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G/B =3/2, 

(G+7)/(B - 2)= 5/2, solve for G, B

G = 18 girls  and   B = 12 boys

For a total of 18 + 12 = 30 students.

They're probably just some haters/trolls that are more skilled in math. I never check my likes, so it's probably a good idea to just leave it.

ah. sorry about that! i think i made a careless mistake :(( (even tho, of course i care! :))

initially,
g = number of girls;
b = number of boys.
Because the ratio of girls to boys is 3:1, therefore
g = 3b                 (1)

finally, we have
g-1 girls because one girl dropped the class;
b+3 boys because three more boys signed up.
Because the new ratio of girls to boys is 5:2, therefore
(g - 1)/(b + 3) = 5/2
Cross multiply.
2(g - 1) = 5(b + 3)
2g - 2 = 5b + 15
2g - 5b = 17            (2)

Substitute (1) into (2) to obtain
2(3b) - 5b = 17
b = 17
g = 3b = 3*17 = 51

Final number of students in the class = 17 + 51 = 68

that is wrong.

8 hours is equal to 480 minutes. So 480/2 = 240. Multiplying 15 by 240 gives 3600 tin cans.

Consider t, b and m represents the cost of each toast, each bagel and each muffin, ( dollars ),

According to the question,

2t + b = 3.15                   ......(1)

b + m = 3.30                    .......(2)

t + 2b + 3m = 9.15        ......(3),

Equation (3) - 3 × equation (2),

t + 2b - 3b = 9.15 - 9.9

t - b = -0.75                   ..........(4),

Equation (1) - 2 × equation (4),

b + 2b = 3.15 + 1.5

3b = 4.65

Hence, the cost of each bagel would be $ 1.55 or 155 cents  ( ∵ 1 dollar = 100 cents )

One bagel = 155 cents

I agree with the first part of Guest's answer; but then I got lost ...

A + n  =  4(B - n)   --->   A + n  =  4B - 4n   --->   5n  =  4B - A

   (multiply by 4):  20n  =  16B - 4A

A - n  =  3(B + n)   --->   A - n  =  3B + 3n   --->   4n  =  A - 3B

   (multiply by 5):  20n  =  5A - 15B

Setting these two equations to each other:  16B - 4A  =  5A - 15B

                                                                             31B  =  9A

                                                                           31 / 9  =  A / B

Let A and B be the amount of money Alice and Bob have, respectively, at the beginning. We know that

A + n = 4(B - n)

A - n = 3(B + n)

Simplifying, we have

A + 5n = 4B

A = 3B + 4n

Subtracting the first equation from the second gives 5n = B - 4n, so B = 9n. Substituing this into the first equation gives A + n = 4(9n - n), from which we get A = 31n.

Therefore, the desired ratio is A/B = 31n/9n = 31/9.

hope this helped !

charis

Yes, but where is it exactly on the calculator on this website?

Nvm I got it

I got  \(x^2=56-x\), but then how do I proceed?

I already know that, but then what?

Hint:  arc(EH)  =  arc(GF)

If a polynomial of degree 3 has zeros at -3, -1, and 4, the polynomial will have this form:

  f(x)  =  a·(x + 3)·(x + 1)·(x - 4)

Since  f(-2)  =  18, we can find the value for a by solving:

   18  =  a·(-2 + 3)·(-2 + 1)·(-2 - 4)

Find the value of  a  and substitute this into:

  f(x)  =  a·(x + 3)·(x + 1)·(x - 4)

The least exterior angle is the one that has the largest interior angle.

Which of the three interior angles is the largest?

sin (-pi/12)  =  sin (-15°)  =  -sin (15°)  =  - sin (45° - sin 30°)   =

- [ sin 45°  cos 30°  -  sin 30° cos 45° ]   =

- [ √2/2 * √3/2  -  1/2  * √2/2]  =

- [ √6  - √2]  / 4    =

√2 - √6

_____

    4

2sin (4x)  =  1                 divide both sides  by 2

sin (4x)  =  1/2

Note  that  sin  (x)  = 1/2  at     pi/6, 5pi/6, 13pi/6, 17pi/6

Dividing  these angles  by 4    gives  us  the solutions

x  =  pi/24 , 5pi/24, 13 pi/24 , 17 pi /24 

cos θ  =  - √3/4

So  sin θ  = -√ [ 4^2  - (-√3)^2 ] / 4  =   - √[  16  - 3 ] / 4   =  -  √13  / 4

tan B = 3/4

sin B = 3/5

cos B =  4/5

So

sin ( θ  + B)  =    sinθ cosB + sinBcosθ   =  

(-√13/4 )  * (4/5)     +  ( 3/5 ) * ( - √3/4 )  =

[ -4√13  -  3√3 ]

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