All Answers 357312 Answers

First one

Note that the diameter forms the hypotenuse of a right triangle

So   x   is just complementary to the 71° angle =   90  - 71   =   19°

Do you see this???

Second one

Arc GEC  and  Arc GFC  sum to  360°

So

230  + arc GFC  =  360     subtract   230 from both sides

arc GFC  = 130°

And  since angle GDC is a central angle intercepting this arc, it has the same measure  = 130°

You are correct  !!!

Last one

WC  and MQ are equal chords....and equal chords in a circle intersect equal arcs

So

arc CW  is congruent to arc  MQ       the  second answer is correct

Yeah but that's for physics. I believe in math it's different. 

A quick google search will help..

"Speed and velocity are both measured using the same units. The SI unit of distance and displacement is the meter. The SI unit of time is the second. The SI unit of speed and velocity is the ratio of two — the meter per second."

ty!!

Which is D. Great job!

Vertex form is     a (x-h)^2 +k = 0    where h,k is the vertex   so let's start with that h,k = 6,-1

a (x-6)^2 +  -1 = y     (this info was given in the question)

       and the point  7,-3 given as a solution to this equation ..now we can substitute this into the equation to find 'a'

a(7-6)^2 -1 = -3

a-1 = -3

a=-2  

so the equation becomes

-2(x-6)^2 -1 = y

CPhill?????????????/

Second one   Multiply the numerator AND denominator by   (sqrt 2 - sqrt 10)  then simplify all of the terms to get

-3/2+1/2 sqrt(5)

Just as in the other problem, RP....we need to find the vertex....review my other answer in how to do this....so we have

x coordinate of the vertex     =     -(28)  / (2 * 2)   =  -7

y coordinate  of the vertex =   2(-7)^2 + 28(-7)  - 2  =  98 - 196 - 2  =  -100

We have a  positive in front of the first term.....thus.....this parabola turns upward

Thus.....the lowest y value  on the graph is    - 100

When we talk about "range", we are just referring to  the y values covered by the graph

So...   the range   is   

y ≥ -100    ⇒   all y values ≥ -100  are covered by the graph

"c"  is correct  

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

=  ( 3^2 * 2 * x * x^6 * y^6)^1/2

=     3 x^3 y^3  sqrt(2 x)

Did I do too many steps at once?

Ty! ^-^

y  =  ( x + 3)^2  -  3

The   " +3 "   inside the parentheses  [ contrary to intuition]   shifts the graph of y = x^2  3 units to the left

If it was  "-3",  it would shift the graph 3 units to the right

The  " - 3 "   at the end shifts this down 3 units

So....."b"  is correct

Here's the graph of the transformations : https://www.desmos.com/calculator/xruxghuvu5

Wow tysm! This really helped ^-^

In the form

y  =  ax^2  + bx + c

The x coordinate of the vertex  is  given  by      -b / [2a]

So....we have

y  = -2x^2 + 28x  -  18       ......    b  = 28     a   =  -2

So...the x coordinate of the vertex  is given by

-(28) / [ 2 * -2]   =   -28 / -4   =  7

So  to find the y coordinate of the vertex...sub this value back into the function

-2(7)^2  + 28(7)  -  18   =

-98 +  196 - 18  =

80

So....the vertex  is  ( 7, 80)

This is a  vertical parabola    ....the  axis  of symmetry  is just   

x    =  the x coordinate of the vertex

x  =  7 

Here's the graph :  https://www.desmos.com/calculator/wcucis6wzt

The arc of an inscribed angle is TWICE the degrees of the angle, so

2(4x-3.5) = 4x+17  solve for x = 6   therefore   4x+17 = 4(6) +17 = 41 degrees

Let's see if I can solve this:

Since $\triangle ABC$ and $\triangle PQR$ are equilateral, then $\angle ABC=\angle ACB=\angle RPQ=60^\circ$.

Therefore, $\angle YBP = 180^\circ-65^\circ-60^\circ=55^\circ$  and $\angle YPB = 180^\circ-75^\circ-60^\circ=45^\circ$ .

In $\triangle BYP$, we have $\angle BYP = 180^\circ - \angle YBP - \angle YPB = 180^\circ - 55^\circ-45^\circ=80^\circ$.

Since $\angle XYC = \angle BYP$ , then $\angle XYC=80^\circ$.

In $\triangle CXY$, we have $\angle CXY = 180^\circ - 60^\circ - 80^\circ = 40^\circ$.

So our final answer is $\boxed{40}$ degrees.

KK: 

To find the axis of symmetry you use the formula: x= -b/2a 

Once you find the axis of symmetry you can plug into the original formula to find the y value. Since the axis of symmetry is the x value of the vertex. 

I need an explanation

C 

Tell me if you need an explanation. 

Glad it helped , Tertre......waiting to see what the answer is to your red/white ball question to see if I got it correct!

Thanks, tertre.....!!!

Great job, CPhil! Amazing Explanation!

Thanks, EP! Great Explanation!

I believe that EP's answer is correct.....we are looking for the number of ways to partition 5  into 2 parts.....these are :

5  0

4  1

3  2   =      3 ways

Amazing Explanation, CPhill! Great job!