# What Is Z When X

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## if z varies jointly as x and y and z

Ask: if z varies jointly as x and y and z is 40 when x is 8 and y is 5 what is z when x is 9 and y is 25​

EQUATION:

## [tex]z = kxy[/tex]

[tex]40 = k(8)(5)[/tex]

[tex]k = frac{40}{(8)(5)} [/tex]

[tex]k = frac{40}{40} [/tex]

[tex]k = 1[/tex]

[tex]z = 1xy[/tex]

[tex]z = (1)(9)(25)[/tex]

## z = 225

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## If y varies directly as x and z, and y

Ask: If y varies directly as x and z, and y = 130 when x = 2 and z = 5, what is y when x = 8 and z = 6?

y = 624

## Solution:

y = kxz

130 = k(2)(5)

130 = 10k

[tex] frac{130}{10} = frac{10k}{10} \ 13 = k[/tex]

y = kxz

y = (13)(8)(6)

y = 624

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## if z varies directly as x and y, and z

Ask: if z varies directly as x and y, and z = 90 when x = 3 and y = 6. What is z when x = 4 and y = 8?​

[tex]qquad[/tex]z varies directly as x and y

[tex]\[/tex]

[tex]bold {EQUATION:}[/tex][tex]boxed{tt z=kxy}[/tex] where k is the constant of the variation.

[tex]bold {GIVEN:}[/tex]

• z = 90 when x =3 and y = 6

[tex]bold {UNKNOWN:}[/tex]

• constant of the variation k
• z when x =4 and y = 8

[tex]bold {SOLUTION:}[/tex]

First, we will find the value of k,

[tex] begin{array}{c} largett z = kxy \ \ large tt 90 = k(3)(6) \ \ large tt 90 = 18k \ \ Large tt frac{90}{18} = frac{18k}{18} \ \ large tt boxed{ tt k = 5} end{array}[/tex]

Now, we will substitute the value of k to find z when x = 4 and y = 8.

[tex] begin{array}{l} large tt z = kxy \ \ large tt z = (5)(4)(8) \ \ large red{ boxed{ tt z = 160}}end{array}[/tex]

[tex]\[/tex]

[tex]thereforeboxed{textsf{z = 160 when x = 4 and y = 8.}}[/tex]

[tex]\ \[/tex]

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## Suppose z varies as y and inversely as x, and

Ask: Suppose z varies as y and inversely as x, and z = 12 when x = 8 and y = 24.
What is x when z = 16?
y

x = 6

y = 32

Step-by-step explanation:

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## If y varies jointly as x and z, find the

Ask: If y varies jointly as x and z, find the constant of variation and missing value.
1. If y = 24 when x = 2 and z = 3, what is y when x = 18 and z = 5?
2. If y = 12 when x = 6 and z = 4, what is x when y = 36 and z = 72?

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## z varies jointly as x and y. and z =

Ask: z varies jointly as x and y. and z = 60 when x = 3 and y = 4. What is the constant (k)?
What is z when x=6 and y=4?

k = 5

z = 120

Step-by-step explanation:

z = kxy

60 = k(3)(4)

60 = 12k

5 = k

z = 5xy

z = 5(6)(4)

z = 5(24)

z = 120

## If z varies directly as x, z = 60 and

Ask: If z varies directly as x, z = 60 and x = 5,  what is x when z = 6?​

## x = 1/2

If z varies directly as x, z = 60 and x = 5,  what is x when z = 6?

[tex]z = kx \ 60 = k(5) \ 60 = 5k \ frac{60}{5} = frac{5k}{5} \ k = 12 \ \ constant : of : variation : = 12[/tex]

[tex]z = kx \ 6 = (12)(x) \ 6 = 12x \ frac{6}{12} = frac{12x}{12 } \ x = frac{1}{2} [/tex]

## If z varies directly as x, z = 60 and

Ask: If z varies directly as x, z = 60 and x = 5, what is z when x =8?

z=yx (the variable depends)

60=5y

divide both sides by 5

12=y or y=12

x=8

z=?

z=(12)(8)

## If z varies directly as x, z = 60 and

Ask: If z varies directly as x, z = 60 and x = 5,  what is x when z = 6?​

x = 1/2

Step-by-step explanation:

z = kx

60 = k 5

60 divided by 5 is 12

k = 12

6 = (12) x

6 divided by 12 is 1/2

x – 1/2