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2 years ago

8.1 Lesson 10 Problem Set (8.EE.A.4)

Mathematics

1 answer:

arsen [322]2 years ago

6 0

Answer:

Step-by-step explanation:

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Points H and F lie on circle c What is the length of line segment GH?

Nina [5.8K]

Answer:

6 units

Step-by-step explanation:

Given: Points H and F lie on circle with center C. EG = 12, EC = 9 and ∠GEC = 90°.

To find: Length of GH.

Sol: EC = CH = 9 (Radius of the same circle are equal)

Now, GC = GH + CH

GC = GH + 9

Now In ΔEGC, using pythagoras theorem,

$(Hypotenuse)^{2} = (Base)^{2} +(Altitude)^{2}$ ......(ΔEGC is a right triangle)

$(GC)^{2} = (GE)^{2} +(EC)^{2}$

$(GH + 9)^{2} = (9)^{2} +(12)^{2}$

$(GH )^{2} + (9)^{2} + 18GH = 81 + 144$

$(GH )^{2} + 81 + 18GH = 81 + 144$

$(GH )^{2} + 18GH = 144$

Now, Let GH = x

$x^{2} +18x = 144$

On rearranging,

$x^{2} +18 x - 144 = 0$

$x^{2} - 6x +24x + 144 = 0$

$x (x-6) + 24 (x - 6) =0$

$(x - 6) (x + 24) = 0$

So x = 6 and x = - 24

∵ x cannot be - 24 as it will not satisfy the property of right triangle.

Therefore, the length of line segment GH = 6 units. so, Option (D) is the correct answer.

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2 years ago

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5+(-5)=0 identify the property

Usimov [2.4K]

Answer: Additive Inverse

Step-by-step explanation: The Additive Inverse tells us that if we add

a number and the opposite of that number, the result will be 0.

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3 years ago

The longest side of an acute isosceles triangle is 12 centimeters. Rounded to the nearest tenth, what is the smallest possible l

anygoal [31]

Answer:

Its 8.5 just took the test

Step-by-step explanation:

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3 years ago

URGENT DUE IN 20 MINUTES FOR GRADE PLEASE HELP 2/3 (x-7)= -2

ASHA 777 [7]

2/3 (x-7)= -2
x - 7 = -2 * 3/2
x - 7 = -3
x = -3 + 7
x = 4

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3 years ago

63 is 63% of what number

san4es73 [151]

63 is only 63% of the number 100.

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3 years ago

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