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Start at F ....BOTH angles there are 90 degrees

   so for the triangle on the RIGHT   (remember all angles of a triangle add to 180 degrees?)

         the angle on the right side at A would equal   180    -    90 - 65 =  25 degrees

             AF BISECTS angle A...so both of the angles at A are equal  at   25 degrees

Now you should be able to figure the angle at D.....

Another way:

Both angles at A are equal       both angles at F are equal    

so the remaining angles at D and N have to be equal.....(remember all angles of a triangle add to 180 degrees?)

True....THAT is the definition of perpindicular

Angle 1   and agle 4   form a straight line   ....they add to 180 degrees...so you should be able to calculate angle 4

Let Sydni's speed in heavy traffic = S

Her speed on 300-mile highway =2S

120 / S  +  300 / (2S) = 9 hours, solve for S

S = 30 mph - her speed in heavy traffic.

EH = 14 is the FALSE statement.   

DH, EH, FH, and GH are all the same length, namely 7.    

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Thanks Gino,

What you need to do Peerless Cucumber  is  graph your formula with Desmos and see if it works.

Remember to use radians, not degrees. 

(Note, Gino was using degrees but you changed it to radians)

Assuming the rock is near enough to the surface of the Earth that we can take its acceleration to be g (=9.81m/s²)' then we can get its velocity at 5m from v_rock = sqrt(2*9.81*5)m/s, and its momentum as m_rock * v_rock (since it starts from rest).  
 

To get Earth's change in velocity use m_Earth*v_Earth = -m_rock*v_rock

Tyace needs at least 40 hot dogs and 40 buns for a cookout.
Packages of hotdogs cost $3.50 and contains 10 hotdogs.
Packages of buns cost $2.50 and contains 8 buns.
The maximum amount of money Tyace can spend on hot dogs and buns is $70.
What are possible combinations of packages that Tyace can buy?

I assume:

\(\text{Let packages of hotdogs $=x$ and $x_{min} = 4$ packages } \\ \text{Let packages of buns $=y$ and $y_{min} = 5$ packages }\)

\(\begin{array}{|rcll|} \hline \mathbf{\dfrac{$3.50}{10~hotdogs} * 10x + \dfrac{$2.50}{8~buns} * 8y} &=& \mathbf{$70} \\\\ \dfrac{$3.50}{ hotdogs} * x + \dfrac{$2.50}{ buns} * y &=& $ 70 \\\\ 3.50x + 2.50y &=& 70 \quad | \quad * 2 \\\\ \mathbf{7x + 5y} &=& \mathbf{140} \\ \hline \end{array}\)

Euler :

\(\begin{array}{|rclrclrcl|} \hline \mathbf{7x + 5y} &=& \mathbf{140} \\ 5y &=& 140 - 7x \\ y &=& \dfrac{140 - 7x}{5} \\ y &=& \dfrac{140 - 5x-2x}{5} \\ y &=& 28 - x - \underbrace{\dfrac{2x}{5}}_{=a} \\ y &=& 28 - x - a & a&=&\dfrac{2x}{5} \\ & & & 5a&=&2x \\ & & & 2x&=&5a \\ & & & x&=&\dfrac{5a}{2} \\ & & & x&=&\dfrac{4a+a}{2} \\ & & & x&=&2a+\underbrace{\dfrac{a}{2}}_{=b} \\ & & & x&=&2a+b & b&=& \dfrac{a}{2} \\ & & & & & & 2b&=& a \\ & & & & & & \mathbf{a}&=& \mathbf{2b} \\ & & & x&=&2(2b)+b \\ & & & \mathbf{x}&=&\mathbf{5b} \\ y &=& 28 - 5b - 2b \\ \mathbf{y} &=& \mathbf{28 - 7b} \\ \hline \end{array}\)

The possible combinations of packages:

\(\begin{array}{|c|r|r|} \hline b & x=5b & y = 28 - 7b \\ \hline 1 & 5 & 21 \\ 2 & 10 & 14 \\ 3 & 15 & 7 \\ \hline \end{array}\)

1.   5 packages of hotdogs and 21 packages of buns

2. 10 packages of hotdogs and 14 packages of buns

3. 15 packages of hotdogs and 7 packages of buns

The “Mendelssohn" Stradivarius violin was estimated to be worth approximately $1,700,000 in 1990. The violin is expected to increase in value by approximately 7.5% each year. Estimate the value of the violin in the year 2010

Here is a z score calculator.

