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there are 10c2 or 45 games total

and there are 5c2 or 10 games where it is boy-v-boy

so it is 10/45 or 2/9

HOPE THIS HELPED!

thank you!!!

thank you both!

y = x^2 + a  is a parabola

y = ax is a line

If the line intersects the parabola, it will be tangent to the parabola

The slope of a line tangent to the parabola at any point is 2x

So...the slope of the line = a = 2x

So....subbing in for a in both equations, we have that

y = x^2 + 2x

y = 2x (x)  = 2x^2

Setting these equal we have that

x^2 + 2x  = 2 x^2   rearranging, we have

x^2 - 2x  = 0      factor

x( x - 2) = 0     setting each factor to 0 and solving for x produces

x = 0      or x =   2

So....a =  2(0)  = 0     or  a = 2(2)  =  4

And the sum of these values for a  is 4

yw!!

Wow! That was fast! And yes it did help a lot! Thanks!!

after x months, plant a grows 10x centimeters, and after x months, plant b grows x(x+1)/2 because of the formula for triangluar numbers. this means those two are equal, so 10x=x(x+1)/2 or 20x=x(x+1), which means 20=x+1 so x=19.

HOPE THIS HELPED!

for this to be true, x^2+a and ax are equal at only one point. that means that x^2-ax+a's discriminant is 0, which means a^2-4a is 0. that means a is 0 or 4, and the sum is 4.

HOPE THIS HELPED!

there are 6 axes of reflection not 2

Thanks! 

10 games.....

To see this, note that the 5th girl plays 4 other girls

The 4th girl plays 3 other girls

The 3rd girl plays 2 other girls

The second girl plays 1 other girl

So...4 + 3 + 2 + 1  =  10

Another way to see this is to count the number of sets formed by choosing any 2 girls from 5....this is

C(5, 2)  =  10   

When we are doing problems like this, we have to get x by itself. To get x by itself we have to divide both sides by 2 to get x=17. We can check our work by inputting x for 17 and multiplying by 2 to get 34 and we know that 34=34, so x=17.

 i can almost solve anything but >11th grade math O.O sorry

i guess i will answer this myself... there are 7 choices for the inner dot, and you can draw a circle around the other six, so the number of ways for those is 6!/6 for rotations. so it is 7*120=840, but there are reflections, so it is 840/2=420.

;( i just say that every answer

he has four choices for what to wear as trousers, seven for shirts, and three for jackets. therefore the answer is 4*7*3 or 84.

HOPE THIS HELPED!

As we found in one of your previous postings    L:M:N   is 3:6:8  

3+6+8 =17     Not between 30 and 50    so let's double them all (this will keep the same ratios

L:M:N  6:12:16      6+12+16 = 34    satisfies the requirements

L=6

M=12

N=16

He has 4 ways to choose a pair of trousers, 7 ways to choose a shirt, and 3 ways to choose a jacket. 

Therefore, answer is \(4\cdot7\cdot3 = 84\).

\(\quad \cos\left(6x\right)\\ =\cos(2\cdot3x)\\ =2\cos^2(3x)-1\\ \text{Know: }\cos(3x) = 4\cos^3(x) - 3 \cos (x)\\ =2\left(4\cos^3(x)-3\cos(x)\right)^2 - 1\\ =2\left(16\cos^6(x)-24\cos^4(x)+9\cos^2(x)\right)-1\\ =32\cos^6(x)-48\cos^4(x)+18\cos^2(x)-1\)

\(\dfrac{111}{\frac{33}{\frac{-22}{-2}}\cdot(-5^2)+(-4)}\\ =\dfrac{111}{\frac{33}{11}\cdot(-25)-4}\\ =\dfrac{111}{-75-4}\\ =\dfrac{-111}{79}\)

I guess you are trying to ask what is the values of m and a.

\(8x + 1 \equiv 5\pmod{12}\\ 8x\equiv4\pmod{12}\\ 8x\equiv16\pmod{12}\\ x\equiv2\pmod{12}\)

In acute triangle ABC, angle A = 68 degrees. Let O be the circumcenter of triangle ABC. Find angle OBC, in degrees.

\(-\sin ^6(x)+\cos ^6(x)-15 \sin ^2(x) \cos ^4(x)+15 \sin ^4(x) \cos ^2(x)\)