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3 years ago

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Marianne is 15 years old and her brother is 5 years old; is the relationship between their ages proportional?

1 answer:

cricket20 [7]3 years ago

4 0

Answer:

The ratio is 15:5 or 3:1. If Marianne is 3 years old, her brother is 1. And it is proportional...

Step-by-step explanation:

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Help pls????????????????

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3 years ago

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HELLO PLEASE GIVE ME THE RIGHT ANSWER ASAP THANK YOU !

seropon [69]

$\large\underline{\sf{Solution-}}$

$\textsf{Given expression;}\\$

$\rm{23 = \frac{7}{9}(6x - 36) + 9 } \\$

$\rm{\longmapsto} \: 23 = \frac{(42x - 256)}{9} + 9 \\$

$\rm{\longmapsto} \: 23 = \frac{(42x - 256 + 81)}{9} \\$

$\rm{\longmapsto} \: 23 = \frac{(42x - 175)}{9} \\$

$\rm{\longmapsto} \: \frac{23}{1} = \frac{(42x - 175)}{9} \\$

$\textsf{By doing cross multiplication, we get}\\$

$\rm{\longmapsto}23(9) = 1(42x - 175) \\$

$\rm{\longmapsto}207 =42x - 175\\$

$\rm{\longmapsto} \: 42x = - 175 - 207 \\$

$\rm{\longmapsto} \: 42x = - 379 \\$

$\rm \therefore \: x = - \frac{375}{42} \\$

$\textsf{Hence, the value of x will be -375/42 respectively.}\\$

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3 years ago

Consider the following initial-value problem. (x + y)2 dx + (2xy + x2 − 2) dy = 0, y(1) = 1 Let ∂f ∂x = (x + y)2 = x2 + 2xy + y2

IRISSAK [1]

$(x+y)^2\,\mathrm dx+(2xy+x^2-2)\,\mathrm dy=0$

Suppose the ODE has a solution of the form $F(x,y)=C$ , with total differential

$\dfrac{\partial F}{\partial x}\,\mathrm dx+\dfrac{\partial F}{\partial y}\,\mathrm dy=0$

This ODE is exact if the mixed partial derivatives are equal, i.e.

$\dfrac{\partial^2F}{\partial y\partial x}=\dfrac{\partial^2F}{\partial x\partial y}$

We have

$\dfrac{\partial F}{\partial x}=(x+y)^2\implies\dfrac{\partial^2F}{\partial y\partial x}=2(x+y)$

$\dfrac{\partial F}{\partial y}=2xy+x^2-2\implies\dfrac{\partial^2F}{\partial x\partial y}=2y+2x=2(x+y)$

so the ODE is indeed exact.

Integrating both sides of

$\dfrac{\partial F}{\partial x}=(x+y)^2$

with respect to $x$ gives

$F(x,y)=\dfrac{(x+y)^3}3+g(y)$

Differentiating both sides with respect to $y$ gives

$\dfrac{\partial F}{\partial y}=2xy+x^2-2=(x+y)^2+\dfrac{\mathrm dg}{\mathrm dy}$

$\implies x^2+2xy-2=x^2+2xy+y^2+\dfrac{\mathrm dg}{\mathrm dy}$

$\implies\dfrac{\mathrm dg}{\mathrm dy}=-y^2-2$

$\implies g(y)=-\dfrac{y^3}3-2y+C$

$\implies F(x,y)=\dfrac{(x+y)^3}3-\dfrac{y^3}3-2y+C$

so the general solution to the ODE is

$F(x,y)=\dfrac{(x+y)^3}3-\dfrac{y^3}3-2y=C$

Given that $y(1)=1$ , we find

$\dfrac{(1+1)^3}3-\dfrac{1^3}3-2=C\implies C=\dfrac13$

so that the solution to the IVP is

$F(x,y)=\dfrac{(x+y)^3}3-\dfrac{y^3}3-2y=\dfrac13$

$\implies\boxed{(x+y)^3-y^3-6y=1}$

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3 years ago

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I think it is 1/4 and -5

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4 years ago

What is the simplest form of 2√2 / √3−√2

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Answer:

A

Step-by-step explanation:

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