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y=2(x-3)²+1     This is the vertex form of a parabola expressed as: y = a(x-h)2+k (Where the vertex is h, k)

y=a(x-h)^2 +k     so -h = -3    or h=3   and k= 1   so the vertex is  (3,1)

ok thanks

The ratio of nuts to total weight is   30 out of 61

Substituting in the numbers you are given  (weight of nuts = 480)  

the ratio of nuts to total weight is 480 to 'x'

30/61 = 480/x      Multiply both sides by 'x'

30/61 * x = 480     Mutiply both sides by 61/30

x = 976

ElectricPavlov, please help me.
How do you get to (3,1)?

Greeting asinus :- )

From Desmos graphing calculator:   (sorry about the size!)

I dont get it

Maybe you do not get it because I made a mistake!!!!  Sorry!

30 out of (30+31) is nuts .... or ...    30/61 is nuts

This problem as a ratio:

30/61 = 480/x     where x = total weight

solve for x = 976 gm total weight

which point is the vertex of y=2(x-3)²+1

\(y=f(x)=2(x-3)^2+1\)

\(f(x)=2(x^2-6x+9)+1 =2x^2-12x+19\)

                                                               1. Derivation = 0

\(f'(x)=4x-12=0 \) Change of page with change of sign

\(x_{min}=3\)                                                                 set x

\(y=2x^2-12x+19=18-36+19=1\)

\(y_{min}=1\)

The vertex of the function is P (3;1)

  !

See some of the following discussion from the last few days:

http://web2.0calc.com/questions/divide-zero-by-zero

" (Some irrational numbers are 'repeating' but some are not,like pi for example.)"

Note that no irrational numbers are repeating.  If they were they would be expressible as the ratio of two integers; i.e. they would be rational!

.

vertex form of a parabola's equation is generally expressed as: y = a(x-h)2+k 

Where the vertex is h, k    so for this one the vertex is   (3,1)

5 out of every 8 are hot, so the total number of hot drinks = 400*5/8 → 250

.

5/8 of the drinks are hot

5/8 x 400 = 250 hot drinks

Straight from Wikipedia:

In optics, the refractive index or index of refraction n of a material is a dimensionless number that describes how light propagates through that medium. It is defined as

n = c/ v ,

where c is the speed of light in vacuum and v is the phase velocity of light in the medium. For example, the refractive index of water is 1.333, meaning that light travels 1.333 times faster in a vacuum than it does in water.

For this problem:   n= (3x10^8) / (1.2 x 10^8) = 2.5

(2x^2y)(-x^3y)(-5xy^2z)

\((2y^{2y})(-x^{3y})(-5xy^{2z})\)

\(10x^{3y+1}y^{2(x+y)}\)

  !

University Theater sold 556 tickets for a play. Tickets cost $22 per adult and $12 per senior citizen. If total receipts were $8492, how many senior citizen tickets were sold?

556 = x+y or total number for both senior and adult tickets sold

x= number of adults tickets sold
y= number of senior tickets sold

\(x\times \$22+y\times \$12=\$8492\)

\(x+y=556\)                                        change of page and sign

\(x=556-y\)                                                          x einsetzen

\((556-y)\times \$22+y\times \$12=\$8492\) multiply and divide by $

\(556\times 22-22y+12y=8492\)          change of page and sign

                                                                                    calculate

\(10y=12232-8492\)                        divide by 10 on both sides

\(y=374\)

\(x=556-y=556-374\)                                              set y

\(x=182\)

\(There \ were \ 182 \ tickets \ for \ adults \)

\(and \ 374 \ tickets \ for \ seniors \ sold.\)

  !

Factors of 141 are 3 and 47

Sqrt (141) = sqrt(3)  x sqrt(47)   which are both irrational because they are  square roots of primes.

So sqrt(141) is irrational.   (Some irrational numbers are 'repeating' but some are not,like pi for example.)

18064773765607550801425251468864907833685590016

18064773765607550801425251468864907833685590016

The radius of each wheel of a car is 25 cm. If each wheel rotates 15 times per second, how many metres does the car travel per second? (Take pi = 3.14. Round off the answer to the nearest whole number.)

Yes.    m₁*v₁ + m₂*v₂

Alan, is the first part timesed together before it its added: m1v1 + m2v2 

3x-8>2x+3(3x)

3x-8>2x+9x

3x-8>11x

-8x-8>0

-8x>8

x<-1