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Original graph  of the problem  : https://www.desmos.com/calculator/xyzfrdpqbv

Because of symmetry......we only need one intersection point

4x^2  +   11y^2    = 29      (1)

x^2    -    6y^2     =    6   →   -4x^2  + 24y^2  =  -24    (2)

Add (1)  and (2)   and we have

35y^2  =  5

y^2  = 5/35  =  1/7

y = sqrt (1/7)

And

x^2  - 6 (1/sqrt(7))^2  =  6

x^2   -  6/7   = 6

x^2  =  6 + 6/7

x^2  =  48/7

x  =  sqrt  (48/7)

(0,0)   will be the center of the  circle

The  radius =   sqrt (48/7  + 1/7) =   sqrt(  49/7)  =  sqrt (7)

The equation of the  circle we need =  x^2  + y^2  = 7

Area =   pi  (sqrt (7))^2  =   7 pi  units^2

Here's the completed graph   :   https://www.desmos.com/calculator/of0i8sikec

You are the first one to notice that!

Some people had to take a wild guess if I was American or not.

I honestly can NEVER spell it right. 🤦‍♂️

THX, Nacirema

[ That's "American"  spelled backwards........such as  "Body Ritual Among the Nacirema "  ]

O is the circumcenter of ΔABC. If OB = OC = BC, what is ∠BAC?

                                       A

                                      O

                         B                      C

If OB = OC  = BC, then triangle  BOC   is equilateral  with central angle  BOC =  60

And angle BAC   is an inscribed angle  subtending  the  same arc as  BC.....so.....its measure  = 1/2  BOC  = 

30

Dooooobleeeee Poooossssstttttt:

In ΔABC, AB = AC and ∠A = 72◦ . What is ∠B?

                          A

                B                    C

Since  AB  = AC   then  angles  B  and C  are equal

So     B =   (180  - 72)   / 2  =      108/2  =   54°

I think the latex screwed up there. I don't think you intended that to happen. But at least I can use latex normally now.

So let shoes be $s$ and hats be $h$. 

Eric: $2s+3h=175$

Jaden: $4s+1h=225$

Solve the system of equations.

We can set them similar to each other by multiplying Eric's by 2 and subtracting all of Jaden's from it.

$2\cdot(2s+3h=175)\\\implies4s+6h=350$

Cancel like terms:

4s+6h=350

-4s+1h=225

-------------------

5h=75

Now we have 5 hats are 75 dollars, so 1 hat is 15 Dollars.

Sub into the secone equation:

$4s+15=225$

$4s=210$

$s=52.5$

Thus a pair of shoes is 52.50 Dollars.

Lines AB and CD intersect at a point O in such a way that ∠DOB = 4∠COB. What is ∠AOD? 

A                C

         O

D                 B

DOB + COB   =180

Then

4COB + COB  =180

5COB  =180

COB = 180/5  = 36

And AOD  is  the vertical angle to COB......so AOD  also  = 36  (degrees)

What is the question?

Double pooooosttttt:

What we want to do is to put them both into books read per day. 

Becky reads 10/4 books, if you do time/quantity, and similarly Sarah reads 50/20.

If we simplify both, 10/4 = 5/2 and by the same token 50/20 = 5/2. 

Thus the answer is YES.

Hi.

1. Rewrite the equation:

     \(-10x+2y=30\\\implies-5x+y=15\text { here we divided the entire equation by 2}\)

2. Slope intercept form is expressed as \(y=mx+b\) where m is the slope and b is the y intercept. Let's now finish up the equation and put the above into slope intercept form:

     \(-5x+y=15\\\text { add 5x to both sides}\\\implies y=15+5x\\\implies \boxed {y=5x+15}\\\text { the slope is 5 and the y-intercept is 15}\)

To be honest, I have played with this and I do not have an answer.

How can we explain why you were wrong when you have not even given us an outline of your working ?

Which calculator?

\(sin^{-1}(x) =arcsin(x) = asin(x) \\ \)

if you want inverse sin on the web2.0 calculator then press   [2nd]    [asin]    then your ratio [ = ]

PEDMAS
-( -54 +20)  -21

-(-34) - 21

34-21 = 13

LiF = Molar mass: 25.939 g/mol         10.2 grams is .393 moles

PbO₂ = Molar mass: 239.2 g/mol       127 gms is .531 moles

2x^2  +  mx    +  18

If we have two distinct rooots.....then the discriminant must  be >  0

So

m^2  - 4(2)(18)  >  0

m^2  - 144 >  0

m^2  >   144

The solutions  for  m  are    ( -inf, -12)   U  ( 12  ,inf )

I'll set  this  up  and you can finish  it......

Call  # boxes of popcorn  = x

Then   #  boxes of  candy = 175  - x

So

Boxes of candy  * Price  +   Boxes of  candy * Price =  Revenue

x *  5    +    (175 - x)  * 2.50  =   687.50

We just  need  to  find the non-integer solutions for this

(n - 2) 180  / n

n = 7, 11, 13, 14, 16,17, 19, 21, 22, 23 

Thank you so much! By any chance can you help me out with the part b too? thanks!

Surface area of hemisphere  =   2pi r^2  =  2pi *(3)^2  =  18pi m^2

Lateral surface area of silo  =  2pi r * h   =  2pi  (3)(12)  =  72 pi m^2

Total area =   (18 + 72) pi  m^2     =  90 pi m^2

Litres of paint needed =   [  90 pi ] / 8.5  ≈  33.3  L    

Inscribed triangle  ABC is a right triangle since its  base is on a diameter

AC  = sqrt ( 4^2  - 1^2 )  = sqrt (15)

Area of  ABC  =(1/2) (1) (sqrt (15))  =  sqrt (15)/2

Area of circle =  pi r^2  = pi * 2^2  = 4pi

Shaded area  =  [4pi  - sqrt (15)/2  ]  cm^2

We  know  that

1001  =  first term + ( number of  terms - 1) * common difference

1001  = first term   +  ( 50  - 1) (6)

1001 =  first term  +  49 * 6

1001  = first term   + 294

1001 - 294  = first term  =  707

Second  term  =  707 + 6 =   713