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KatRina [158]
3 years ago
8

Using the diagram, calculate the values of the unknown variables: a, b, and c.

Mathematics
1 answer:
Lady_Fox [76]3 years ago
3 0

Answer:

a = 82

b = 130

c = 118

Step-by-step explanation:

A quadrilateral is inscribed in a circle. So, it is a cyclic quadrilateral.

Opposite angles of a cyclic quadrilateral are supplementary.

Therefore,

a° + 98° = 180°

a° = 180° - 98°

a° = 82°

a = 82

By inscribed angle theorem:

a° = 1/2(b° + 34°)

82° * 2 = b° + 34°

164° - 34° = b°

b° = 130°

b = 130

Again by inscribed angle theorem:

76° = 1/2(c° + 34°)

76° *2 = c° + 34°

152° - 34° = c°

c° = 118°

c = 118

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5/12 or 0.41666667 pound

Step-by-step explanation:

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3 years ago
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A collection of nickels and dimes is worth $9.45. If the number of dimes is doubled, the value is
eduard

Answer:

The number of nickels is 45 and the number of dimes is 72.

Step-by-step explanation:

Let

x ----> number of nickels

y ----> number of dimes

Remember that

1\ nickel=\$0.05

1\ dime=\$0.10

so

0.05x+0.10y=9.45 ------> equation A

0.05x+0.10(2y)=16.65

0.05x+0.20y=16.65 ------> equation B

<em>Solve the system by substitution</em>

we have

0.05x+0.10y=9.45 ------> equation A

0.05x+0.20y=16.65 ------> equation B

Multiply both equations by 100 both sides

5x+10y=945 ---->5x=945-10y --> equation C

5x+20y=1,665 ----> equation D

substitute equation C in equation D

(945-10y)+20y=1,665

solve for y

945+10y=1,665

10y=1,665-945

10y=720

y=72\ dimes

Find the value of x

5x=945-10y

5x=945-10(72)

5x=225

x=45\ nickels

<em>Alternative Method</em>

Solve the system by graphing

Remember that the solution is the intersection point both graphs

using a graphing tool

the solution is the point (45,72)

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3 years ago
In the question, "35 is what percent of 40?" what is the 35?
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Answer:

35 is the 'is' and 40 is the 'of'

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cross-multiply to get:

40x = 3500

x = 3500/40

x = 87.5

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