   c  = 1

a + b + c  =  abc

If we restrict the answer to positive integers then  a  = 1 b = 2 and c  = 3   may be the only possibility....

a=1, b=2, c=3

1+2+3=6  and 1x2x3=6

sqrt ( x + 15)  +  sqrt (x)  = 15              subtract sqrt (x) from both sides

sqrt ( x + 15)   = 15  - sqrt (x)               square both sides

x + 15  =     225  - 30 sqrt (x)  + x        subtract x from both sides

15  = 225  - 30sqrt(x)                           rearrange as

30sqrt (x)  =  210                               divide both sides by 30

sqrt (x)  = 7                                         square both sides again

x  = 49

Check  

sqrt ( 49 + 15 )  + sqrt (49)  = 15   ???

sqrt (64)  + sqrt (49)   = 15   ??

8 + 7  = 15      OK!!!

what is 2.365360334076211e-27

It is computer language for:  2.365360334076211 x 10^-27

Look at the following diagram :

If you include  point E as (2, - 2)....we have a rectangle ABED  whose width  = AB = 5  and height  = BE  = 4

So...its total area is just  width * height  = 5 * 4  = 20 sq units

And triangle DEC has a base DE  = 5  and a height EC  = 2....so  its area  is [ b * h ] / 2  = [ 5 * 2 ] / 2  = 10 / 2  = 5 sq units

So....the toal area is just 20 + 5   = 25 sq units

Is it 25?????

 Z is the circumcenter of Triangle ABC , so \(\angle YAZ = \angle XAY\)  (very useful fact in geometry). Thus also Triangle ZAC=0, then we have \(\triangle ABC \sim \triangle XAC \implies 2 \theta = ?\)

We can use the Pythagorean Theorem, here

BM  =  sqt [ (4sqrt(2) ^2 + 1^2 ]  =    sqrt ( 32 + 1 )  =   sqrt (33) ≈  5.74

Here's a pic :

This question isn't possible unless you have a given value of e.