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My name is Ann [436]
3 years ago
13

Answer the question in the picture.

Mathematics
2 answers:
Marysya12 [62]3 years ago
7 0

Answer:

r=9

Step-by-step explanation:

We can use the Pythagorean to solve, since this is a right triangle

The leg lengths are r and 12

The hypotenuse is (r+6)

a^2 + b^2 = c^2

r^2 + 12^2 = (r+6)^2

Foiling out the right hand side

(r+6)(r+6_ = r^2+6r+6r+36

r^2 +144 = r^2 +12r+36

Subtracting r^2 from each side

r^2-r^2 +144 = r^2-r^2 +12r+36

144 = 12r+36

Subtract 36 from each side

144-36 = 12r+36-36

108 = 12r

Divide each side by 12

108/12 = 12r/12

9=r

rewona [7]3 years ago
5 0

AC=AB+BC

AC=6+r

AD=12

DC=r

by Pythagorus theorem

AC*2=AD*2+DC*2

(6+r)*2=12*2+r*2

36+12r+r*2=144+r*2

12r+r*2-r*2=144-36

12r=108

r=108/12

r=9

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Step-by-step explanation:

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Read 2 more answers
Pentagon RSTUV is circumscribed about a circle. What is the value of x if RS = 8, ST = 12, TU = 15, UV = 9, and VR = 12?
ivanzaharov [21]

Answer:

The value of x is 7 ⇒ 1st answer

Step-by-step explanation:

* Lets revise a fact in the circle

- The two tangents drawn from a point out side the circle are equal

∵ RSTUV is circumscribed about a circle

∴ Each side of the pentagon is a tangent to the circle

- Look to the attached figure to know how we will solve the problem

- Each tangent divided into two parts

# RS = x + y

∵ RS = 8

∴ x + y = 8 ⇒ (1)

# RV = x + n

∵ RV = 12

∴ x + n = 12 ⇒ (2)

- Subtract (2) from (1)

∴ y - n = -4 ⇒ (3)

# ST = y + z

∵ ST = 12

∴ y + z = 12 ⇒ (4)

# TU = z + m

∵ TU = 15

∴ z + m = 15 ⇒ (5)

- Subtract (5) from (4)

∴ y - m = -3 ⇒ (6)

# UV = m + n

∵ UV = 9

∴ m + n = 9 ⇒ (7)

- Add (6) and (7)

∴ y + n = 6 ⇒ (8)

- Lets solve equation (3) and equation (8) to find y

∵ y - n = -4 ⇒ (3)

∵ y + n = 6 ⇒ (8)

- Add (3) and (8)

∴ 2y = 2 ⇒ divide two sises by 2

∴ y = 1

- Lets substitute the value of y in equation (1)

∵ x + y = 8 ⇒ (1)

∵ y = 1

∴ x + 1 = 8 ⇒ subtract (1) from both sides

∴ x = 7

* The value of x is 7

3 0
3 years ago
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