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-7, 3, |-4|, |4.5|

bottom one

definition of a right triangle

sin m - h/p and sin p = h/m

substitution property of equity

divsion property of equity

sin c = h/a

area= (1/2)(b)(asin c)

area= (1/2)(ab)(sin c)

all the non-double/non-repeated options should be listed

1x2=2  

1x3=3

1x4=4

1x5=5

1x6=6

2x3=6

2x4=8

2x5=10

2x6=12

3x4=12

3x5=15

3x6=18

4x5=20

4x6=24

5x6=30

as you can see 6 and 12 are listed twice,

those would be the expected value and both equaly likely to happen

Yes I know what I answered.

I answered the question that was asked.

Tahnk you so much :)

Hey layla!

Once again, we use the formula:

\(S_{abc}=AB\sin{c}\)

Where A and B are the adjacent sides to the angle c. 

We could apply the formula in this problem:

\(\text{area}=13\cdot13\sin{44.8}\)

After solving the right side, you got the area. 

I hope this helped,

Gavin 

Hey Guest! 

This is a basic trigonometrey relationship. 

We use cosine in this case, where cosine is adjacent over hypotenuse. 

\(\cos{30º}=\frac{x}{10}\)

\(\frac{\sqrt3}{2}=\frac{x}{10}\)

\(x=\boxed{5\sqrt3}\)

I hope this helped,

Gavin

What is the area of △ABC△ABC ?

Enter your answer, as a decimal, in the box.

Round only your final answer to the nearest tenth.

 units²

I had the same Question, the answer is: The circles are similar because you can translate Circle 1 using the transformation rule (−4, −10) and then dilate it using a scale factor of 1/2​

Good work Azsun.   

Nvm got it

Sin(30) = y / 6

1 / 2 = y / 6         cross multiply

2y = 6                 divide both sides by 2

y = 3

To find  g(25)  , let's first find what values of  x  make  f(x) = 25

f(x)  =  25

                         Substitute  3x² - 2  in for  f(x) .

3x² - 2  =  25

                         Add  2  to both sides of the equation.

3x²  =  27

                         Divide both sides by  3 .

x²  =  9

                         Take the  ±  square root of both sides.

x  =  ±√9

x  =  ± 3

So...     f(3)  =  25     and     f(-3)  =  25

g( f(x) )  =  x² + x +1

                                     Let's plug in  3  for  x .

g( f(3) )  =  3² + 3 + 1

                                     Now we can substitute  25  in for  f(3)  because we know that  f(3)  =  25 .

g( 25 )  =  3² + 3 + 1

                                     And now simplify the right side of the equation.

g( 25 )  =  13                 This is one possible value of  g( 25 ) .

g( f(x) )  =  x² + x +1

                                            Now let's plug in  -3  for  x .

g( f(-3) )  =  (-3)² + (-3) +1

                                            Substitute  25  in for  f(-3)  since  f(-3)  =  25 .

g( 25 )  =  (-3)² + (-3) +1

                                            Simplify the right side.

g( 25 )  =  7                          This is the other possible value of  g( 25 ) .

The two possible values of  g( 25 )  are  13  and  7 .

13 + 7  =  20

Cos(x) = 28 / 72

Cos(x) =0.38888...

x = arccos(0.38888.....)

x =~67.1

Why did you post your question in the "Answers Section"?

Cos(28) = x / 64

0.8829476 = x / 64         cross multiply

x = 64 x 0.8829476

x =~56.5

5 + sinx/n (shorten the N) = 5 + six = 5 + 6 = 11

Sarcasm is obvious, rite?

Mr. BB may have caught a mistake by Sir CPhill, but he didn’t get the solution quite right (no surprises, here).  For one, 14 choose 2 is NOT 90, it’s 91. He didn’t set up an equation for the solution; he solved this intuitively and added some blarney slop, which is his usual method.

The equation is different from the one presented by Sir CPhill. It will look like this:

\(\dfrac{n !}{2!( n-2)!} + \dfrac{n !}{1!(n-1)!} + 1 = 106 \leftarrow \small \text{ solve for n }\\\)

This is much more difficult to solve; it’s an educated guessing process. For small sums, like this one, it’s easy; for large sums, a perusal of Pascal’s triangle would speed up the search, or a computer algorithm.   

Anyway, I eat crow frequently; we chimps like them.  

^{A certain, annoying troll should read his messages more often.}

GA 

You can have an infinite number of solutions:

We can choose "a" to be 140 in base ten = 165 in base 9

We can choose "b" to be 105 in base ten = 253 in base 6

Now, we can convert 140 and 105 from base 10 to base 3:

140 in base 10 =1 2012 in base 3, and:

105 in base 10 =1 0220 in base 3. So:

1 2012 - 1 0220 =1022 in base 3.

Thank you! Do you have any ideas for number 3?

What about 2?

(2011*2012*2013*2014) mod 5 = 4

That is correct tertre, but we need a solution.

Like what tertre said, let's cycle through the powers of \(3\) and \(7\), and see if there's a pattern.

We have, for the powers of \(3\): \(3^1=3, 3^2=9, 3^3=27, 3^4=81\) . Woah, we found a pattern! The units digit (\(3,9,7,1\)), will repeat forever with a power of \(3.\) Since we have to find the units digit of \(3^{17}\) , we can simply do: \(\frac{17}{4}=4 R1\) . A remainder of \(1\) , means the first number in the pattern, which is \(3\) . Next, on to the powers of \(7.\)

We have, for the powers of 7: \(7^1=7, 7^2=49, 7^3=343, 7^4=2401\) . We found a pattern here, again! The units digit 

(\(7,9,3,1\)), will repeat forever with a power of \(7.\) Since we have to find the units digit of \(7^{23}\) , we simply do \(\frac{23}{4}=5 R3\) . A remainder of \(3\) means the third number in the pattern, which is \(3.\)

We then have a units digit of \(3\) for \(3^{17}\) , and a units digit of \(3\) for \(7^{23}\).

Thus, we have, \(3*3=\boxed{9}\)