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https://web2.0calc.com/questions/power-meassurement

x  - y^2  +  8y  =   13

Rearrange  as

x =  y^2  -  8y  +  13         complete the  square on y

take (1/2)  of 8  =4.....square it  = 16      add  and  subtract on the right side

x  =  y^2  -  8y  +  16 +  13  -16           factor  and simplify

x =  (y - 4)^2    -  3       add 3 to both sides

(x + 3)  = ( y -4)^2

We have  the  form     ( x - h)  =  ( y - k)^2     where  the  vertex  =  ( h , k)

So  the  vertex  is  ( -3, 4)

See the graph here : https://www.desmos.com/calculator/6pqzy8femz

2 min at hyper-turbo is   2 out of 20 battery usage    = 1/10 used

18 minutes at turbo   is  18 out of 40 battery usage =  9/20  used

1/10 + 9/20 = 11/20 used     soooo   9/20 remains

9/20 x 60 minutes normal speed = 27 minutes runtime at normal

"A"   looks to  be correct   !!!

A  is   correct   !!!!

Let  x   be  the  number of  .50   increases

Note  that  she really only makes    ( $8 -$4) =  $4  on the sale of each bracelet

So

Profit  =  Sales Price  *   Units sold

Profit  =    ( 4 + .50x)  ( 40  - 4x)

P =  160  +  20x - 16x - 2x^2        rearrange  as

P  = -2x^2   +  4x   +  160

The  number of .50   increases  that max  the profit  =    -4 / ( 2 (-2))  =    4/4 =   1

So......the selling  price  that would max  the profit  =  8 + .50    =   $8.50

Sorry, for some reason the question got messed up:

Poppy produces bead necklaces. The material for each necklace costs 4 dollars. She has been selling them for $8 each and averages sales of 40 necklaces per week. If she increases the price by $0.50, she would lose 4 sales per week. What should be the selling price to maximize her profit.

2. I would say, D

3.    Arithmetic

      Common difference, d ,  =  -9

       First term  = 99

Explicit rule

a_n  = 99  - 9 (n - 1)     where  a_n is the nth term

Note  that this also  could  be written  as      

a_n  =  108  - 9n       (depending  upon the form your teacher wants )

4.  Geometric

     Common  ratio  =  1/2

      First term   = 50

Explicit rule

a_n =  50 (1/2)^(n -1)    where an is the nth term

{The most important  thing is to  recognize  if we have an arithmetic or a geometric series  }

Assuming  that we  can have repeated letters, numbers

(26)^3  *( 5)^2  *  (26)^2     =  297,034,400 

Set h = 0, (because the ground is at zero height here) then solve the quadratic -16t² + 32t + 128 = 0 for t.  There will be two values, one negative and one positive.  Take the positive value.

Let the two numbers be a and b:

a = 5b + 6

a + b = 24

Replace a in the second equation using the first equation, then simplify to find b.  Substitute b back into the the first equation to find a.

Can you take it from here?

This is unclear!  

As follows:

Total------> 43,472 Adults

Women--> 4000 + Men

W + M = 43,472

M + M + 4000 = 43,472

2M = 39,472

M = 19736

Therefore there are 19736 men at the football match.

Hope that helps!!!!

🙃🙃👌

Note that \(x^{1/3}=\frac{x}{x^{2/3}}=\sqrt[3]x\)  so let \(u=x^{1/3}\) and we have \(4u-2u=7+u\)

Simplifying, we get \(u=7\)  so \(x=u^3=7^3=343\)

Initially there are 12 marbles.  and 2 of those are blue.

so the chance of choosing a blue one is  2/12 

That marble is not put back so there are now 11 marbles and only 1 of them is blue.  So the chance of choosing a blue one this time will be 1/11

The chance of getting 2 blue marbles is     \(\frac{2}{12}\times \frac{1}{11}=\frac{1}{66}\) 

Here is the graph

I am sure you can answer at least some of these questions on your own.

If you do not already use desmos graphing calc, you should start now.  It is an invaluable tool.

Corrections:

OR = sqrt(ON2 + NR2) = sqrt(6² + 7²)

3 bags of chips+ 2 bottles= 7.61 so now focus on 2 bottles 7.61 divided by 2= 3.805 so 2 bottles = 3.805 now divide it 1 more time so it = 1.9025 so 1 bottle = 1.9025 now 3 bags of chips are easy, just divide 3.805 by 3 = 1.268 (i think) so now add all of it to get  7.61 now 1 bottle=1.9025 and 1 bag of chip = 1.268 (im not sure on the bag of chips but i am sure on the bottle i think ok.)

The area of the unpainted region is 40*sqrt(5).

Answer: 4

On average, 1 out of 10 times you will draw the AwesomeBall (and this wins all by itself so we don't care what the other balls are) for a winning probability of 0.10.

Now, for the 9 out of ten times that you do not draw the AwesomeBall:

We will have to get a losing blue ball, I'll call that B (and the probability of getting that losing ball is 0.90).

We can win by getting two or more of the white balls. I'll classify a winning white ball (whose probability is 1/10 = 010)

as W and a losing white ball as L (whose probability is 9/10 = 0.90).

So, we can still win if we have this:

B x W x W x W   =   (0.90) x (0.10) x (0.10) x (0.10)   =  0.0009

B x W x W x L    =   (0.90) x (0.10) x (0.90) x (0.10)   =  0.0081

B x W x L x W    =   ...

B x L x W x W    =   ...

Since these are independent, add the above 5 results together, to get 47/200.

there is a 3/8 chance to get the Ace, a 3/7 chance to get a 2, and a 1/2 chance to get the 3. That adds up to a total probability of 3/56.

C. 3.2/2 = a/8

a = (3.2 * 8)/2 = 12.8

3.2 / 2 = 1.6

12.8 / 8 = 1.6

f(x) = 3x^5 - 9x^4 + 6x^3.