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xxTIMURxx [149]
3 years ago
7

Henry is three more than twice Nicholas’ age. Marcus is 9 less than six times Nicholas’s age. If Henry and Marcus are twins, how

old is Nicholas?
Mathematics
1 answer:
blagie [28]3 years ago
8 0

Answer:

Step-by-step explanation:

Henry is 3 more than twice Nicholas' age. You can write this as :

H = 3 + 2N

Marcus is 9 less than 6 times Nicholas' age:

M = 6N - 9

Since Henry and Marcus are twins, this means H = N.

3 + 2N = 6N - 9

Add 9 to both sides

12 + 2N = 6N

Subtract 2N from both sides

12 = 4N

Divide both sides by 4 to find N.

N = 12/4 = 3

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3 years ago
What is the value of x, when -2(2+3(x+5))=-64?​
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Please help me answer this question
avanturin [10]

By <em>direct</em> substitution and simplification, the <em>trigonometric</em> function z = cos (2 · x + 3 · y) represents a solution of the <em>partial differential</em> equation  \frac{\partial^{2} t}{\partial x^{2}} - \frac{\partial^{2} t}{\partial y^{2}} = 5\cdot z.

<h3>How to analyze a differential equation</h3>

<em>Differential</em> equations are expressions that involve derivatives. In this question we must prove that a given expression is a solution of a <em>differential</em> equation, that is, substituting the variables and see if the equivalence is conserved.

If we know that z = \cos (2\cdot x + 3\cdot y) and \frac{\partial^{2} t}{\partial x^{2}} - \frac{\partial^{2} t}{\partial y^{2}} = 5\cdot z, then we conclude that:

\frac{\partial t}{\partial x} = -2\cdot \sin (2\cdot x + 3\cdot y)

\frac{\partial^{2} t}{\partial x^{2}} = - 4 \cdot \cos (2\cdot x + 3\cdot y)

\frac{\partial t}{\partial y} = - 3 \cdot \sin (2\cdot x + 3\cdot y)

\frac{\partial^{2} t}{\partial y^{2}} = - 9 \cdot \cos (2\cdot x + 3\cdot y)

- 4\cdot \cos (2\cdot x + 3\cdot y) + 9\cdot \cos (2\cdot x + 3\cdot y) = 5 \cdot \cos (2\cdot x + 3\cdot y) = 5\cdot z

By <em>direct</em> substitution and simplification, the <em>trigonometric</em> function z = cos (2 · x + 3 · y) represents a solution of the <em>partial differential</em> equation  \frac{\partial^{2} t}{\partial x^{2}} - \frac{\partial^{2} t}{\partial y^{2}} = 5\cdot z.

To learn more on differential equations: brainly.com/question/14620493

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