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3 years ago

Find the value of x.

Mathematics

2 answers:

Shalnov [3]3 years ago

8 0

Answer:

74 degrees

Step-by-step explanation:

The arc degree measurement of the arc that is colored in orange is given as 254 degrees.

The remaining part is the part in green.

The green part plus the orange part should equal 360 degrees because that would make a full rotation around the circle.

$360-254=106$ .

The green arc has measurement 106 degrees.

We can find x by computing half the difference of the arcs there.

That is,

$x=\frac{1}{2}(254-106)$

$x=\frac{1}{2}(148)$

$x=74$

shutvik [7]3 years ago

6 0

Answer:

74°

Step-by-step explanation:

There are at least a couple of ways to get there.

1) Find the central angle between the radii to the points of tangency. It will be ...

360° - 254° = 106°

The measure of x is the supplement of this:

x = 180° -106° = 74°

2) Find half the difference of the subtended arcs. The arc shown is 254°; the one not shown is 360° -254° = 106°. Half the difference of these is ...

(254°-106°)/2 = 148°/2 = 74°

3) Perhaps more simply, we can find this measure symbolically. Let y represent the large arc shown as 254°. Then the smaller one is 360°-y and their difference is ...

difference = y - (360° -y) = 2y -360°

Half this value, the value of angle x is ...

(2y -360°)/2 = y -180°

For y=254°, this is ...

x = 254° -180° = 74°

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3 years ago

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katrin2010 [14]

Answer: See explanation

Step-by-step explanation:

Let the cost for insuring the applicant = a.

Let the cost for insuring the spouse = b

Let the cost for insuring the first child= c

Let the cost for insuring the second child = d

A 35-year-old health insurance plan and that of his or her spouse costs $301 per month. This means that:

a + b = $301.

That rate increased to $430 per month if a child were included. This means the cost of a child will be:

= $430 - $301

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The rate increased to $538 per month if two children were included. This means the cost for the second child will be:

= $538 - $430

= $108

The rate dropped to $269 per month for just the applicant and one child. His will be the cost of the applicant and a single child. This can be written as:

a + $129 = $269

a = $269 - $129

a = $140

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$140 + b = $301

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