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2 years ago

Which equation is equivalent to the given equation? x^2+16x=22

Mathematics

1 answer:

Vaselesa [24]2 years ago

6 0

Answer:answer is a (x+8)^2=86

Step-by-step explanation:

x+8=±√

86

2 Break down the problem into these 2 equations.

x+8=\sqrt{86}x+8=√

86

x+8=-\sqrt{86}x+8=−√

86

3 Solve the 1st equation: x+8=\sqrt{86}x+8=√

86

 .

x=\sqrt{86}-8x=√

86

 −8

4 Solve the 2nd equation: x+8=-\sqrt{86}x+8=−√

86

 .

x=-\sqrt{86}-8x=−√

86

 −8

5 Collect all solutions.

x=\sqrt{86}-8,-\sqrt{86}-8x=√

86

 −8,−√

86

 −8

 +16x−22=0

2 Use the Quadratic Formula.

x=\frac{-16+2\sqrt{86}}{2},\frac{-16-2\sqrt{86}}{2}x=

−16+2√

86

 ,

−16−2√

86

3 Simplify solutions.

x=-8+\sqrt{86},-8-\sqrt{86}x=−8+√

86

 ,−8−√

86

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defon

Answer:

(5) The perpendicular height of the triangle is 8.48 mm.

(6) The 1184.86 cm far up the wall the ladder reach.

Step-by-step explanation:

Part (5):

When a perpendicular is drawn in an isosceles triangle then the perpendicular divided the base into 2 equal parts.

The figures is shown below.

In ΔABC,

CB = 6 mm

So,

CD = BD = 3 mm

Now calculating the perpendicular height of the triangle.

Using Pythagoras theorem in ΔADC:

$(AC)^2=(CD)^2+(AD)^2\\\\(9)^2=(3)^2+(AD)^2\\\\81=9+(AD)^2\\\\(AD)^2=81-9\\\\(AD)^2=72\\\\AD=8.48mm$

Thus, the perpendicular height of the triangle is 8.48 mm.

Part (6):

The figure is shown below.

Converting meter to centimeter:

1 m = 100 cm

So,

12 m = 1200 cm

Using Pythagoras theorem in ΔXYZ:

$(XZ)^2=(YZ)^2+(XY)^2\\\\(1200)^2=(190)^2+(XY)^2\\\\1440000=36100+(XY)^2\\\\(XY)^2=1440000-36100\\\\(XY)^2=1403900\\\\XY=1184.86cm$

Thus, 1184.86 cm far up the wall the ladder reach.

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