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3 years ago

42 vanilla to 48 chocolate

Mathematics

1 answer:

nydimaria [60]3 years ago

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1) Given: circle k(O), ED= diameter ,m∠OEF=32°, m(arc)EF=(2x+10)° Find: x

qaws [65]

1. The major arc ED has measure 180 degrees since ED is a diameter of the circle. The measure of arc EF is $(2x+10)^\circ$ , so the measure of arc DF is

$m\widehat{DF}=360^\circ-180^\circ-(2x+10)^\circ=(170-2x)^\circ$

The inscribed angle theorem tells us that the central angle subtended by arc DF, $\angle DOF$ , has a measure of twice the measure of the inscribed angle DEF (which is the same angle OEF) so

$m\angle DOF=2m\angle OEF=64^\circ$

so the measure of arc DF is also 64 degrees. So we have

$170-2x=64\implies106=2x\implies\boxed{x=53}$

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2. Arc FE and angle EOF have the same measure, 56 degrees. By the inscribed angle theorem,

$m\angle EOF=2m\angle EDF\implies56^\circ=2m\angle EDF\implies m\angle EDF=28^\circ$

Triangle DEF is isosceles because FD and ED have the same length, so angles EFD and DEF are congruent. Also, the sum of the interior angles of any triangle is 180 degrees. It follows that

$m\angle EFD+m\angle EDF+m\angle DEF=180^\circ\implies\boxed{m\angle EFD=76^\circ}$

Triangle OFE is also isosceles, so angles EFO and FEO are congruent. So we have

$m\angle EFO+m\angle FEO+m\angle EOF=180^\circ\implies\boxed{m\angle EFO=62^\circ}$

7 0

3 years ago

Solve for x.show your work please<br><br> - 1/2x < -12

Ratling [72]

Answer:

x <24

Step-by-step explanation:

first cancel negative signs

then transfer 2 to right side

3 0

3 years ago

Read 2 more answers

I need help on 1&2 pls

Rus_ich [418]

Answer:

Step-by-step explanation:

1. Slope

2. Hypotenuse

7 0

3 years ago

Which inequality statement best represents the graph?

Akimi4 [234]

Answer:

Step-by-step explanation:

If you have choices, you really should list them.

Here is the graph for y = (x + 0.25)(x - 1.75) which will look like yours. There are all sorts of variations that are possible, but at least I could reproduce a similar looking graph.