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ivann1987 [24]
3 years ago
5

Geometry question finding radius and area Thank You!!

Mathematics
1 answer:
aleksklad [387]3 years ago
7 0

Answer:

The radius of Circle D is 8 cm.

The perimeter of ΔABC is (24 + 6√7) cm.

Step-by-step explanation:

First, let the intersection point below D be K and let the intersection point between A and B be J.

Since segment BK, which passes through the center of the circle, is perpendicular to chord AC, BK also bisects AC. Hence, AK = CK.

Connect points A and D to create radius AD. Note that BD is also a radius. Hence, AD = BD.

For ΔABK, by the Pythagorean Theorem:

AB^2=(BD+1)^2+AK^2

Since AB = 12:

144=(BD+1)^2+AK^2

For ΔADK, by the Pythagorean Theorem:

AD^2=1^2+AK^2

Since AD = BD:

BD^2=1+AK^2

Subtract the second equation into the first:

144-(BD^2)=(BD+1)^2+AK^2-(1+AK^2)

Simplify:

144-BD^2=BD^2+2BD+1-1

Hence:

2BD^2+2BD-144=0

Simplify:

BD^2+BD-72=0

Factor:

(BD+9)(BD-8)=0

By the Zero Product Property:

BD=-9\text{ or } BD=8

Since the radius must be positive, the radius is 8 cm.

Since we already know AB and BC, we need to find AC to find the perimeter.

Note that AC = AK + CK = 2AK.

From the second equation:

BD^2=1+AK^2

Thus:

AK=\sqrt{BD^2-1}=\sqrt{(8)^2-1}=\sqrt{63}=3\sqrt{7}

Hence:

AC=2(AK)=2(3\sqrt7)=6\sqrt7

Therefore, the perimeter of ΔABC is:

P=(12)+(12)+(6\sqrt7)=24+6\sqrt7\text{ cm}

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Answer: See explanation

Step-by-step explanation:

Let the number of hamburger he ate on Monday be represented by x.

Monday = x

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Wednesday = x + 4

Thursday = 0

Friday = 3(x + 4)

Total hamburgers ate = 26

To find the amount of hamburger ate each day we add the number of hamburger ate per day all together. This will be:

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2x + 4 + 3x + 12 = 26

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5x = 26 - 16

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x = 10/5

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3 years ago
Find the missing side of this right
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Answer:

x = 13

Step-by-step explanation:

First start with the blank equation

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Answer:

1) n = 84

2) n = 78

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4) n = 16

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Step-by-step explanation:

To solve each proportion, we apply cross multiplication.

Question 1:

\frac{5}{12} = \frac{35}{n}

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Simplifying both sides by 5

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\frac{18}{n} = \frac{21}{28}

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\frac{10}{16} = \frac{n}{56}

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Simplifying by 2, both sides

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