z varies directly with x and inversely with y^2. When x = 2 and y = 5, z = 8. What is the value of z when x = 4 and y = 9?

2 answers:

4 0

Direct variation is y = kx

Inverse variation is y = k/y

if z varies directly with x, then the equation would be z = kx

if z varies inversely with y^2 then the equation would be z = k/y^2. Combining, these two, we have z = kx/y^2

We use the first set of values to find the constant k:

x = 2, y = 5, z = 8:

8 = 2x/25, k = 100. Now we use the second set of values to find z:

x = 4, y = 9, k = 100 and z is unknown:

z = (4X100)/9^2

z = 400/81--> this is your final final answer.

*plz rate brainliest

Kaylis [27]3 years ago

3 0

The Answer is definitely..

400/81

You might be interested in

Find angle B It’s says I need 20Characters to ask the question so here u go

Ber [7]

The answer is 50 degrees

Can I have brainliest

7 0

3 years ago

What is 4 pi cubed divided by 3

zloy xaker [14]

52.6378901393 should be correct.

4 0

3 years ago

Solve x2 - 8x - 9 = 0. Rewrite the equation so that it is of the form x2 + bx = c.

stira [4]

X^2 - 8x-9=0
D = b^2- 4*a*c = 64- 4* (-9) = 64+36=100 =10^2
X1 = (8-10)/2 = -1
X2= (8+10)/2= 9

7 0

3 years ago

There are 20 students in a math class who have brown hair. This represents 80 percent of the students in the class. Which equati

Reptile [31]

Answer:

The answer is C

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

Please help! Thank you!

KIM [24]

The correct answer is: [B]: " (2, 5) ".
__________________________________________
Given:
__________________________________________
-5x + y = -5 ;
  -4x + 2y = 2 .
___________________________________________
Consider the first equation:
___________________________
-5x + y = -5 ; ↔ y + (-5x) = -5 ;

↔ y - 5x = -5 ; Add "5x" to each side of the equation; to isolate "y" on one side of the equation; and to solve in terms of "y".
_____________________________________________
   y - 5x + 5x = -5 + 5x

   y = -5 + 5x ; ↔ y = 5x - 5 ;
____________________________________________
Now, take our second equation:
______________________________
     -4x + 2y = 2 ; and plug in "(5x - 5)" for "y" ; and solve for "x" :
_____________________________________________________
         -4x + 2(5x - 5) = 2 ;
______________________________________________________
Note, 2(5x - 5) = 2(5x) - 2(5) = 10x - 10 ;
__________________________________________
So:   -4x + 10x - 10 = 2 ;

On the left-hand side of the equation, combine the "like terms" ;

-4x +10x = 6x ; and rewrite:

6x - 10 = 2 ;

Now, add "10" to each side of the equation:

6x - 10 + 10 = 2 + 10 ;

to get:

           6x = 12 ; Now, divide EACH side of the equation by "6" ; to isolate "x" on one side of the equation; and to solve for "x" ;

           6x/6 = 12 / 6 ;

                 x = 2 ;
_________________________________
Now, take our first given equation; and plug our solved value for "x" ; which is "2" ; and solve for "y" ;
_____________________________________
-5x + y = -5 ;

-5(2) + y = -5 ;

-10 + y = -5 ; ↔
                              y - 10 = -5 ;

Add "10" to each side of the equation; to isolate "y" on one side of the equation; and to solve for "y" ;

         y - 10 + 10 = -5 + 10 ;

                   y = 5 .
_____________________________
So, we have, x = 2 ; and y = 5 .
____________________________
Now, let us check our work by plugging in "2" for "x" and "5" for "y" in BOTH the original first and second equations:
______________________________
first equation:

-5x + y = -5 ;

-5(2) + 5 =? -5?

-10 + 5 =? -5 ? YES!
______________________
second equation:

-4x + 2y = 2 ;

-4(2) + 2(5) =? 2 ?

-8 + 10 =? 2 ? Yes!
_______________________________________________________
So, the answer is:
___________________________________________________________
          x = 2 , y = 5 ; or, "(2, 5)" ; which is: "Answer choice: [B] " .
___________________________________________________________

3 0

3 years ago