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4 months ago

N(17+x)=34x−r I need to solve for x

Mathematics

2 answers:

Svet_ta [12.7K]4 months ago

4 0

Answer:

The solution for x is shown here: $x= \frac{17N+r}{34-N}$

Explanation:

Given: $N(17+x)=34x-r$

The distributive property allows multiplying a single term by each term within a parenthesis individually.

If $a\cdot(b+c) =a\cdot b + a\cdot c$ ,

applying the distributive property to the left side produces:

$N\cdot 17+N\cdot x = 34x-r$ or $17N+Nx = 34x-r$

The addition property of equality means adding the same quantity to both sides maintains the equation's balance.

Add r to both sides:

$17N+Nx+r=34x-r+r$

Simplify:

$17N+Nx+r=34x$

The subtraction property of equality allows subtracting the same value from both sides.

Subtract Nx from each side:

$17N+Nx+r-Nx=34x-Nx$

Simplify:

$17N+r=34x-Nx$

$17N+r=x(34-N)$

The division property of equality permits dividing both sides by the same nonzero number.

Divide both sides by (34-N):

$\frac{17N+r}{34-N}= \frac{x(34-N)}{34-N}$

Upon simplification:

$x= \frac{17N+r}{34-N}$

tester [12.3K]4 months ago

3 0

The value of x equals (17N + r) divided by (34 minus N).

Starting from N(17 + x) = 34x - r,

expand left side: 17N + Nx = 34x - r

Group the x terms together.

The expression rearranged is (17N + r) over (34 - N).

Thus, the solution is

(17N + r) / (34 - N).

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The yearly income for an individual with an associate’s degree in 2001 was $53,166 and in 2003 it was $56,970. What is the ratio

Zina [12379]

Response:

8861: 9495

Detailed explanation:

The income ratio for the years 2001 to 2003:

53,166: 56,970

To simplify, divide both sides by 6:

8,861: 9,495

This can't be simplified further, so that is the final result!

8861: 9495

I hope this helps! Have a great day:)

6 0

3 months ago

Read 2 more answers

A fox sees a rabbit 35 feet away and starts chasing it. As soon as the fox starts moving the rabbit sees it and starts running a

zzz [12365]

The fox’s speed needs to exceed that of the rabbit to successfully catch up. Thus, the required speed for the fox is expressed as 35/t + 40.

The distance separating the rabbit from the fox is 35 feet.

The speed of the rabbit is 40 feet per second.

Fox's speed = F

To calculate a precise speed for the fox, a specific time for the pursuit must be provided.

Let’s denote the time as t.

Recall that:

Speed = distance / time

Distance = speed × time

The distance the rabbit moves away from the fox after time t will be:

35 + (40 × t) = 35 + 40t

The distance traveled by the fox after time t is: fox speed × t = F × t.

To catch the rabbit, both the fox and rabbit must cover the same distance:

Rabbit's distance at time t equals Fox's distance at that time.

35 + 40t = Ft

To determine F, the fox's speed:

Dividing both sides by t yields:

(35 + 40t) / t = Ft/t

35/t + 40 = F

<pThus, the speed of the fox should be: 35/t + 40

To find out the exact speed of the fox, a specific time value must be provided.

Learn more:

4 0

3 months ago

1. X^4(dy/dx) +x^3y =- sec (xy)<br><br>Integral by separation of variables? <br>

PIT_PIT [12445]

Answer:

Step-by-step explanation:

Considering the differential equation x^4(dy/dx) + x^3y = -sec(xy). We will solve it employing the method of separation of variables;

$x^{4} \frac{dy}{dx} +x^{3}y = -sec(xy)\\x^{3}(x\frac{dy}{dx} + y) = -sec(xy)\\let \ v=xy\\\frac{dv}{dx} = x\frac{dy}{dx} + y(implicit \ in\ nature)\\$

By substituting v and dv/dx into the previous equation, we acquire;

$x^{3}\frac{dv}{dx} = -secv$

We then separate the variables:

$-\frac{dv}{secv} = \frac{dx}{x^{3} }$

$-cosvdv = x^{-3}dx\\ integrating\ both\ sides\\-\int\limits {cosv} \, dv = \int\limits {x^{-3} } \, dx\\-sinv = \frac{x^{-2} }{-2} + C\\since\ v = xy\\-sinxy = \frac{x^{-2} }{-2} + C\\2sin(xy) = x^{-2} -2C\\2 sin(xy) = \frac{1}{x^{2} } -K (where\ K = 2C)\\$

The end expression provides the solution to the differential equation.

8 0

3 months ago