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Neporo4naja [7]
3 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]3 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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Aleksandr [31]

Answer:

2×(1+10)

Step-by-Step

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5 0
3 years ago
Identify the equation in slope-intercept form for the line containing the point (-4,1) and (2,3)
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Answer:

The point slope formula is

(y−y1)=m(x−x1)

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(x1,y1)(x2,y2)

(-4 , 1) (-2 , 3)

Solve for the slope

m = 3−1−2−(−3) = 21 = m = 2

(y−3)=2(x−(−2)) Plug in known values.

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7 0
2 years ago
PLS HELP RN <br> $4000 student loan. 10% compound interest annually. Total loan amount by 4 years?
ddd [48]

Answer:

$2,400

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4,000 ÷ 10 = 400

To get the amount that 4,000 is subtracted by we multiply 400 by 4.

400 × 4 = 1,600

To get the answer we subtract 4,000 by 1,600.

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3 0
3 years ago
Mrs Lim packs 35 big and small bags of candies for her pupils. Each big bag contains 12 candies and each small bag contains 7 ca
Anastasy [175]

Answer:

there are 11 big-bags and 24 small-bags.

Step-by-step explanation:

there are x big-bags and y small-bags.

so now we can know:

(1) x + y = 35

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in (1),we can do like this:

both left and right x7

then (x + y)x7 = 35 x 7

then 7x + 7y = 35 x 7  

then 7x + 7y = 245

now,

(1)7x + 7y =245

(2)12x + 7y = 300

we can both left and right do this: (2) - (1)

then

(12x + 7y) - (7x + 7y) = 300 -245

then

12x + 7y - 7x - 7y = 300 -245

then

12x - 7x +7y - 7y =300 -245

then

5x =55

then

5x ÷ 5 = 55 ÷ 5

then

x = 11

because

x + y =35;x=11

so

11 + y =35

11+ y -11 = 35 -11

then

y = 24

now we know:there are 11 big-bags and 24 small-bags.

3 0
3 years ago
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