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Neporo4naja [7]
2 years ago
13

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

Mathematics
1 answer:
qaws [65]2 years ago
7 0

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}

###

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}

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Answer: First half was 24 minutes

Step-by-step explanation:

Let the time taken to finish the second half be y.

Since the student used 2/3 of the second half time to finish the first half, first half = 2/3 × y = 2y/3

The entire exam is an hour which equals 60 minutes

First half + Second half = 60minutes

Note that first half is denoted as 2y/3 and second half is denoted by y.

2y/3 + y = 60

5y/3 = 60

Cross multiply

5y = 60 × 3

5y = 180

y = 180/5

y = 36

Second half took 36 minutes

Since first half is 2y/3, it will be:

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3 years ago
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Danielle found an outfit she liked at two different stores. Store 1 marked the outfit down by 15%. They then marked down the red
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Sally works 40 hours a week and makes $20 an hour, but her kids are in child care each day and the day care center charges her $
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$11.25

Step-by-step explanation:

Multiply the number of hours she works by how much she gets paid per hour.

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Subtract the 350 from the 800

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Divide the 450 by the number of hours worked per week

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Greg evaluated his spending and found that he was spending about $50 more per month on utilities than he has budgeted. He can tr
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The percent of his monthly income that will be budgeted for the utilities will be approximately 5.21%.

According to the question,

We have the following information:

Greg evaluated his spending and found that he was spending about $50 more per month on utilities than he has budgeted. He can transfer money from other categories to increase his utilities budget to $125 per month. If his total monthly income is $2,400.

Now, let's take the percent to be x.

We have the following expression:

2400*x/100 = 125

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Hence, the percent of his monthly income that will be budgeted for the utilities will be approximately 5.21%.

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