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https://www.khanacademy.org/math/algebra2/functions-and-graphs/function-introduction/v/what-is-a-function

A recent order was being readied to go out on the next flight.

Five types of pizza were being shipped:

59      reindeer sausage and onion;                               59 pizzas were to have reindeer sausage;

25      Polynesian chicken and green peppers;             Chicken topped 5/28 of the pizza;       5/28*140 = 25

A       pepperoni, reindeer sausage, and bacon;           10% of the pizzas were to have pepperoni.

B       green peppers, tomatoes, and onions;

C       bacon and tomatoes.

Sets of toppings had to be placed on 140 pizzas.

40% of the pizzas were to have tomatoes;      40% of 140 = 56         B+C=56

34 pizzas were to have bacon;                                                            A+C=34

How many of the five types of pizzas were to be made? How many sets of toppings had to be prepared? Solve, show your work, label your answers and explain your work.

A+B+C= 140-59-25 = 56

B+C=56

A+C=34

A+B+2C=90   but   A+B+C=56      subtract and you get    C=34

so

B+34=56         B=22

A+34=34         A=0

oh dear, I have done something wrong.   I must have been drinking Chrismas cheer with all those reindeer around you really could not blame me.      

x+ 2y+ 3z+ 4u=20    (1)

-x + 5 y +2 u=13      (2)

x+ y+ z+ u =10        (3)

-x+y-z+u= -2            (4)

Add (3)  and (4)   →  2y + 2u = 8 →   y + u = 4  →  y = 4 -  u  (5)

Sub this into (2)

-x + 5(4 - u) + 2u = 13 →  -x + 20 - 5u + 2u  = 13  → -x - 3u  = - 7  →   x + 3u = 7  → x  = 7 - 3u    (6)

Subbing into (1) and (4) for x and y we have the following system ;

[7 - 3u] + 2(4 - u] + 3z + 4u = 20 

[3u - 7] + [ 4 - u] - z + u = -2

Simplifying both of these, we have

-1u  + 3z =  5     (7)

 3u   - 1z   =  1

Multiply the top equation by 3 and add to the bottom, and we have

8z = 16   →  z = 2

Subbing this into (7),    -1u + 3(2)  = 5 →  -1u = -1  →  u = 1

Subbing this result into (6), we have   x = 7 - 3(1)   = 4

And subbing  u = 1 into (5), we have   y = 4 - 1  = 3

So

{x , y,  z , u }   =  { 4,  3, 2, 1 }

inversely if y is 35 and x is 13 what is k

y=k/13

35=k/13

k=35*13

[11 + (0 00 + 16 ━ 0) + 10O =?} =

is it meant to be

11 + (0.00 + 16 ━ 0) + 100

= 11+16-100

=27-100

=-(100-27)

= - 73

Calculate the value of the function f(x)=10x for x=0:

It just means to replace the x with 0

f(0) = 10*0 = 0

(3^(1/2))^(4/3). =  

\((\sqrt3)^{4/3}=((\sqrt3)^4)^{1/3}=9^{1/3}=\sqrt[3]{9}\)

using the forum calc

9^{1/3} = 2.080083823051904

88ft/s = 60mph

607200ft/ hr = 607200/3600 = about 506/3 ft/s

So

60 / 88 = x / [506 / 3]    cross-multiply

[506 / 3] (60)  = 88x      divide both sides by 88

[ (506 / 3) (60) / 88 ] =  115 mph

Thanks Guest,

That was a lot of work  !!      

Normally this would be done with matrices.  I am really rust on matrices I would have to watch a you tube clip or something on how to do it.    You answer is great.    Did you check that all the numbers made the equations true ?     I guess the asker can do that him/herself :))

3/4 divided by 5 1/5

(3/4)/(5+1/5) = 0.1442307692307692

What a pity, the calc has not included the fractional answer :((

OUR FORUM CALC IS BACK !!       Thanks Admin     

It has not been here long has it  ???

9.7*10 = 97       

Hallo

I like this answer   

https://www.khanacademy.org/math/pre-algebra/exponents-radicals/scientific-notation/v/scientific-notation

if I borrow $3000 and there is a 6% interest on 36 month loan what is my monthly payment

This is a present value of an ordinary annuity.

Just use this formula,   C=unknown,  i=0.06/12      n=36        PV=3000 

9.7 cm ......each cm contains 10mm....so.....

9.7 cm =  97 mm

Sorry.....I did not fully read Melody' answer before posting mine.......they are essentially the same "can of peas"   [ canopies  ???  ]

1.   I assume this is supposed to be :   [ 200 + 13q] / q  and [ 300 + 25q ] / 2q...if so....we have

( 2 [200 + 13q] )  + [ 300 + 25q]  / 2q   =

[400 + 26q + 300 + 25q] / 2q =

[ 700 + 51q ] / 2q  this is the sum of the costs

[ 700 + 51q ] / 4q   = the average of this sum

2. Usihg D/R = T, we have :

  3d / 185  + 5d / 200  = T

[200(3d) + 185(5d)] / [ 185 * 200]   = T

[600d + 925d ]  / 37000 = T

[ 1525d ] / 37000 = T

[ 61d ] / 1480 = T

Thanks Chris,

I did not see the bit about there being exactly 20 questions.    

Here's a simpler solution:

Imagine that the silo is a"tube" which we can roll out into a flat plane.....assuming that the staircase  makes only one complete turn from the bottom to the top of the silo.......we will have a rectangle   that will be 37 ft high and will have a width of pi*d = pi* 14 ≈ 43.98 ft......and the staircase will be the diagonal of this rectangle....and the angle of inclination will be given by:

tan^-1 (37 / 43.98)  =  about 40.07°

5x + 2y = 48 and 3x + 2y = 32

Here's another method of solving this......manipulating the first equation, we have that  2y = 48 - 5x

Substituting this into the second, we have

3x + 48 - 5x = 32     simplify

-2x + 48 = 32    subtract 48 from both sides

-2x = -16    divide both sides by -2

x = 8

And subbing this into either equation, we have

5(8) + 2y = 48

40 + 2y = 48    subtract 40 from both sides

2y = 8     divide both sides by 2

y = 4

Let C be the number of T/F questions and M be the number of multiple choice questions....and we have this system of equations :

C + M = 20  →   3C + 3M  = 60    →  - 3C - 3M = -60  (1)

3C + 11M = 100  (2)        

Add (1) and (2) together

8M = 40    divide both sides by 8

M = 5      this is the number of multiple choice questions

C + 5  = 20   →  C = 15   this is the number of T/F questions

Hallo guest

3T+11M=100

So if could be

2 Multiple choice and 26 T/F      check     2*11+26*3 = 100

5 Multiple choice and 15 T/F      check      5*11+15*3 = 100

8 Multiple choice and 4 T/F        check       8*11+4*3 =   100

Incidentally this is a diophantine equation because all solutions must be integers.

There is a more formal way of solving so that all solutions are found.  (including negative solutions)

Of course you problems does not have any negative solutions :))

Do it as follows

\(\frac{o+p}{2}=1.48\\\\\frac{p+1.63}{2}=1.52\)

So p = 2*1.52 + 1.63 so p = ...

and o = 2*1.48 + p  so o = ...

I'm sure you can now complete the calculations.