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urw, keep doing a good job.

16x - 4 = 2*6x

16x - 4 = 12x

4x = 4

x = 1

FH = 2*6x = 12

thanks jugoslav!

greeting

  !

We count the tallies to see that 5 students scored in the  range. Now we count tallies to find that there are 25 students in the class. The percent of the class that received a score in the 60-69 % range is  5/25 which is 20% . The answer is 20%. Hope this helped, im new to web 2 calc. 

220 = 700 x  (0.939)^m

220/700 = (0.939)^m

m = Log(220/700) / Log(0.939)

m =18.4 minutes

G is midpoint of FH, which means:

FG = GH. But FG =6x. So:

6x + 6x = FH. But FH = 16x - 4. So:

6x +6x =16x - 4

12x = 16x - 4

16x - 12x = 4

4x = 4   and x = 1. And:

FH =16x - 4 = 16*1 - 4 

FH = 12

$\boxed{3}$ is the correct answer. lmfao

set the equation to  6x+x=16x-4. find x, and plug it in for the 16x-4 to find FH.

:)

The ratio is: 90% / 40% =0.9 / 0.4 =2.25 : 1

Yes, this is called: Intersecting chords theorem. (Wikipedia has a solid explanation of this theorem)

Since the diameter is the longest chord of a circle, it's included in this theorem.

jugoslav 4 hours ago

As I said in the solution, the picture in the diagram might not be to scale.

But why does the angle size in the diagram not match your answer?

Ok. So, to do this problem, we first need to find the angle measure of x.

The problem says that \(m\angle PKS = 3x + 10\) and also \(m\angle SKR = x - 12, m\angle RKP = 62\). We know that the latter two angles sum up to make \(\angle PKS\), so we get the equation:

\((x-12)+62=3x+10\)

From this, we can solve for x (I'm going to spare you the details of that, since you probably already know how).

\(x=20\)

Now, since we have the value of x, all we have to do is plug it into \(m\angle PKS = 3x + 10\) and \(m\angle SKR = x - 12\), getting:

\(m\angle PKS = 70\), \(m\angle SKR = 8\)

I hope this helped! 

NOTE: The image was probably not to scale and all that, so this answer will seem incorrect. But if you check it, it will work.

x - 6 + x + 4x = 18

6x = 24

x = 4

The integers are:   -2,   4,   16             ( -2 + 4 + 16 = 18) 

The sum of three integers is 18. The third integer is four times the second. The second integeris 6 more than the first. Find the integers.    

How about   –2,  4,  16  

_.

The answer is 109. We know that a supplementary angles are two angles that add up to 180, and A and B follow this rule. This means, 8x - 27 + 4x + 3 = 180. Adding like terms, we get 12x - 24 = 180, 12x = 204, and finally, x = 17. But the problem is asking for the degree measure of angle A, so, 8*17 - 27 = 109.

T[2016]  -  T[2015]  = 2016 =T[63]

T[63] =[63 x 64] / 2 = 2016

sin A = sin(90º) = 1 

hint:     Use sine for y and cosine for x

The smallest b that works is 45^2 = 2025.

The roots are (1 - sqrt(-199))/2 and (1 + sqrt(-199))/2, and their sum is 1.

Since are looking for a cubic polynomial, let it be ax^3 + bx^2 + cx + d = 0.  So

\(a(\sqrt[3]{2} + \sqrt[3]{4})^3 + b(\sqrt[3]{2} + \sqrt[3]{4})^2 + c(\sqrt[3]{2} + \sqrt[3]{4}) + d = 0\)

This expands to

\(a (2 + 3 \sqrt[3]{2^2} \sqrt[3]{4} + 3 \sqrt[3]{2} \sqrt[3]{4^2} + 4) + b(\sqrt[3]{2^2} + 2 \sqrt[3]{2} \sqrt[3]{4} + \sqrt[3]{4^2}) + c(\sqrt[3]{2} + \sqrt[3]{4}) + d = 0\)

Expanding everything out, and comparing the coefficients, we get

a + 3b + 3c + d = 16,
-6b + 3c + 3d = -24,
c - 3d = 22,
d = -6.

The solution to this system is a = 1, b = 3, c = 4, d = -6, so the cubic is x^3 + 3x^2 + 4x - 6.

So what is the answer?

Yes, this is called: Intersecting chords theorem. (Wikipedia has a solid explanation of this theorem)

Since the diameter is the longest chord of a circle, it's included in this theorem.

Good job, asinus!