2coolforuser
Answered

Discover answers to your most pressing questions at Westonci.ca, the ultimate Q&A platform that connects you with expert solutions. Connect with professionals on our platform to receive accurate answers to your questions quickly and efficiently. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.

how do i write and solve for this inequality

How Do I Write And Solve For This Inequality class=

Sagot :

sqdancefan

9514 1404 393

Answer:

  -7/4 < x < 8

Step-by-step explanation:

The value of y can be determined from the sum of the angles, so you know each of the angles exactly. That means you know the ratio of side lengths exactly, which lets you solve for x exactly.

__

Setting that aside, we observe that angle C is greater than angle A, so side AB will be longer than side BC.

  3x +15 > 4x +7

  8 > x . . . . . . . . . . subtract 3x+7

We also know that the lengths of these sides must be positive. Since BC is the shorter side, we require ...

  4x +7 > 0

  4x > -7

  x > -7/4

So, the allowable values of x are ...

  -7/4 < x < 8

_____

More complete solution

If we read the figure correctly, the sum of angles is ...

  (2y +12) +(4y +12) +(y -18) = 180

  7y +6 = 180

  y = (180 -6)/7 = 24 6/7°

Then (in degrees) ...

  ∠A = 2(24 6/7) +12 = 61 5/7, and ∠C = 4(24 6/7) +12 = 111 3/7

The Law of Sines tells us ...

  AB/sin(C) = BC/sin(A)

  sin(A)(3x +15) = sin(C)(4x+7)

  x(4sin(C) -3sin(A)) = 15sin(A) -7sin(C)

  x = (15sin(A) -7sin(C))/(4sin(C) -3sin(A))

  x ≈ 6.1872652

Visit us again for up-to-date and reliable answers. We're always ready to assist you with your informational needs. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Keep exploring Westonci.ca for more insightful answers to your questions. We're here to help.