What is the solution to the inequality x^2 >64

Mathematics

1 answer:

Gnom [1K]3 years ago

4 0

Answer:

see explanation

Step-by-step explanation:

Consider

x² = 64 ( take the square root of both sides )

x = 8 , x = - 8 ← are the critical points

Then for x² > 64

x < - 8 or x > 8

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2 years ago

Triangle VXW is similar to triangle ZXY. Triangle V X W. Side V W is 12 miles and side V X is 14 miles. Triangle Z X Y. Side Y Z

amid [387]

Answer: Kara should have written the proportion in step 1 as;

Start Fraction 12 Over 72 End Fraction = Start Fraction 14 Over x End Fraction (that is 12/72 = 14/x)

Step-by-step explanation: The two similar triangles are given with the following dimensions;

Triangle VXW with side VW = 12 and side VX = 14. Also Triangle ZXY with side YZ = 72 and side XZ = x.

For two triangles to be similar, then there must be a similarity ration that is consistent with all sides in both triangles. This means if in the first triangle a side measures 1 unit and the similar side in the other triangle measures 5 units, then the ratio of similarity of corresponding sides shall be ratio 1 : 5. So for every corresponding side in the second triangle the measurement shall be times five of the side that corresponds in the first triangle.

Therefore, in triangle VXW and triangle ZXY, the corresponding sides are as follows;

VX = ZX

VW = ZY

XW = XY

What Kara did was as follows;

VX/ZY = VW/ZX

Which translates to 14/72 = 12/x

This was a wrong calculation because the side that corresponds to VX is ZX and not ZY.

The correct step should therefore have been;

VW/ZY = VX/ZX

12/72 = 14/x (Step 1)

12x = (72) (14) {Step 2}