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3 years ago

Work out the following, giving your answers in their simplest form:

Mathematics

2 answers:

Lostsunrise [7]3 years ago

8 0

Answer:

2 1/3÷1/4=7/3÷1/4=28/3

4/25÷1 1/5=4/25÷6/5=2/15

blondinia [14]3 years ago

7 0

Answer:

a) 28/3 b) 4/55

Step-by-step explanation:

a) 2 1/3 x 4/1 = 7/3 x 4/1 = 28/3

b) 4/25 x 5/11 = 20/275 = 4/55

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3 years ago

70 POINTS!!!!!!!!!! Given: E, F, Q, D∈k(O),O ∈ ED, m∠DFQ = 10°, measure of arc EF = 28° Find: Angles of △EFQ

Likurg_2 [28]

Answer:

The measures of angles of triangle EFQ are

1) $m\angle EFQ=100\°$

2) $m\angle FEQ=66\°$

3) $m\angle EQF=14\°$

Step-by-step explanation:

step 1

Find the measure of arc QD

we know that

The inscribed angle is half that of the arc it comprises.

$m\angle DFQ=\frac{1}{2}(arc\ QD)$

substitute the given value

$10\°=\frac{1}{2}(arc\ QD)$

$20\°=(arc\ QD)$

$arc\ QD=20\°$

step 2

Find the measure of arc FQ

we know that

$arc\ QD+arc\ FQ+arc\ EF=180\°$ ---> because ED is a diameter (the diameter divide the circle into two equal parts)

substitute the given values

$20\°+arc\ FQ+28\°=180\°$

$arc\ FQ=180\°-48\°=132\°$

step 3

Find the measure of angle EFQ

we know that

The inscribed angle is half that of the arc it comprises.

$m\angle EFQ=\frac{1}{2}(arc\ QD+arc\ ED)$

substitute the given value

$m\angle EFQ=\frac{1}{2}(20\°+180\°)=100\°$

step 4

Find the measure of angle FEQ

we know that

The inscribed angle is half that of the arc it comprises.

$m\angle FEQ=\frac{1}{2}(arc\ FQ)$

substitute the given value

$m\angle FEQ=\frac{1}{2}(132\°)=66\°$

step 5

Find the measure of angle EQF

we know that

The inscribed angle is half that of the arc it comprises.

$m\angle EQF=\frac{1}{2}(arc\ EF)$

substitute the given value

$m\angle EQF=\frac{1}{2}(28\°)=14\°$

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4 years ago