AlgebraGuru

Let \(x\) be the number of kids in the French class not including Max and Liz and let \(y\) be the number of kids in the English class not including Max and Liz. Since all 25 kids are either just in English, just in French, or in both (Max and Liz), we know that \(x+y+2=25\) or \(x+y=23\). Furthermore, we know that \(2(x+2)=y+2\) since \(x + 2\) and \(y = 2\) represent the total number of kids in each of the two classes. Rewriting the last equation gives us \(2x+2=y\) which can be substituted into the first equation to give us \(x+(2x+2)=23\), which gives \(x=7\). Substituting this value into any of the equations gives us \(y=\boxed{16}\).

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As Guest said

5/6  divided by  4/1 = 5/6  * 1/4 because we can switch the denomerator and numerator of the second fraction and then change division so multiplication

Thus our answer is  5/24

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This is how to solve ABC:

In my estimations you have a triangle with 2 angles and an altitude or height.  You have to find the base of the triangle in order to find the area.  I set up the triangle and sine the 60 degree angle was bisected I know that the vertex angle is 30 in my right triangle.  I used the tangent ratio of 30 to find the base of that triangle and then multiplied it by 2 to get that the whole base measure is 27.71281292.  Then I multiplied it by the height I was given of 24 and divided the whole mess in half to get the area.  332.553 units squared.

Somewhere in my explanation I gave a hint to the legnth of BC.

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From https://web2.0calc.com/questions/what-is-the-value-of-b-c-if-x-2-bx-c-gt-0-only-when

What is the value of 

\(\text{b+c if }\;\;x^2+bx+c>0\qquad \text{only when }\;\;x\in (-\infty, -2)\cup(3,\infty)?\)

Well that means that  y cannot not be positive for  x in [-2,3]

So the roots are x=-2 and x=3 and it is concave up

so the expression is

\((x+2)(x-3) = x^2-x-6\)

You can do the addition.

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\(1/4(2)(71)6\) = 213

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Here's a "mock"  pic

           C

    10                    20            

A              15                B   

Side  AB  = 15......side  BC  =  20   

If B is bisected....we have this ratio

BC / AB   =  longer segment  DC / shorter segment AD 

20/15   =  DC / AD

4/3  =  DC / AD

Thus.......AC  is split into 7 equal parts...and  DC  is 4 of these....so its length is

(4/7)  * 10   =   40/7 units

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Midpoint Formula: (x, y) = [(x1 + x2)/2, (y1 + y2)/2]

Plug in the numbers and get (1.5, -1).

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Who is that supposed to be for?

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Yeah, like electricpovlov said. Maybe ask a few questions, but 15 is waaaay tooooo much.

This link is blocked on my computer. Could you instead post the image in your question?

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There isn't enough information.

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Since, a circle is inscribed in a square, it means that the side of a square is equal to the diameter of a circle.

Since, the perimeter of a square is 32 inches.

A perimeter is a path that surrounds the two dimensional shape.

Perimeter of square is given by 

side 

side = 8 inches.

Since, side of a square = diameter of a circle

Therefore, diameter of a circle = 8 inches.

radius of a circle =  , where d is the diameter

radius =  = 4 inches.

The perimeter of a circle is termed as Circumference.

You can solve from here.

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k, i think it's perpendicular or skew. Not sure completely. Not a geometry expert.

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(x + 7) / (x2 - x - 2)  =  A / (x - 2) + B / (x + 1)

Since  x2 - x - 2  =  (x - 2)(x + 1)

--->   (x + 7) / (x2 - x - 2)  =  (x + 7) / [ (x - 2)(x + 1) ]  =

(x + 7) / [ (x - 2)(x + 1) ]  =  A / (x - 2) + B / (x + 1)

Writing with the common denominator of  (x - 2)(x + 1)

(x + 7) / [ (x - 2)(x + 1) ]  =  [ A(x + 1) ] / [ (x - 2)(x + 1) ] + [B(x - 2) ] / [ (x - 2)(x + 1) ]

Since the denominators are equal, they can be ignored:

x + 7  =  A(x + 1) + B(x - 2)

x + 7  =  Ax + A + Bx - 2B

x + 7  =  Ax + Bx + A - 2B

Set the x-term on the left side equal to the x-terms on the right side:  x  =  Ax + Bx

   --->   x  =  (A + B)x   --->   1x  =  (A + B)x   --->   1  =  A + B

Set the number term on the left side equal to the number terms on the right side:  7  =  A - 2B

Solving:  A +   B  =  1   --->   x -1   --->   -A -  B  =  -1

                A - 2B  =  7                      --->    A - 2B  =  7

Adding down the columns:                         -3B  =  6

                                                                           B  =  -2

Since  B = -2:   A + B  =  1   --->   A + -2  =  1   --->   A  =  3

(-2, 3)

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