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2 years ago

O is the centre of the circle. AB is a diameter.

Mathematics

1 answer:

viktelen [127]2 years ago

3 0

Answer:

The value of a is 63° and the value of b is 27°

Step-by-step explanation:

In the given figure

∵ OA, OB, and OC are radii of the circle O

→ The radii of a circle are equal

∴ OA = OB = OC

In Δ AOC

∵ OA = OC

∴ Δ AOC is an isosceles triangle

→ Base angles of the isosceles triangle are equal

∵ ∠OAC and ∠OCA are the base angles of the triangle

∴ m∠OAC = m∠OCA

∵ m∠OAC = a°

∴ m∠OCA = a°

→ The sum of angles in any triangle is 180°

∵ a° + a° + m∠AOC = 180°

∵ m∠AOC = 54°

∴ a° + a° + 54 = 180°

→ Add the like terms

∴ 2a° + 54 = 180°

→ Subtract 54 from both sides

∴ 2a° = 126°

→ Divide both sides by 2

∵ m∠OAC = m∠OCA = 126 ÷ 2

∴ a° = 63

∴ The value of a is 63°

In ΔBOC

∵ OB = OC

∴ Δ BOC is an isosceles triangle

→ Base angles of the isosceles triangle are equal

∵ ∠OBC and ∠OCB are the base angles of the triangle

∴ m∠OBC = m∠OCB

∵ m∠OBC = b°

∴ m∠OCB = b°

∵ ∠AOC is an exterior angle of ΔBOC at the vertex O

→ The measure of the exterior angle equals the sum of the measure

of the opposite interior angles to this vertex

∵ ∠OBC and ∠OCB are the opposite interior angle of ∠AOC

∴ m∠OBC + m∠OCB = m∠AOC

→ Substitute their measures

∵ b° + b° = 54°

→ Add the like terms

∴ 2b° = 54

→ Divide both sides by 2

∴ b° = 27

∴ The value of b is 27°

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3 years ago

The graph of F(x), shown below, resembles the graph of G(x) = x2, but it has

mariarad [96]

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2 years ago

I GIVE BRAINLIEST PLS HELP

ioda

The answer is 8
Here's why:
${ ( \frac{( {6}^{7}) \times ( {3}^{3}) }{( {6}^{6}) \times ( {3}^{4} ) } )}^{3} = \\ ( \frac{6}{3} ) ^{3} = \\ \frac{216}{27} = 8$
The exponents are subtracted one from another when divided.
$\frac{ a ^{b} }{ {a}^{c} } = {a}^{b - c}$
We can look at the problem this way:
$( \frac{6^{7} }{6 ^{6} } \times \frac{3^{3} }{ {3}^{4} } ) = (6^{7 - 6} \times {3}^{3 - 4} ) = \\ ({6}^{1} \times {3}^{ - 1} )$
Since we have the power of -1 on the 3, we apply this rule:
${a}^{ - b} = \frac{1}{ {a}^{b} }$
Also this rule because we have the power of 1 on the 6:
${a}^{1} = a$
Then we get this:
$(6 \times \frac{1}{3} )^{3} = ( \frac{6}{3} )^{3}$
We apply the rule:
$( \frac{a}{b}) ^{c} = \frac{ {a}^{c} }{ {b}^{c} }$
We get this:
$\frac{{6}^{3} }{ {3}^{3} } = \frac{216}{27} = 8$

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2 years ago

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Wewaii [24]

Answer:

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2 years ago