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4 years ago

If y varies directly with x and y = 16 when x = 4, find x when y = 8.

Mathematics

2 answers:

VladimirAG [237]4 years ago

7 0

Answer: X = 2

Step-by-step explanation:

Y & X

Y = KX

K = Y/X = 16/4 = 4

Y= 8

K =4

X=?

X = Y/K

X = 8/4 = 2

Luba_88 [7]4 years ago

5 0

Step-by-step explanation:

$Given: \\ y \: \alpha \: x \\ \therefore \: y = kx..(k = constant)..(1) \\ \\ let \: us \: substitute \: x = 4 \: and \: y = 16 \: \\ in \: equation \: (1)\\ \\ 16 = 4k \: \\ \implies \: k = \frac{16}{4} \\ \implies \: k = 4 \\ substituting \: k = 4 \: in \: equation \: \\ (1) \: we \: find : \\ y = 4x....(2) \\ now \: we \: need \: to \: find \: x \: when \: y = 8 \\ \therefore \: 8 = 4x \\ \implies \: x = \frac{8}{4} \\ \huge \orange{ \boxed{\implies \: x = 2}}$

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tatyana61 [14]

Answer:

Step-by-step explanation:

From the figure attached,

If the figures shown are congruent (Equal in shape and size), length of all the sides must be equal.

Therefore, sides sides CD and GH must be equal in measures.

Distance between the two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by,

d = $\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Length of the side CD having ends C(-4, 4) and D(0, 5) will be,

CD = $\sqrt{(-4-0)^2+(4-5)^2}$

CD = $\sqrt{(16+1)}$

= $\sqrt{17}$

Length of GH having ends G(0, -4) and H(4, -5) will be,

GH = $\sqrt{(0-4)^2+(-4+5)^2}$

= $\sqrt{16+1}$

= $\sqrt{17}$

Therefore, m(CD) = m(GH)

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3 years ago

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umka2103 [35]

Answer:

(-n^4 - 4 m^7 x^4 y^2)/(3 x^4)

Step-by-step explanation:

Simplify the following:

(-6 n^5 x^3)/(18 n x^7) + (12 m^8 y^6)/(-9 m y^4)

The gcd of -6 and 18 is 6, so (-6 n^5 x^3)/(18 n x^7) = ((6 (-1)) n^5 x^3)/((6×3) n x^7) = 6/6×(-n^5 x^3)/(3 n x^7) = (-n^5 x^3)/(3 n x^7):

(-1 n^5 x^3)/(3 n x^7) + (12 m^8 y^6)/(-9 m y^4)

Combine powers. (-n^5 x^3)/(3 n x^7) = (n^(5 - 1) x^(3 - 7) (-1))/3:

-(n^(5 - 1) x^(3 - 7))/3 + (12 m^8 y^6)/(-9 m y^4)

5 - 1 = 4:

-(n^4 x^(3 - 7))/3 + (12 m^8 y^6)/(-9 m y^4)

3 - 7 = -4:

-(n^4 x^(-4))/3 + (12 m^8 y^6)/(-9 m y^4)

The gcd of 12 and -9 is 3, so (12 m^8 y^6)/(-9 m y^4) = ((3×4) m^8 y^6)/((3 (-3)) m y^4) = 3/3×(4 m^8 y^6)/(-3 m y^4) = (4 m^8 y^6)/(-3 m y^4):

(4 m^8 y^6)/(-3 m y^4) - (n^4)/(3 x^4)

Combine powers. (4 m^8 y^6)/(-3 m y^4) = (4 m^(8 - 1) y^(6 - 4))/(3 (-1)):

-(n^4)/(3 x^4) + (4 m^(8 - 1) y^(6 - 4))/(-3)

8 - 1 = 7:

-(n^4)/(3 x^4) + (4 m^7 y^(6 - 4))/(-3)

6 - 4 = 2:

-(n^4)/(3 x^4) + (4 m^7 y^2)/(-3)

Multiply numerator and denominator of (4 m^7 y^2)/(-3) by -1:

-4/3 m^7 y^2 - (n^4)/(3 x^4)

Put each term in -(n^4)/(x^4×3) - (4 m^7 y^2)/3 over the common denominator 3 x^4: -(n^4)/(x^4×3) - (4 m^7 y^2)/3 = (-n^4)/(3 x^4) - (4 m^7 x^4 y^2)/(3 x^4):

-n^4/(3 x^4) - (4 m^7 x^4 y^2)/(3 x^4)

-n^4/(3 x^4) - (4 m^7 x^4 y^2)/(3 x^4) = (-n^4 - 4 m^7 x^4 y^2)/(3 x^4):

Answer: (-n^4 - 4 m^7 x^4 y^2)/(3 x^4)

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3 years ago