There are others around if this one is inadequate.

EXACTLY  

so, new one

y = 6 + sin x

notice, that could also be written as 

y= sinx  + 6

so for that what would be

a) y intercept

b) the midline

c) the wavelength

d) the amplitude.

See if you can graph it by hand and then check it with Desmos graphing calculator.

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Hi there...

Justin runs a 100meter race.
Justin reaches his maximum speed after running 35m in 7s.

After which he runs an additional "35m in 5s". <<---(Maximum speed).

For the next 2s he runs "X"m.

Which adds up to "(35m+"X"m)" in 9s and/or "(35m+((3/4)"X"m))" in 8.5s, away from the starting line.

I hope that helped?

Kind regards
BizzyX

 

PS...:

Unless you are meant to calculate acceleration, the first two lines are pretty useless calculation wise.
The only useful thing it tells you is "the distance from the starting line".
And that it was after this point in the race that he had reached his maximum speed, but it doesn't indicate the maximum speed.
For that you have to look at line three...
After that it's pretty simple math.


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That's a smart way to think about it. Thank you for the help, geno!!! 

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Hi there...

Here is how it lays out.

Statistics...: 

-------------------------------------------
Pairs of White socks = 4 

Pairs of Black socks = 3 

Pairs of Navy socks = 2 

Pairs of Red socks = 1 

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Total pairs of socks = 10 

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Grabing one pair of socks out of the drawer equals a 1 in 10 choice, or a 10% choice.

But there's a 1 in 10, or 10%, chance that the one she picks will be Red.
Or  there's a 2 in 10, or 20%, chance that the one she picks will be Navy.
Or  there's a 3 in 10, or 30%, chance that the one she picks will be Black.

In turn there's a "X" in 10, or X%, chance that the one she picks will be White.

I hope that helped...

Kind regards
BizzyX


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[490 + 430] / 2 =460 mph - its speed in still air

[490 - 430] / 2 =30 mph - speed of the wind.

It created an upward shift by 3?

There are 4 isosceles triangles:  ABD,  CDE,   BCE,  and   AEC.

Δ ABD  =>   45° + 67.5° + 67.5° = 180°

Δ CDE  =>   45° + 67.5° + 67.5° = 180°

Δ BCE  =>    45° + 90° + 45° = 180°

Δ AEC  =>    45° + 67.5° + 67.5° = 180°    

  Triangle   AEC  is an isosceles triangle, because 2 of its 3 angles are equal, and as a result of that, 2 of its sides are equal as well.            

https://web2.0calc.com/questions/help-please_25780

4 cuts will make 5 slice- pieces of cake

   then  5 cuts across those 5 peices will make 30 pieces....      soooo     9 cuts?

16 have all three ribbons.

Because 32 have a blue ribbon and a green ribbon and 16 have all three ribbons,

     32 - 16  =  16 have blue and green ribbons only (no white ribbon).

Because 31 have green and white ribbons and 16 have all three ribbons,

     31 - 16  =  15 have green and white ribbons only.

Because 39 have blue and white ribbons and 16 have all three ribbons,

     39 - 16  =  23 have blue and white ribbons only..

Since 62 have blue ribbons, subtracting those that have all three ribbons (16) and those that also have a green ribbon (16) and those that also have a white ribbon (23), we are left with 7 that have only a blue ribbon.

You can work in a similar fashion to determine how many only have a green ribbon and how many have only a white ribbon.

Finally, subtract all these non-overlapping groups to find out how many have no ribbons at all.

Y es that is all great.

So you had the graphs  

y=sinx

and

y=sinx   +3

What changed?  I mean how is the second graph different from the first one?

A short computer code, in Python, gives the following 30 distinct combinations.

(112, 113, 114, 115, 122, 123, 124, 125, 133, 134, 135, 144, 145, 155, 223, 224, 225, 233, 234, 235, 244, 245, 255, 334, 335, 344, 345, 355, 445, 455)>>Total =30

Is the amplitude dictated in relation to the midline? So, instead of being 4, would it be 1?

Regarding the equation on the centerline, that would be y = 3.

Is the wavelength just 2π?

Really?

The long piece is X   

The other piece is X – 16  

Add the two pieces together to get the original 24 foot long string   

X + ( X – 16 ) = 24  

X + X – 16 = 24   

2X = 40 

X = 20                                        The long piece is 20           

The other piece is 20 – 16   

                                                   The short piece is 4             

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